Application of 2D base force element method with complementary energy principle for arbitrary meshes

Abstract

Purpose

The purpose of this paper is to present a two-dimensional (2D) model of the base force element method (BFEM) based on the complementary energy principle. The study proposes a model of the BFEM for arbitrary mesh problems.

Design/methodology/approach

The BFEM uses the base forces given by Gao (2003) as fundamental variables to describe the stress state of an elastic system. An explicit expression of element compliance matrix is derived using the concept of base forces. The detailed formulations of governing equations for the BFEM are given using the Lagrange multiplier method. The explicit displacement expression of nodes is given. To verify the 2D model, a program on the BFEM using MATLAB language is made and a number of examples on arbitrary polygonal meshes and aberrant meshes are provided to illustrate the BFEM.

Findings

A good agreement is obtained between the numerical and theoretical results. Based on the studies, it is found that the 2D formulation of BFEM with complementary energy principle provides reliable predictions for arbitrary mesh problems.

Research limitations/implications

Due to the use of Lagrange multiplier method, there are more basic unknowns in the control equation. The proposed method will be improved in the future.

Practical implications

This paper presents a new idea and a new numerical method, and to explore new ways to solve the problem of arbitrary meshes.

Originality/value

The paper presents a 2D model of the BFEM using the complementary energy principle for arbitrary mesh problems.

Citation

Peng, Y., Zong, N., Zhang, L. and Pu, J. (2014), "Application of 2D base force element method with complementary energy principle for arbitrary meshes", Engineering Computations, Vol. 31 No. 4, pp. 691-708. https://doi.org/10.1108/EC-10-2011-0125