HKU Scholars Hubhttp://hub.hku.hkThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 23 Jan 2022 13:23:54 GMT2022-01-23T13:23:54Z502151- Computer graphics in engineering applicationshttp://hdl.handle.net/10722/32429Title: Computer graphics in engineering applications
Authors: Lo, Sai-huen.; 羅世煊
Fri, 01 Jan 1982 00:00:00 GMThttp://hdl.handle.net/10722/324291982-01-01T00:00:00Z
- An automatic adaptive refinement finite element procedure for 2D elastostatic analysishttp://hdl.handle.net/10722/149989Title: An automatic adaptive refinement finite element procedure for 2D elastostatic analysis
Authors: Lee, CK; Lo, SH
Abstract: An automatic adaptive refinement procedure for finite element analysis is presented. The procedure is applied to two-dimensional elastostatic problems to obtain solutions of prescribed accuracy. Through the combined use of new mesh generator using contour developed by Lo and the concept of strain energy concentration, high-quality graded finite element meshes are generated. The whole process is fully automatic and no user intervention is required during the successive cycles of the mesh refinements. The Zienkiewicz and Zhu error estimator is found to be effective and has been adopted for the present implementation. In the numerical examples tested, the error estimator gives an accurate error norm estimation and the effectivity index of the estimator converges to a value close to unity.
Wed, 01 Jan 1992 00:00:00 GMThttp://hdl.handle.net/10722/1499891992-01-01T00:00:00Z
- Visualisation of 3D solid finite element mesh by the method of sectioninghttp://hdl.handle.net/10722/149943Title: Visualisation of 3D solid finite element mesh by the method of sectioning
Authors: Lo, SH
Abstract: The technique of showing the internal structure of a 3D solid finite element mesh by the method of plane sectioning is presented. The cut section of a solid finite element mesh can be obtained by considering the intersection between the sectional plane and each individual element of the mesh one at a time. Computational procedure for different types of solid finite elements is described, and examples are given to demonstrate the proposed algorithm. © 1990.
Mon, 01 Jan 1990 00:00:00 GMThttp://hdl.handle.net/10722/1499431990-01-01T00:00:00Z
- Experimental study of moderately reinforced concrete beams strengthened with bolted-side steel plateshttp://hdl.handle.net/10722/185746Title: Experimental study of moderately reinforced concrete beams strengthened with bolted-side steel plates
Authors: Li, L; Lo, SH; Su, RKL
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1857462013-01-01T00:00:00Z
- Vertex-Ball Spring Smoothing: An efficient method for unstructured dynamic hybrid mesheshttp://hdl.handle.net/10722/202731Title: Vertex-Ball Spring Smoothing: An efficient method for unstructured dynamic hybrid meshes
Authors: Lin, TJ; Guan, ZQ; Chang, JH; Lo, SH
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2027312014-01-01T00:00:00Z
- Boundary recovery for 3D Delaunay triangulationhttp://hdl.handle.net/10722/202722Title: Boundary recovery for 3D Delaunay triangulation
Authors: Liu, Y; Lo, SH; Guan, ZQ; Zhang, HW
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2027222014-01-01T00:00:00Z
- Shear transfer in bolted side-plated reinforced concrete beamshttp://hdl.handle.net/10722/199046Title: Shear transfer in bolted side-plated reinforced concrete beams
Authors: Su, KL; Li, L; Lo, SH
Abstract: Reinforced concrete (RC) beams strengthened with bolted steel plates on their vertical faces are known as bolted side-plated (BSP) beams. The behaviour and performance of BSP beams are controlled by the arrangement of the steel plates and the interfacial slips caused by the shear deformation of anchor bolts due to shear force transfer. In this study, a nonlinear finite element model validated by available experimental results has been used to investigate the shear stress transfer in BSP beams. The effects of loading arrangements and the stiffnesses of RC beams, steel plates and bolt connections were investigated in detail by a parametric study. The results of this study shed light on the basic understanding of the internal shear transfer mechanism between steel plates and RC beams. A new design approach is also provided to help structural engineers in the determination of the shear transfer profile and the critical bolt shear force in the design of BSP beams.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1990462013-01-01T00:00:00Z
- Adaptive Meshinghttp://hdl.handle.net/10722/118123Title: Adaptive Meshing
Authors: Lo, SH
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10722/1181232001-01-01T00:00:00Z
- Delaunay triangulation of non-convex planar domainshttp://hdl.handle.net/10722/149924Title: Delaunay triangulation of non-convex planar domains
Authors: Lo, SH
Abstract: This paper investigates the possibility of integrating the two currently most popular mesh generation techniques, namely the method of advancing front and the Delaunay triangulation algorithm. The merits of the resulting scheme are its simplicity, efficiency and versatility. With the introduction of 'non-Delaunay' line segments, the concept of using Delaunay triangulation as a means of mesh generation is clarified. An efficient algorithm is proposed for the construction of Delaunay triangulations over non-convex planar domains. Interior nodes are first generated within the planar domain. These interior nodes and the boundary nodes are then linked up together to produce a valid triangulation. Through the study of numerous examples of various characteristics, it is found that high-quality triangular element meshes are obtained by the proposed algorithm, and the mesh generation time bears a linear relationship with the number of elements/nodes of the triangulation.
Sun, 01 Jan 1989 00:00:00 GMThttp://hdl.handle.net/10722/1499241989-01-01T00:00:00Z
- Volume discretization into tetrahedra-II. 3D triangulation by advancing front approachhttp://hdl.handle.net/10722/149956Title: Volume discretization into tetrahedra-II. 3D triangulation by advancing front approach
Authors: Lo, SH
Abstract: Existing methods of automatic mesh generation for 3D solid objects are reviewed. Although the 3D Delaunay triangulation recently aroused much attention, its suitability as a finite element mesh generator is questioned. Although in 2D Delaunay triangulation, the 'max-min' angle criterion can be verified over the entire domain, no equivalent or similar criterion can be defined for its extension to 3D situations to ensure that tetrahedron elements so generated are well proportioned for numerical calculations. In this paper, a simple but versatile 3D triangulation scheme based on the advancing front technique for the discretization of arbitrary volumes is presented. To ensure that the tetrahedron elements generated are as equilateral as possible, the ratio of volume of the element to the sum of squares of edges put into a dimensionless form is adopted to judge the quality of a tetrahedron element. The quality of the finite element mesh can thus be ensured if the shape of each tetrahedron element is carefully controlled in the mesh construction process. Through the study of numerous examples of various characteristics, it is found that high-quality tetrahedron element meshes are obtained by the proposed algorithm. © 1991.
