A LEAST-SQUARES APPROACH FOR UNIFORM STRAIN TRIANGULAR AND TETRAHEDRAL FINITE-ELEMENTS

A least-squares approach is presented for implementing uniform strain triangular and tetrahedral finite elements. The basis for the method i s a weighted least-squares formulation in which a linear displacement field is fit to an element's nodal displacements. By including a great er number of nodes on the element boundary than is required to define the linear displacement field, it is possible to eliminate volumetric locking common to fully integrated lower-order elements. Such results can also be obtained using selective or reduced integration schemes, b ut the present approach is fundamentally different from those. The met hod is computationally efficient and can be used to distribute surface loads on an element edge or face in a continuously varying manner bet ween vertex, mid-edge and mid-face nodes. Example problems in two- and three-dimensional linear elasticity are presented. Element types cons idered in the examples include a six-node triangle, eight-node tetrahe dron, and ten-node tetrahedron. (C) 1998 John Wiley & Sons, Ltd.