Mass Matrix Integration Scheme for Fifteen-node Wedge Element

TL;DR

This paper introduces a new ten-point integration scheme for the mass matrix of fifteen-node wedge elements, offering improved accuracy and efficiency over the traditional eighteen-point method.

Contribution

A novel ten-point integration rule is derived using polynomial approximation, simplifying implementation and enhancing accuracy compared to the standard eighteen-point scheme.

Findings

The ten-point scheme outperforms the eighteen-point scheme in accuracy.

The new method reduces computational effort.

Numerical tests confirm superior performance across mesh types.

Abstract

At present, mass matrix of solid fifteen node wedge element is computed by means of eighteen-point (Gauss points) numerical integration scheme. Herein, this widely accepted scheme is being challenged. We derive a novel, easy-to-implement, ten-point integration rule. To this end, the metric (Jacobian determinant) is approximated using special second order interpolation, requiring ten evaluation points. This polynomial approximation permits further analytical integration, which is accompanied by convenient coefficient matrix definition. Coefficient matrices (equivalent to weights), allow the new rule to be formulated in a well-known manner. Preliminary numerical study considering both fine and a coarse mesh is conducted. In fact, significant accuracy superiority over eighteen-point scheme is established for all the coarseness range. In conclusion, our ten-point mass matrix scheme over-performs the standard 18-point integration rule in both the accuracy and in computational effort.