Tue, 01 Jan 1991 00:00:00 GMThttp://hdl.handle.net/10722/1499561991-01-01T00:00:00Z
- Improvement on the 10-node tetrahedral element for three-dimensional problemshttp://hdl.handle.net/10722/150167Title: Improvement on the 10-node tetrahedral element for three-dimensional problems
Authors: Lo, SH; Ling, C
Abstract: By decomposing the strain part of the conforming 10-node tetrahedral element T10 and relaxing the compatibility condition for the constant strain term, the performance of the element can be improved. By introducing the incompressible condition in the high order strain term, the element can be made very efficient for the analysis of the nearly incompressible problem. Numerical results show that the modified element, in general, has better accuracy and reliability compared to the classical displacement-based tetrahedral element T10 for a wide range of structural problems, including the analysis of thin and slender structures.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10722/1501672000-01-01T00:00:00Z
- An automatic adaptive refinement procedure using triangular and quadrilateral mesheshttp://hdl.handle.net/10722/150048Title: An automatic adaptive refinement procedure using triangular and quadrilateral meshes
Authors: Lee, CK; Lo, SH
Abstract: An automatic adaptive refinement procedure for finite element analysis for two-dimensional stress analysis problems is presented. Through the combined use of the new mesh generator developed by the authors (to appear) for adaptive mesh generation and the Zienkiewicz-Zhu [Int. J. numer. Meth. Engng31, 1331-1382 (1992)] error estimator based on the superconvergent patch recovery technique, an adaptive refinement procedure can be formulated which can achieve the aimed accuracy very economically in one or two refinement steps. A simple method is also proposed to locate the existence and the position of singularities in the problem domain. Hence, little or no a priori knowledge about the location and strength of the singularities is required. The entire adaptive refinement procedure has been made fully automatic and no user intervention during successive cycles of mesh refinements is needed. The robustness and reliability of the refinement procedure have been tested by solving difficult practical problems involving complex domain geometry with many singularities. We found that in all the examples studied, regardless of the types of meshes employed, triangular and quadrilateral meshes, nearly optimal overall convergence rate is always achieved. © 1995.
Sun, 01 Jan 1995 00:00:00 GMThttp://hdl.handle.net/10722/1500481995-01-01T00:00:00Z
- A new scheme for the generation of a graded quadrilateral meshhttp://hdl.handle.net/10722/150034Title: A new scheme for the generation of a graded quadrilateral mesh
Authors: Lee, CK; Lo, SH
Abstract: A new scheme for the generation of a quadrilateral element mesh is presented. The algorithm makes use of the fact that a triangular element mesh bounded by an even number of line segments can always be converted into quadrilaterals. By using the advancing front technique for schematically merging of triangular elements, high-quality well-graded quadrilateral meshes can be formed without any tedious treatment for isolated triangles. Unlike many other methods, no cut-lines or manual division of the problem domain into simpler subregions is required before conversion. As the number and the position of the boundary nodes are not altered during the mesh generation process, different material regions sharing common boundary lines can be treated individually. Since a background triangular mesh is all that is needed, the process can be applied to any arbitrary 2D domain with or without internal openings. In fact, the method has an equal area of application as a general triangulator. This also implies that the proposed scheme can be used to generate strongly graded quadrilateral meshes of the same gradation effect as the background triangular meshes for adaptive finite element analysis. © 1994.
Sat, 01 Jan 1994 00:00:00 GMThttp://hdl.handle.net/10722/1500341994-01-01T00:00:00Z
- Automatic adaptive 3-D finite element refinement using different-order tetrahedral elementshttp://hdl.handle.net/10722/150095Title: Automatic adaptive 3-D finite element refinement using different-order tetrahedral elements
Authors: Lee, CK; Lo, SH
Abstract: Automatic refinement finite element analyses were carried out employing three different-order tetrahedral solid elements for the solution of 3-D stress analysis problems. Numerical results indicated that the adaptive refinement procedure could eliminate effectively the effect of singularities and the optimal convergence rate was achieved in all the examples tested. The preconditioned conjugate gradient technique was used for the solution of the large system of simultaneous equations. By interpolating the initial guess of the iteration solver from the previous converged solution, the number of iterations needed for the solution is lower than expected. Furthermore, when the mesh density distribution pattern has converged, it became even more efficient and independent of the number of degrees of freedom in the finite element mesh. The relative efficiency of the three different-order tetrahedral elements has also been compared in terms of storage and computational cost needed for achieving a certain accuracy. It is found that although the cubic T20 element can achieve the highest convergence rate, the T10 element is the most competitive and effective element in terms of storage and computational cost needed. © 1997 by John Wiley & Sons, Ltd.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/10722/1500951997-01-01T00:00:00Z
- Pyramid elements in 3-D hexahedral mesh generationhttp://hdl.handle.net/10722/110700Title: Pyramid elements in 3-D hexahedral mesh generation
Authors: Lo, SH
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10722/1107002004-01-01T00:00:00Z
- Displacement-based rapid seismic assessment procedure for building structureshttp://hdl.handle.net/10722/111191Title: Displacement-based rapid seismic assessment procedure for building structures
Authors: Tsang, HH; Su, RKL; Lam, NTK; Lo, SH
Abstract: Seismic assessment of building structures can be a very involved process. This paper presents a simplified and rational manual procedure for rapid predictions of maximum inter-storey drift demand in tall buildings, which does not require frame analysis nor finite element analysis to be carried out and can be expedited by the use of a spreadsheet program. The methodology comprises a series of stages, beginning with the development of an elastic design response spectrum (or a uniform hazard spectrum) for specifying the level of seismic hazard, followed by the inclusion of a site-specific factor which represents the effects of soil amplification. The maximum seismic inter-storey drift demand of the building is then predicted from the displacement response spectrum for a given height and the estimated lateral natural periods of the building. The proposed manual procedure can be further developed to cater for limited ductility demand behaviour in the building. The predicted drift demand is an important indicator of potential seismic damage (risk), and may be utilized for the rapid assessment of damage and loss (cost) for considered earthquake scenarios.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1111912009-01-01T00:00:00Z
- A twelve-node hybrid stress brick element for beam/column analysishttp://hdl.handle.net/10722/54262Title: A twelve-node hybrid stress brick element for beam/column analysis
Authors: Sze, KY; Lo, SH
