The equivalent parallelogram and parallelepiped, and their application to stabilized finite elements in two and three dimensions

A new class of quadrilateral and hexahedral elements (four- and eight-noded in two and three dimensions, respectively) is presented. These elements ar e obtained by combining the concept of the equivalent parallelogram for pla ne problems. and the equivalent parallelepiped for three-dimensional proble ms, with the notion of incompatible modes. A key feature of the new element s is that integration of the element stiffness matrices is carried out usin g one-point integration. The use of affine-equivalent elements (parallelogr ams and parallelepipeds) permits a closed-form eigenvalue analysis which in cludes the incompatible modes, and a stabilization procedure based on the e igenvalue analysis ensures the full rank of the stiffness matrix. Numerical results for problems in elasticity and plasticity indicate equivalent or s uperior performance of the new elements, when compared with various element s based on enhanced strains of incompatible modes. (C) 2001 Elsevier Scienc e B.V. All rights reserved.