A family of rectangular bending elements

Abstract

By using separate independent transverse and rotational displacement variables in terms of a polynomial it is possible to produce high order conforming elements for plate bending and, at the same time, to include the effect of shear deformation in the analysis. The procedure for constructing a family of conforming rectangular plate bending elements with any number of nodes and the derivation of the stiffness matrix are illustrated. A computer programme is developed to generate the stiffness coefficients of the elements in this family; whereupon the characteristics of elements with as many as 17, 21 or 25 nodes and so on can be investigated. It is demonstrated that accurate results can be obtained for thin and moderately thick plates with various boundary conditions under bending by using just one or a few high order elements in this family. Hence the procedure for solving a problem in plate bending can be much simplified and the total number of nodes in a problem can be much reduced. Highlight in this family is the 17-node element which yields good results without involving too many nodes for many plate bending problems. © 1979.