Abstract: In this paper, a hybrid stress 12-node brick element is presented. Its assumed stress field is derived by first examining the deformation modes of a geometrically regular element and then generalizing to other element configurations using tensorial transformation. The total number of stress modes is 30 which is minimal for securing the element rank. To reduce the computational cost associated with the fully populated flexibility matrix, the admissible matrix formation is employed to induce high sparsity in the matrix. Popular beam bending benchmark problems are examined. The proposed elements deliver encouraging accuracy.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10722/542621999-01-01T00:00:00Z
- Popular benchmark problems for geometric nonlinear analysis of shellshttp://hdl.handle.net/10722/54269Title: Popular benchmark problems for geometric nonlinear analysis of shells
Authors: Sze, KY; Liu, XH; Lo, SH
Abstract: In most, if not all, of the previous work on finite element formulation and nonlinear solution procedures, results of geometric nonlinear benchmark problems of shells are presented in the form of load-deflection curves. In this paper, eight sets of popularly employed benchmark problems are identified and their detailed reference solutions are obtained and tabulated. It is hoped that these solutions will form a convenient basis for subsequent comparison and that the tedious yet inaccurate task of reconstructing data points by graphical measurement of previously reported load-deflection curves can be avoided. Moreover, the relative convergent difficulty of the problems are revealed by the number of load increments and the total number of iterations required by an automatic load incrementation scheme for attaining the converged solutions under the maximum loads. © 2003 Elsevier B.V. All rights reserved.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10722/542692004-01-01T00:00:00Z
- A stabilized eighteen-node solid element for hyperelastic analysis of shellshttp://hdl.handle.net/10722/54265Title: A stabilized eighteen-node solid element for hyperelastic analysis of shells
Authors: Sze, KY; Zheng, SJ; Lo, SH
Abstract: The objective of the present study is to develop a solid element for large deformation analysis of hyperelastic shell structures. To attain high computational efficiency and annihilate shear and membrane lockings, a hybrid-strain stabilization approach is adopted. To overcome the thickness locking of the element, the enhanced assumed thickness strain modes are incorporated. Starting from the virtual work principle and a weak form that enforces the equality of the hybrid-strain and the strain arising from the displacement and the enhanced assumed strain, an eighteen-node element for large deformation analysis of hyperelastic shells is developed. The salient feature of the present element for higher computational efficiency is that the element uses only the second-order quadrature for integration along the two in-plane natural coordinates and the stabilization vectors can be formed without using any integration loops. Efficacy of the element is illustrated by popular benchmark problems. © 2003 Elsevier B.V. All rights reserved.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10722/542652004-01-01T00:00:00Z
- Optimization of reinforced concrete structures with genetic algorithmhttp://hdl.handle.net/10722/111793Title: Optimization of reinforced concrete structures with genetic algorithm
Authors: Wong, KI; Lo, SH
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10722/1117932005-01-01T00:00:00Z
- A refined nonconforming quadrilateral element for couple stress/strain gradient elasticityhttp://hdl.handle.net/10722/139095Title: A refined nonconforming quadrilateral element for couple stress/strain gradient elasticity
Authors: Zhao, J; Chen, WJ; Lo, SH
Abstract: C0-1 patch test (Int. J. Numer. Meth. Engng 2004; 61:433-454) proposed by Soh and Chen is a reliable method to ensure convergence of nonconforming finite element for the couple stress/strain gradient elasticity. The C0-1 patch test function is a complete quadratic polynomial that satisfies the equilibrium equations. To pass the C0-1 patch test, the element displacement functions used to calculate strains must satisfy C0 continuity (or weak C0 continuity) and quadratic completeness. In this paper, a 24-DOF (degrees of freedom) quadrilateral element (CQ12+RDKQ) for the couple stress/strain gradient elasticity is developed by combining the refined thin plate element RDKQ and the nonconforming element CQ12. The element RDKQ, which satisfies weak C1 continuity, is used to calculate strain gradients, whereas strains are computed by the element CQ12, which is established based on an extended variational functional and satisfies weak C0 continuity and quadratic completeness. Numerical examples show that the element (CQ12+RDKQ) passes the C0-1 patch test and it is also more efficient than the existing available triangular and quadrilateral elements in stress concentration problems with size effects. © 2010 John Wiley & Sons, Ltd.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1390952011-01-01T00:00:00Z
- An improved in-plane displacement model for the stability analysis of laminated composites with general lamination configurationshttp://hdl.handle.net/10722/139084Title: An improved in-plane displacement model for the stability analysis of laminated composites with general lamination configurations
Authors: Lo, SH; Zhen, W; Sze, KY; Wanji, C
Abstract: This paper describes how the derivatives of lateral displacement are eliminated in the general displacement field of the global-local higher-order theory for stability analysis of laminated composite and sandwich plates with general lamination configurations. In contrast to previous models, the present model is applicable not only to the cross-ply but also to the angle-ply laminated composite and sandwich plates. Based on known traction forces on the surface boundaries, the derivatives of transverse displacement have been taken out from the general displacement field, so that C 0 interpolation functions are only required for the finite element implementation. To verify the proposed theory, the classical quadratic six-node C 0 triangular element is employed for the interpolation of all the displacement parameters defined at each nodal point on the composite plate. Numerical results show that following the proposed theory simple C 0 finite elements could accurately predict the critical loads of sandwich plate with soft core, which has long been a difficult case for the other global higher-order theories. © 2011 Elsevier Ltd.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1390842011-01-01T00:00:00Z
- Adaptive meshing and analysis using transitional quadrilateral and hexahedral elementshttp://hdl.handle.net/10722/124836Title: Adaptive meshing and analysis using transitional quadrilateral and hexahedral elements
Authors: Lo, SH; Wu, D; Sze, KY
