Avoidance of Parasitic Shear in Plane Element

A method for avoiding parasitic shear in displacement-based finite elements is proposed. Internal degrees-of-freedom are not required, and the resulting element is valid whether rectangular or of general quadrilateral shape. The element is improved by adding internal degrees-of-freedom, but it is questionable whether the improvement is worth the added computational expense. The new elements may be immediately adapted to the analysis of solids of revolution. Computational test has shown that the new elements, with or without internal degrees-of-freedom, pass the patch test in axisymmetric problems. The test cases considered were radial loads on a disk of constant thickness and axial loads on a cylinder of constant thickness. Non-rectangular elements were used in both cases. The proposed method of formulation might similarly benefit the eight-node linear isoparametric solid element. As there are many ways to divide a hexahedron into component tetrahedra, the crudest acceptable division must be sought in order to achieve computational efficiency.