A new strain-based finite element for plane elasticity problems

Purpose In this paper, a new quadrilateral strain-based element is developed. The element has five nodes, four at the corners as well as an internal node. Design/methodology/approach Through the introduction of the internal node, the numerical performance of the element proved to be superior to existing elements in the literature, even though a static condensation is required. Findings From several numerical examples, it is shown that convergence can be achieved with the use of only a small number of finite elements. The proposed element can be used to solve general plane linear elasticity problems resulting in excellent results. Originality/value The results obtained are comparable with those given by the robust element Q8.

A Remarkable Tensor in Plane Linear Elasticity

It is shown that any two-dimensional elastic tensor can be orthogonally and uniquely decomposed into a symmetric tensor and an antisymmetric tensor. To within a scalar multiplier, the latter turns out to be equal to the right-angle rotation on the space of two-dimensional second-order symmetric tensors. On the basis of these facts, several useful results are derived for the traction boundary value problem of plane linear elasticity.