Abstract: In adaptive finite element analysis, h-type refinement can be achieved basically in two ways: (i) small elements are connected directly to large elements with full compatibility at element interfaces and (ii) transitional elements are employed to link up elements of different sizes. While there is no difficulty in generating gradation triangular and tetrahedral meshes, generation of quadrilateral and hexahedral meshes of varying element sizes without severe element distortion proved to be a formidable task. The use of transitional elements allows meshes to be refined without element distortion, and the price that we have to pay is to develop general and efficient transitional elements in two and three dimensions. Transition elements, which satisfy the patch test, can be formulated by means of the enhanced assumed strain (EAS) method, which are in general more efficient than the incompatible elements. Alternatively, in this paper, we try to develop a series of versatile transition elements based on the hybrid stress approach. Direct designing stress fields for transition elements is just too complicated and especially impractical for 3D transition hexahedral elements. However, we found that the same stress field could be used for transition elements with variable number of nodes. By means of elimination and through numerical studies on some benchmark problems, 7- and 24-mode stress fields are adopted, respectively for 2D quadrilateral and 3D hexahedral hybrid stress transition elements. Strategy for generating refinement transition element meshes will be discussed, and the size of elements generated by the 1-irregular mesh restriction is compared with the predicted element size. The comparison shows that the meshing strategy employed in this study can effectively lead to an optimal mesh whose solution error is smaller than the prescribed one. © 2009 Elsevier B.V. All rights reserved.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1248362010-01-01T00:00:00Z
- On the thermal expansion effects in the transverse direction of laminated composite plates by means of a globallocal higher-order modelhttp://hdl.handle.net/10722/139087Title: On the thermal expansion effects in the transverse direction of laminated composite plates by means of a globallocal higher-order model
Authors: Zhen, W; Cheung, YK; Lo, S; Wanji, C
Abstract: In this paper, a new efficient globallocal higher-order model is proposed for the thermoelastic analysis of laminated composite and sandwich plates. The proposed model takes into account explicitly the contribution of thermal expansion in the transverse displacement component. To satisfy the transverse displacement continuity along the thickness direction, the continuity condition of transverse displacement at interfaces, which is not satisfied in many other schemes, has been a priori enforced. This model fully satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. As the number of variables of the proposed model is independent of the number of layers of laminates, compared to the 1,23 theory proposed by Li and Liu (1997) [20], the present model offers some significant improvements, and is able to predict accurately thermoelastic response of laminated plates under uniform temperature without a corresponding increase in the number of unknowns. The governing equations of equilibrium are derived by means of the principle of virtual displacements involving the thermal strain field. Applying Navier's technique, analytical solutions in terms of a double trigonometric series for simply supported laminated plates are presented. Results of benchmark examples are compared with the three-dimensional thermoelastic solutions as well as other published works. Numerical results show that the proposed model is more rigorous and can better predict the thermoelastic response in comparison with the 1,23 theory and other two-dimensional models. © 2010 Elsevier Ltd. All rights reserved.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1390872010-01-01T00:00:00Z
- The importance of crustal shear wave velocity profile for ground motion modellinghttp://hdl.handle.net/10722/71092Title: The importance of crustal shear wave velocity profile for ground motion modelling
Authors: Tsang, HH; Lam, NTK; Lo, SH
Abstract: The potential seismic amplification and attenuation properties of an area are well correlated with the shear wave velocity (SWV) profile of crustal rock. When local strong motion records are lacking, the a ttenuation behaviour of future earthquakes can be inferred fro m a crustal SWV model that is representative of the area of interest. Details of the SWV profile close to the e arth surface (1-2 km depth) are particularly critic al. Unfortunately, such details cannot be obtained by c onventional seismic reflection/refraction surveys. This study demonstrates the use of information from a combination of sources to produce a set of composite SWV profiles for four principal geological formations that are p revalent in Hong Kong. Their respective local upper crustal modification factors have been computed and the significant differences have been highlighted.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/710922007-01-01T00:00:00Z
- 3-D vibration analysis of annular sector plates using the Chebyshev-Ritz methodhttp://hdl.handle.net/10722/139096Title: 3-D vibration analysis of annular sector plates using the Chebyshev-Ritz method
Authors: Zhou, D; Lo, SH; Cheung, YK
Abstract: The three-dimensional free vibration of annular sector plates with various boundary conditions is studied by means of the Chebyshev-Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. The product of Chebyshev polynomials satisfying the necessary boundary conditions is selected as admissible functions in such a way that the governing eigenvalue equation can be conveniently derived through an optimization process by the Ritz method. The boundary functions guarantee the satisfaction of the geometric boundary conditions of the plates and the Chebyshev polynomials provide the robustness for numerical calculation. The present study provides a full vibration spectrum for the thick annular sector plates, which cannot be given by the two-dimensional (2-D) theories such as the Mindlin theory. Comprehensive numerical results with high accuracy are systematically produced, which can be used as benchmark to evaluate other numerical methods. The effect of radius ratio, thickness ratio and sector angle on natural frequencies of the plates with a sector angle from 120° to 360° is discussed in detail. The three-dimensional vibration solutions for plates with a re-entrant sector angle (larger than 180°) and shallow helicoidal shells (sector angle larger than 360°) with a small helix angle are presented for the first time. © 2008 Elsevier Ltd. All rights reserved.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1390962009-01-01T00:00:00Z
- Generic Theoretical Formulae for Estimating Site Effectshttp://hdl.handle.net/10722/111739Title: Generic Theoretical Formulae for Estimating Site Effects
Authors: Tsang, HH; Lam, NTK; Asten, MW; Lo, SH
Abstract: Significant modification of the seismic ground shaking may be developed in sites pertaining to soil
resonance behaviour. Generic theoretical formulae have been developed to estimate the amplification for soil sites,
and directly address potential soil resonance behaviour. The development of these formulae has taken into account
the effects of soil damping, stiffness degradation, impedance contrast at soil-bedrock interface and soil plasticity.
The microtremor array method with the spatial auto-correlation (SPAC) processing technique has been
recommended for obtaining the shear wave velocity (SWV) model of the site.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/1117392007-01-01T00:00:00Z
- Stress evaluation algorithms for rate constitutive equations in finite deformation analysishttp://hdl.handle.net/10722/144821Title: Stress evaluation algorithms for rate constitutive equations in finite deformation analysis
Authors: Lo, SH
Abstract: The stress integration algorithm for hypoelastic constitutive equations proposed by Pinsky et al.3 is extended for the treatment of finite deformation elastoplastic constitutive relations. Another approach based on the polar decomposition of the deformation gradient tensor F = R · U is also introduced. Numerical examples and a discussion on these two approaches are given.
