Eight-node solid brick element high-order stiffness matrix template

TL;DR

This paper develops a high-order stiffness matrix template for an eight-node solid brick finite element based on an assumed stress method derived from the Hellinger-Reissner principle, enhancing stability and accuracy.

Contribution

It introduces a novel high-order stiffness matrix template for solid brick elements using an assumed stress approach, improving finite element modeling precision.

Findings

Decomposition of stiffness into basic and high-order parts

Enhanced stability and accuracy in finite element analysis

Framework applicable to three-dimensional solid modeling

Abstract

In this paper, the template will be developed from an assumed Stress Method, which its formulation is based on the Hellinger-Reissner principle developed according to Kang's study in 1986. The element stiffness is decomposed into a basic part that takes care of consistency and mix-ability, and a HO element stiffness part that takes care of stability (also known as rank sufficient) and accuracy. In the FE method, the HO stiffness is based on a displacement formulation, whereas the basis stiffness is method independent. To start, one should be familiar with the definition of a solid brick element. Solid brick element is three-dimensional finite elements that can model solid bodies and structures without any a priori geometric simplification.