4 - ‘Standard’ and ‘hierarchical’ element shape functions: Some general families of C0 continuity

Abstract

Linear elasticity and other problems can be formulated and solved using very simple element forms. Once the element and the corresponding shape functions are determined, subsequent operations follow a standard, well-defined path. It is possible to program a computer to deal with wide classes of problems by specifying only the shape functions. This chapter presents some rules for the generation of several families of one-, two-, and three-dimensional elements. In addition, it focuses on the scalar shape function forms, calling these simply Na. This chapter describes shape functions that satisfy the following criteria: the continuity of the unknown can only occur between elements criteria and the function has to allow any arbitrary linear form to be taken, so that the constant strain criterion can be observed in each element. They are thus applicable to all the problems requiring Co continuity.