Fri, 01 Jan 1988 00:00:00 GMThttp://hdl.handle.net/10722/1448211988-01-01T00:00:00Z
- A new mesh generation scheme for arbitrary planar domainshttp://hdl.handle.net/10722/144822Title: A new mesh generation scheme for arbitrary planar domains
Authors: Lo, SH
Abstract: This paper describes a new algorithm to generate interior nodes within any arbitrary multi-connected regions. The boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner. Owing to the generality of the central generation program, the global domain is allowed to be divided into as many irregular subdomains as desired, in order to model closely the actual physical situation. Moreover, the boundaries of the sub-domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner, generating radiating mesh from a prescribed node, generating mesh between two circular arcs, etc. Despite its flexibility and capabilities, data for triangulation have been kept to a minimum by a logical input module; no connectivity information between subregions is needed, and common boundaries are defined once only. All these features have contributed to a powerful method to generate 3-node or 6-node triangular element meshes of great variety within the most irregular heterogeneous regions.
Tue, 01 Jan 1985 00:00:00 GMThttp://hdl.handle.net/10722/1448221985-01-01T00:00:00Z
- 3-D vibration analysis of circular rings with sectorial cross-sectionshttp://hdl.handle.net/10722/139089Title: 3-D vibration analysis of circular rings with sectorial cross-sections
Authors: Zhou, D; Cheung, YK; Lo, SH
Abstract: The free vibration characteristics of circular rings with sectorial cross-section are studied based on the three-dimensional (3-D), small strain, linear elasticity theory. The complete vibration spectrum has been obtained by using the Ritz method. A set of three-dimensional orthogonal coordinates composing of the polar coordinates (r,θ) at the origin of the sectorial cross-section and circumferential coordinate φ{symbol} around the ring is developed to describe the variables in the analysis. Each of the displacement components is taken as a triplicate series: two Chebyshev polynomial series, respectively, about the r and θ coordinates, and a trigonometric series about the φ{symbol} coordinate. Frequency parameters and vibration mode shapes are computed by means of the displacement-based extremum energy principle. Upper bound convergence of the first eight frequency parameters accurate to at least five significant figures is presented. The effect of radius ratio, subtended angle, and initial slope angle on frequency parameters is investigated in detail. All major modes such as flexural modes, thickness-shear modes, stretching modes, and torsional modes, etc. are presented in the paper. The present results may serve as a benchmark reference to validate the accuracy of various approximate theories and other computational techniques for the vibration of circular rings. © 2009 Elsevier Ltd. All rights reserved.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1390892010-01-01T00:00:00Z
- A full 3D finite element analysis using adaptive refinement and PCG solver with back interpolationhttp://hdl.handle.net/10722/71379Title: A full 3D finite element analysis using adaptive refinement and PCG solver with back interpolation
Authors: Lee, CK; Lo, SH
Abstract: In this paper, adaptive refinement finite element analyses were carried out for full 3D problems. In order to achieve an optimal computation cost and to eliminate the effects of singular points, the adaptive refinement procedure was applied in conjunction with a back interpolation for the construction of a good initial guess for the solution of the linear equations system. The combined use of the adaptive refinement procedure, the back interpolation scheme and the preconditioned conjugate gradient (PCG) solver lead to a significant reduction in the operations for the solution of the simultaneous linear equations in the adaptive refinement analysis. In many cases the number of iterations needed by the PCG solver to reach a converged solution is independent of the number of equations in the global system. The numerical results obtained indicated that for a series of carefully designed adaptive meshes, the computational cost required to solve the linear system could be made only proportional to the number of degrees of freedom in the mesh. To our knowledge, this is the first time that the global stiffness equations in 3D stress analysis have been solved with this efficiency. The same set of numerical results also showed that, in general, the total computational cost of the adaptive refinement procedure can usually be minimized by gradually reducing the target relative error of the solution during successive refinements rather than employing a constant target relative error throughout the whole adaptive analysis. © 1999 Elsevier Science S.A. All rights reserved.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10722/713791999-01-01T00:00:00Z
- Universal three-dimensional connection hexahedral elements based on hybrid-stress theory for solid structureshttp://hdl.handle.net/10722/139091Title: Universal three-dimensional connection hexahedral elements based on hybrid-stress theory for solid structures
Authors: Wu, D; Lo, SH; Sheng, N; Sze, KY
Abstract: High-performance hybrid-stress hexahedral solid elements are excellent choices for modeling joints, beams/columns walls and thick slabs for building structures if the exact geometrical representation is required. While it is straight-forward to model beam-column structures of uniform member size with solid hexahedral elements, joining up beams and columns of various cross-sections at a common point proves to be a challenge for structural modeling using hexahedral elements with specified dimensions. In general, the joint has to be decomposed into 27 smaller solid elements to cater for the necessary connection requirements. This will inevitably increase the computational cost and introduce element distortions when elements of different sizes have to be used at the joint. Universal connection hexahedral elements with arbitrary specified connection interfaces will be an ideal setup to connect structural members of different sizes without increasing the number of elements or introducing highly distorted elements. In this paper, the requirements and the characteristics of the hexahedral connection elements with 24 and 32 nodes will be discussed. Formulation of the connection elements by means of Hellinger-Reissner functional will be presented. The performance of connection elements equipped with different number of stress modes will be assessed with worked examples. © 2009 John Wiley & Sons, Ltd.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1390912010-01-01T00:00:00Z
- Three-dimensional vibration analysis of toroidal sectors with solid circular cross-sectionshttp://hdl.handle.net/10722/139086Title: Three-dimensional vibration analysis of toroidal sectors with solid circular cross-sections
Authors: Zhou, D; Cheung, YK; Lo, SH
