Linear Strain Element with Curved Edges

Abstract

A finite element is developed that accurately models the strain states it is designed to represent regardless of its initial configuration. In other words, the interpolation polynomials are unchanged hy element distortion. The formulation of this element is based on the transformation of a specified set of linearly independent strain states into the desired stiffness matrix. This stiffness matrix exactly reproduces the strain energy content and the pointwise strain of the continuum for the strain states designated in its formulation. This insures that the polynomial bases of the approximation remains constant. Instead of computing the strain quantities at a number of points in the element, the strain distribution information is given in terms of rigid body and strain gradient terms for a designated point. This form of the strain data supplies information about the state of convergence in the problem and the location of regions of high strains. The computational speed of the linear strain element is competitive with the isoparametric formulation procedure.