An efficient rotation-free triangle and its application in cloth simulations

Abstract

In this thesis, an efficient rotation-free (RF) triangle is proposed and applied to drape/cloth simulations in which the cloth often under large displacements and rotations. The RF model is a class of thin plate/shell computational models possessing only 3 translational degrees of freedom per director whilst their domains of influence are larger than their domains of integration. An important advantage of RF models is that they do not use rotational degrees of freedom and, thus, are not plagued by the complication in finite rotations. Among the quadrilateral and triangular RF models, the latter possesses no practical restriction on the nodal distribution and appears to be a good candidate for drape/cloth simulations.

The geometrical linear formulation of the RF model is firstly considered. For straight beams and plates, the curvature is directly obtained through a complete quadratic interpolation of the transverse deflection. For linear curved beams and shells, the curvature change is again derived by the interpolation and the transverse deflection is through projection. The linear RF model is then extended to the geometrical nonlinear analyses by using the corotational framework as well as the small strain and small curvature assumptions. For the RF straight beam and plate, constant tangential bending stiffness matrices which do not need to be updated during the iterative solution process are derived. For the RF curved beam and shell, the bending energies and bending internal forces become a bit complicated. However, the tangential bending stiffness matrices can still be approximated by using the constant matrices as if they are initially straight/flat. The constant approximation exhibits negligible adverse effect on the convergence. Comparing with other exiting RF models, the present RF triangle is simple and physical yet its accuracy is competitive. In its application to static drape simulations, realistic drape configurations with obvious folds are predicted.

The RF beam is extended to consider static and dynamic analyses of cable structures. Under the same nodal distributions, the present RF model can tolerate larger load increment and time step in static and explicit dynamic analyses, respectively, with respect to the two-node C0beam finite element model.

For virtual sewing and dynamic cloth simulations, an integrated system is developed by synergizing the RF triangle, explicit time integration, adaptive remeshing, collision handling, human body modeling, sewing forces and a supplementary bending energy to suppress the non-physical sharp fold formation. The predicted steady-state configurations of the garments after sewing appear to be realistic and agree with our daily perception. The predictions for cloth dynamic deformations on human body model also look realistic and natural. This thesis proposes a simple and efficient rotation-free triangle which is especially suitable for the problems involving large displacements and rotations. Its application in drape/cloth simulations and integration of various techniques in cloth simulations are explored. The present study is of significance in cloth simulations.