Abstract: This paper studies the free vibration of circular toroidal sectors with circular crosssections based on the three-dimensional small-strain, linear elasticity theory. A set of orthogonal coordinates, composing the polar coordinate (r,θ) with the origin on the cross-sectional centerline of the sector and the circumferential coordinate φ with the origin at the curvature center of the centerline, is developed to describe the displacements, strains, and stresses in the sector. Each of the displacement components is taken as a product of four functions: a set of Chebyshev polynomials in φ and r coordinates, a set of trigonometric series in θ coordinate, and a boundary function in terms of φ. Frequency parameters and mode shapes have been obtained via a displacement-based extremum energy principle. The upper bound convergence of the first eight frequency parameters accurate up to five figures has been achieved. The present results agree with those from the finite element solutions. The effect of the ratio of curvature radius R to the cross-sectional radius a and the subtended angle φ0 on the frequency parameters of the sectors are discussed in detail. The three-dimensional vibration mode shapes are also plotted. © 2010 by ASME.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1390862010-01-01T00:00:00Z
- An algorithm for the intersection of quadrilateral surfaces by tracing of neighbourshttp://hdl.handle.net/10722/71167Title: An algorithm for the intersection of quadrilateral surfaces by tracing of neighbours
Authors: Lo, SH; Wang, WX
Abstract: The use of discrete data to represent engineering structures as derivatives from intersecting components requires algorithms to perform Boolean operations between groups of quadrilateral and triangular surfaces. In the intersection process, an accurate and efficient method for the determination of intersection lines is a crucial step for large scale and complex surface intersections. An algorithm based on tracing the neighbours of intersecting quadrilaterals is proposed to determine the intersection lines. A background grid is employed to limit the scope of searching for candidate quadrilaterals that may intersect. This will drastically cut down the time of geometrical check for intersections between quadrilaterals, making the surface intersection and mesh generation a quasi-linear process with respect to the number of elements involved. Given the node numbers at the vertices of the candidate quadrilaterals, the neighbour relationship is then established. In the determination of intersection, each quadrilateral is divided into two triangles and four fundamental cases are identified and treated systematically to enhance robustness and reliability. Tracing the neighbours for the determination of intersection lines not only greatly increases the efficiency of the process, it also improves the reliability as branching and degenerated cases can all be dealt with in a consistent manner on the intersecting surfaces concerned. Examples on a great variety of surface and mesh characteristics are given to demonstrate the effectiveness and robustness of the algorithm. © 2003 Elsevier Science B.V. All rights reserved.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/711672003-01-01T00:00:00Z
- On using meshes of mixed element types in adaptive finite element analysishttp://hdl.handle.net/10722/71034Title: On using meshes of mixed element types in adaptive finite element analysis
Authors: Lo, SH; Lee, CK
Abstract: Four different automatic mesh generators capable of generating either triangular meshes or hybrid meshes of mixed element types have been used in the mesh generation process. The performance of these mesh generators were tested by applying them to the adaptive finite element refinement procedure. It is found that by carefully controlling the quality and grading of the quadrilateral elements, an increase in efficiency over pure triangular meshes can be achieved. Furthermore, if linear elements are employed, an optimal hybrid mesh can be obtained most economically by a combined use of the mesh coring technique suggested by Lo and Lau and a selective removal of diagonals from the triangular element mesh. On the other hand, if quadratic elements are used, it is preferable to generate a pure triangular mesh first, and then obtain a hybrid mesh by merging of triangles. © 1992.
Wed, 01 Jan 1992 00:00:00 GMThttp://hdl.handle.net/10722/710341992-01-01T00:00:00Z
- Generation of quadrilateral mesh over analytical curved surfaceshttp://hdl.handle.net/10722/71136Title: Generation of quadrilateral mesh over analytical curved surfaces
Authors: Lau, TS; Lo, SH; Lee, CK
Abstract: An automatic adaptive quadrilateral mesh conversion scheme for the generation of adaptive refinement meshes over analytical curved surfaces is proposed. The starting point of the quadrilateral mesh generator is a background triangular mesh of the curved surface. By a carefully controlled process to merge two triangles at a time the triangular mesh can be completely converted to quadrilaterals. A rapidly graded quadrilateral mesh with node spacing compatible with the desired element size distribution can be obtained from a well-graded triangular mesh. The quality of the quadrilateral mesh can be subsequently enhanced by a series of mesh modifications and element shape improvement procedures. The present scheme can be used in conjunction with an adaptive surface triangular mesh generator to generate quadrilateral meshes suitable for adaptive shell refinement analysis. © 1997 Elsevier Science B.V.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/10722/711361997-01-01T00:00:00Z
- Numerical solution for elastic inclusion problems by domain integral equation with integration by means of radial basis functionshttp://hdl.handle.net/10722/70674Title: Numerical solution for elastic inclusion problems by domain integral equation with integration by means of radial basis functions
Authors: Dong, CY; Lo, SH; Cheung, YK
Abstract: The unknown strains in the inclusions are expressed in terms of a series of radial basis functions (RBF) and polynomials in global coordinates. Based on the radial integration method proposed by Gao [J. Appl. Mech., Trans. ASME 69 (2002) 154, Engng Anal. Bound. Elem. 26 (2002) 905], the volume integrals for the evaluation of strains can be transformed into contour integrals on the inclusion boundaries. As a result of this transformation, there is no need to discretize the inclusions into finite elements. For the determination of the strains, collocation points are distributed at the interior of the inclusions to form a system of linear equations. Numerical results are compared with available analytical solutions and those based on a finite element discretization of the volume integrals. © 2003 Elsevier Ltd. All rights reserved.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10722/706742004-01-01T00:00:00Z
- On bandsolver using skyline storagehttp://hdl.handle.net/10722/70730Title: On bandsolver using skyline storage
Authors: Lo, SH
Abstract: A simple out-of-core bandsolver using skyline storage is presented. Without dividing the equations into blocks, the efficiency of the working vector can be greatly improved by a dynamic storage scheme to hold as many equations as possible at any one time. Compared to the blocked-skyline method, the total number of data transfers from core to disk and vice versa is reduced and the amount of active coefficients being processed in a single data transfer is maximized. The matrix decomposition without using direct-access files is first presented to explain how triangulation is done on a one-dimensional working array using skyline profile storage. Its extension to allow for out-of-core storage is then discussed in detail. Computer codes for both versions with and without using out-of-core storage are given in the Appendix. © 1992.
