A least-squares approach for uniform strain triangular and tetrahedral finite elements

✍ Scribed by C. R. Dohrmann; S. W. Key; M. W. Heinstein; J. Jung

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 131 KB
• Volume: 42
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19980815)42:7<1181::aid-nme402>3.0.co;2-p

✦ Synopsis

A least-squares approach is presented for implementing uniform strain triangular and tetrahedral ÿnite elements. The basis for the method is a weighted least-squares formulation in which a linear displacement ÿeld is ÿt to an element's nodal displacements. By including a greater number of nodes on the element boundary than is required to deÿne the linear displacement ÿeld, 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, 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 linear elasticity are presented. Element types considered in the examples include a six-node triangle, eight-node tetrahedron, and ten-node tetrahedron. ?