Strain-smoothed element method for improving low-order solid and shell finite elements

Abstract

A new strain smoothing method called the strain-smoothed element (SSE) method has been proposed. The SSE method does not require additional degrees of freedom, and provides highly accurate solutions by fully utilizing the strains of neighboring finite elements. Unlike with previous strain smoothing methods, special smoothing domains are not created, and more continuous and accurate strain fields are constructed within elements. The SSE method was first applied to linear solid elements (also called constant strain elements), i.e., 3-node triangular 2D and 4-node tetrahedral 3D solid elements. A further study has been conducted to extend the method to general low-order finite elements, and as a result, a strain-smoothed 4-node quadrilateral 2D solid element was developed. Using the SSE method, a strain-smoothed MITC3 + shell finite element was developed that exhibits much improved membrane behavior compared with the original MITC3+ shell finite element. Then, we present the total Lagrangian formulation of the strain-smoothed MITC3+ shell element for geometric nonlinear analysis. A variational principle for the SSE method was constructed and convergence and stability analyses were performed based on the defined variational principle.