Wed, 01 Jan 1992 00:00:00 GMThttp://hdl.handle.net/10722/707301992-01-01T00:00:00Z
- An exact solution for the three-phase thermo-electro-magneto-elastic cylinder model and its application to piezoelectric-magnetic fiber compositeshttp://hdl.handle.net/10722/71796Title: An exact solution for the three-phase thermo-electro-magneto-elastic cylinder model and its application to piezoelectric-magnetic fiber composites
Authors: Tong, ZH; Lo, SH; Jiang, CP; Cheung, YK
Abstract: A three-phase cylindrical model for analyzing fiber composite subject to in-plane mechanical load under the coupling effects of multiple physical fields (thermo, electric, magnetic and elastic) is presented. By introducing an eigenstrain corresponding to the thermo-electro-magnetic-elastic effect, the complex multi-field coupling problem can be reduced to a formal in-plane elasticity problem for which an exact closed form solution is available. The present three-phase model can be applied to fiber/interphase/matrix composites, such that a lot of interesting thermo-electro-magnetism and stress coupling phenomena induced by the interphase layer are revealed. The present model can also be applied to fiber/matrix composites, in terms of which a generalized self-consistent method (GSCM) is developed for predicting the effective properties of piezoelectric-magnetic fiber reinforced composites. The effective piezoelectric, piezomagnetic, thermoelectric and magnetoelectric moduli can be expressed in compact explicit formulae for direct references and applications. A comparison of the predictions by the GSCM with available experimental data is presented, and interesting magnification effects and peculiar product properties are discussed. As a theoretical basis for the GSCM, the equivalence of the three sets of different average field equations in predicting the effective properties are proved, and this fact provides a strong evidence of mathematical rigor and physical realism in the formulation. © 2008 Elsevier Ltd. All rights reserved.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10722/717962008-01-01T00:00:00Z
- Effects of higher-order global-local shear deformations on bending, vibration and buckling of multilayered plateshttp://hdl.handle.net/10722/71273Title: Effects of higher-order global-local shear deformations on bending, vibration and buckling of multilayered plates
Authors: Wu, Z; Cheung, YK; Lo, SH; Chen, W
Abstract: In this paper, the effects of higher-order shear deformations on bending, natural frequencies and buckling loads of multilayered plates are studied. Based on the power series expansion of displacement components along thickness coordinate z and the double-superposition hypothesis proposed by Li and Liu [Li XiaoYu, Liu D. Generalized laminate theories based on double superposition hypothesis. Int J Numer Meth Eng 1997;40:1197-212], the mth-order global-local theory which satisfies the free surface conditions and the geometric and transverse shear stress continuity conditions at interfaces is presented. A refined four-node quadrilateral element is proposed for the numerical modeling of the global-local theory. In the process of finite element implementation, both the first and the second derivatives of transverse displacement w appear in the strain components. Transverse displacement functions satisfying C 0 and C 1 weak-continuity between elements are derived based on the refined element methods. Numerical results show that the transverse shear stress of multilayered plates, the natural frequency and the buckling loads of soft-core sandwich plates predicted by the proposed models of higher-order shear deformation are more accurate in comparison with the results based on the third-order global local theory and other lower order theories. © 2007.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10722/712732008-01-01T00:00:00Z
- An integral equation approach to the inclusion-crack interactions in three-dimensional infinite elastic domainhttp://hdl.handle.net/10722/71383Title: An integral equation approach to the inclusion-crack interactions in three-dimensional infinite elastic domain
Authors: Dong, CY; Cheung, YK; Lo, SH
Abstract: In this paper, an integral equation method to the inclusion-crack interaction problem in three-dimensional elastic medium is presented. The method is implemented following the idea that displacement integral equation is used at the source points situated in the inclusions, whereas stress integral equation is applied to source points along crack surfaces. The displacement and stress integral equations only contain unknowns in displacement (in inclusions) and displacement discontinuity (along cracks). The hypersingular integrals appearing in stress integral equation are analytically transferred to line integrals (for plane cracks) which are at most weakly singular. Finite elements are adopted to discretize the inclusions into isoparametric quadratic 10-node tetrahedral or 20-node hexahedral elements and the crack surfaces are decomposed into discontinuous quadratic quadrilateral elements. Special crack tip elements are used to simulate the √r variation of displacements near the crack front. The stress intensity factors along the crack front are calculated. Numerical results are compared with other available methods.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/713832002-01-01T00:00:00Z
- Solving crack problems by an adaptive refinement procedurehttp://hdl.handle.net/10722/71246Title: Solving crack problems by an adaptive refinement procedure
Authors: Lo, SH; Lee, CK
Abstract: The effect of using collapsed quarter-point elements (CQPE) in conjunction with the adaptive refinement procedure in solving crack problems is investigated. It is found that by using the collapsed quarter-point elements around the tip of the crack, the efficiency of the adaptive procedure can be increased considerably. The number of times of remeshing, and hence the computation time, required for achieving a solution with the same prescribed accuracy is much reduced. In addition, it is demonstrated that by using a simple swapping procedure to control the mesh layout surrounding the crack tip, it is possible to obtain highly accurate estimates of stress intensity factors by the adaptive refinement procedure. From the results of the uniform and adaptive finite element analysis on a set of problems, we conclude that in general there is no strong correlation between the relative error in energy norm of the solution and the relative percentage error of the stress intensity factors. The latter is much more dependent on the mesh geometry around the crack tip. © 1992.
Wed, 01 Jan 1992 00:00:00 GMThttp://hdl.handle.net/10722/712461992-01-01T00:00:00Z
- Anisotropic thin plate bending problems by Trefftz boundary collocation methodhttp://hdl.handle.net/10722/71464Title: Anisotropic thin plate bending problems by Trefftz boundary collocation method
Authors: Dong, CY; Lo, SH; Cheung, YK; Lee, KY
Abstract: Trefftz boundary collocation method is used to analyse the bending of anisotropic thin plates. Compared with the existing collocation methods employing complicated fundamental solutions in which the source points are located outside the plate, boundary collocation method presented in this article is relatively simple. It requires only the general solution of anisotropic thin plate bending problems and no singular integrals appear in the formulation. The collocation points are located along the plate edges. The implementation of the related computer codes is fairly straightforward. Numerical results are generally more accurate compared with existing solutions. © 2004 Elsevier Ltd. All rights reserved.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10722/714642004-01-01T00:00:00Z
- A hidden-line algorithm using picture subdivision techniquehttp://hdl.handle.net/10722/144823Title: A hidden-line algorithm using picture subdivision technique
Authors: Lo, SH
Abstract: An algorithm is presented for removing hidden lines for isometric or perspective projections of three-dimensional objects. Lines connecting nodal points are first retrieved from the model to be displayed. Instead of testing against the entire population of the projected planes to see if a line is totally or partially hidden, only potential covering planes belonging to a certain neighbourhood of the line are considered. Shifting from a global view to a local view, the efficiency of the algorithm is much improved; in fact the CPU time required for a plot increases only linearly with the number of planes present in the model. Improvement can also be found in the hidden-line elimination process (search for intersection and hidden portions) where classifications and case subdivisions are generalised and combined, and calculations for their determinations are also simplified. Examples of various degrees of complexity are given. © 1987.
