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 nite ele- ments. The basis for the method is a weighted least-squares formulation in which a linear displacement eld is t to an elementʹs nodal displacements. By including a greater number of nodes on the element boundary than is required to de ne the linear displacement eld, it is possible to eliminate volumetric locking common to fully integrated lower-order elements. Such results can also be obtained using selective or reduced integra- tion schemes, but the present approach is fundamentally di erent from those. The method is computationally e cient and can be used to distribute surface loads on an element edge or face in a continuously varying manner between vertex, mid-edge and mid-face nodes. Example problems in two- and three-dimensional lin- ear elasticity are presented. Element types considered in the examples include a six-node triangle, eight-node tetrahedron, and ten-node tetrahedron.