M. W. Heinstein

Node‐based uniform strain elements for three‐node triangular and four‐node tetrahedral meshes

A family of uniform strain elements is presented for three-node triangular and four-node tetrahedral meshes. The elements use the linear interpolation functions of the original mesh, but each element is associated with a single node. As a result, a favorable constraint ratio for the volumetric response is obtained for problems in solid mechanics. The uniform strain elements do not require the introduction of additional degrees of freedom and their performance is shown to be significantly better than that of three-node triangular or four-node tetrahedral elements. In addition, nodes inside the boundary of the mesh are observed to exhibit superconvergent behavior for a set of example problems.

Methods for connecting dissimilar three-dimensional finite element meshes†

Two methods are presented for connecting dissimilar three-dimensional finite element meshes. The first method combines the concept of master and slave surfaces with the uniform strain approach for finite elements. By modifying the boundaries of elements on a slave surface, corrections are made to element formulations such that first-order patch tests are passed. The second method is based entirely on constraint equations, but only passes a weaker form of the patch test for non-planar surfaces. Both methods can be used to connect meshes with different element types. In addition, master and slave surfaces can be designated independently of relative mesh resolutions. Example problems in three-dimensional linear elasticity are presented. Published in 2000 by John Wiley & Sons, Ltd.

A method for connecting dissimilar finite element meshes in two dimensions

A method is presented for connecting dissimilar finite element meshes in two dimensions. The method combines standard master–slave concepts with the uniform strain approach for finite elements. By modifying the definition of the slave boundary, corrections are made to element formulations such that first-order patch tests are passed. The method can be used to connect meshes which use different element types. In addition, master and slave boundaries can be designated independently of relative mesh resolutions. Example problems in two-dimensional linear elasticity are presented. Copyright

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 is a weighted least-squares formulation in which a linear displacement field is fit to an elements nodal displacements. By including a greater 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, but the present approach is fundamentally different from those. The method is computationally efficient 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.