Fri, 01 Jan 1988 00:00:00 GMThttp://hdl.handle.net/10722/1448231988-01-01T00:00:00Z
- Finite element mesh generation over curved surfaceshttp://hdl.handle.net/10722/144824Title: Finite element mesh generation over curved surfaces
Authors: Lo, SH
Abstract: A general program is developed to generate finite element mesh over curved surfaces. The domain to be triangulated can be any combination of the five elementary surfaces-spatial plane, cylinder, cone, sphere and surface of revolution. For developing surfaces, discretization into finite elements can be done on a plane which are then put into place by suitable transformations. As for spherical surfaces and surfaces of revolution, mesh generation is done directly in space. The efficiency and capability of the program owes a lot to its possibility of combining irregular parts of these basic surface types almost in any order, forms and orientations. Surfaces of arbitrary forms can also be triangulated and matched to other surface parts. Special attention has been paid to the data structure, particularly in the definition and coordination of different surface types. © 1988.
Fri, 01 Jan 1988 00:00:00 GMThttp://hdl.handle.net/10722/1448241988-01-01T00:00:00Z
- Automatic mesh generation over intersecting surfaceshttp://hdl.handle.net/10722/70749Title: Automatic mesh generation over intersecting surfaces
Authors: Lo, SH
Sun, 01 Jan 1995 00:00:00 GMThttp://hdl.handle.net/10722/707491995-01-01T00:00:00Z
- Volume discretization into tetrahedra-I. Verification and orientation of boundary surfaceshttp://hdl.handle.net/10722/149954Title: Volume discretization into tetrahedra-I. Verification and orientation of boundary surfaces
Authors: Lo, SH
Abstract: Three-dimensional triangulation of an arbitrary volume is a time-consuming process, and the boundary surfaces of the object have to be checked very carefully to ensure no error is made. The data verification and preparation work for a general 3D mesh generation problem is best done more or less automatically by another program which not only detects any error in the data but also generates from the given triangular facets all the boundary surfaces with the correct orientations for the next step of volume discretization into tetrahedra, using the advancing front approach. This paper describes such a boundary data pre-processor for discretization of arbitrary objects into tetrahedron elements. In this data-checking and preparation process, first the size and quality of the given randomly numbered triangular facets will be examined, then the closure and orientability of the surfaces that can be constructed from the triangular elements will be verified. Each valid closed surfaces will be given a correct orientation according to its type (interior or exterior surface). The volumes so defined by these surfaces are identified and labelled for 3D mesh generation. © 1991.
Tue, 01 Jan 1991 00:00:00 GMThttp://hdl.handle.net/10722/1499541991-01-01T00:00:00Z
- Perspective projection of non-convex polyhedrahttp://hdl.handle.net/10722/144825Title: Perspective projection of non-convex polyhedra
Authors: Lo, SH
Abstract: An algorithm is presented for removing hidden lines for isometric and perspective projections of three-dimensional objects. An object can be regarded as being made up of a number of planes, and the whole picture can therefore be visualized as only a collection of planes. Considering planes as the basic element of a picture, non-convex polyhedra can be displayed directly without prior subdivisions into convex ones. Lines connecting nodal points are first retrieved from the model to be plotted by a simple but efficient technique. On the picture planes, each unique line is examined in turn to see if it is totally or partially hidden. The intersections between a unique line and a projected plane (with or without openings) are determined by a new method which, even in the presence of numerical errors, will always give correct intersection information. Unlike many classical algorithms, intersections are determined by a single formula without tedious case subdivisions. With little additional calculations, object penetrations can also be tackled.
Fri, 01 Jan 1988 00:00:00 GMThttp://hdl.handle.net/10722/1448251988-01-01T00:00:00Z
- Automatic decomposition of discretized surfaces for parallel processinghttp://hdl.handle.net/10722/140734Title: Automatic decomposition of discretized surfaces for parallel processing
Authors: Lo, SH; Borouchaki, H; Laug, P
Abstract: In this paper, a generic surface decomposition algorithm is presented which could subdivide a general open or closed discretized surface into n pieces following any specified geometrical criteria. The cut lines are formed by taking unique lines (edges) on the discretized surface, so that only topological operations are involved, and hence individual partitioned surfaces could be processed independently before being put back together to recover the original surface. A surface marching process is proposed to balance the specified geometrical quantities of the cut surfaces following a distance map readily determined from the element adjacency relationship. The cut line can be further refined by a backward marching procedure within a potential cutting zone, so that other geometrical quantities such as sharp dihedral angles and deviation angles, etc. can also be taken into account. The time complexity of the surface decomposition process is basically linear as only the element adjacency relationship and the system of unique lines are referred to in all the steps for surface decomposition.
Description: Session - Domain Decomposition Methods in Engineering Computations: paper 14
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1407342011-01-01T00:00:00Z
- 3D Delaunay triangulation of 1 billion points on a PChttp://hdl.handle.net/10722/211001Title: 3D Delaunay triangulation of 1 billion points on a PC
Authors: Lo, SH
Abstract: Of course, there is not enough memory on a PC with 16 GB RAM, and tetrahedra constructed have to be output to leave rooms for the creation of new tetrahedra in the next round of point insertion. A segmental zonal insertion scheme is developed, in which large data sets of more than 100 million points are partitioned into zones, each of which is triangulated in turn by the parallel zonal insertion module. An overlapping zone between two steps of insertion has to be allowed to ensure Delaunay tetrahedra formed at the boundary between two insertion zones.
Tetrahedra between zones can be easily eliminated by the minimum vertex allocation method. The collection of all the tetrahedra from each insertion zone/step will produce the required triangulation for the point set. As the work of each typical step for the insertion of an equal number of points is very much similar, the processing time bears roughly a linear relationship with the number of points in the set, at a construction rate of more than 5 million Delaunay tetrahedra per second for the triangulation of 1 billion randomly generated points.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2110012015-01-01T00:00:00Z