Exact integration scheme for six-node wedge element mass matrix

TL;DR

This paper introduces an exact, efficient integration scheme for six-node wedge element mass matrices, improving accuracy and reducing computational effort compared to traditional numerical methods.

Contribution

The paper presents a novel seven-point exact integration rule for mass matrices of six-node wedge elements, including new schemes with fewer points and enhanced accuracy.

Findings

Exact integration scheme with seven points derived

New one- and four-point schemes proposed

Improved accuracy over existing numerical methods

Abstract

Currently, mass matrices are computed by means of sufficiently accurate numerical integration schemes. Two-point and nine-point (Gauss) quadrature remain frequently used. We derive an exact, easy to implement integration rule for six-node wedge element mass matrices based on seven points only. Both consistent and lumped mass matrices have been considered. New metric (jacobian determinant) interpolation accompanied by analytical integration permits computing effort reduction next to accuracy increase of integration rule. In addition, one and four point mass matrices integration schemes have been proposed. Accuracy superiority over equivalent schemes is established.