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.

Base force element method based on the complementary energy principle for the damage analysis of recycled aggregate concrete

“…In previous works, the complementary energy functional is as follows: …”

“…In addition, the node displacements are obtained as an explicit expression. In previous works, 38,39 the complementary energy functional is as follows:…”

“…In this article, a new concept named the base force and a new FEM named the base force element method (BFEM) are introduced. According to the basic theory and the BFEM on the complementary energy principle, the element compliance matrix can be represented by a uniform explicit expression .…”

A Novel Shape-Free Plane Quadratic Polygonal Hybrid Stress-Function Element

“…By applying the Hellinger-Reissner variational principle, Zhang and Katsube [35,36] developed the hybrid polygonal element (HPE) to simulate materials with inclusions and holes. Peng et al [37,38] proposed a novel base force element method by using the principle of minimum complementary energy and developed quadratic polygonal elements to solve problems with concave polygonal meshes.…”

Application of Base Force Element Method on Complementary Energy Principle to Rock Mechanics Problems

“…However, the conventional finite element method (FEM) based on the displacement model has some shortcomings, such as large deformation, treatment of incompressible materials, bending of thin plates, and moving boundary problems. In the past decades, numerous efforts techniques have been proposed for developing finite element models which are robust and insensitive to mesh distortion, such as the hybrid stress method [1][2][3][4], the equilibrium models [5,6], the mixed approach [7], the integrated force method [8][9][10][11], the incompatible displacement modes [12,13], the assumed strain method [14][15][16][17], the enhanced strain modes [18,19], the selectively reduced integration scheme [20], the quasiconforming element method [21], the generalized conforming method [22], the Alpha finite element method [23], the new spline finite element method [24,25], the unsymmetric method [26][27][28][29], the new natural coordinate methods [30][31][32][33], the smoothed finite element method [34], and the base force element method [35][36][37][38][39][40][41][42]…”