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

Yijiang Peng,Zhaofeng Zhang,Yanyan Shan,Qing Guo

doi:10.1155/2015/292809

Yijiang Peng, Zhaofeng Zhang + Show 2 more

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https://doi.org/10.1155/2015/292809

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Abstract

The four-mid-node plane model of base force element method (BFEM) on complementary energy principle is used to analyze the rock mechanics problems. The method to simulate the crack propagation using the BFEM is proposed. And the calculation method of safety factor for rock mass stability was presented for the BFEM on complementary energy principle. The numerical researches show that the results of the BFEM are consistent with the results of conventional quadrilateral isoparametric element and quadrilateral reduced integration element, and the nonlinear BFEM has some advantages in dealing crack propagation and calculating safety factor of stability.

Highlights

The finite element method (FEM) has been playing a very important role in solving various problems in engineering and science
The methods to simulate the gravity of an element, the crack propagation and the safety factor of stability are proposed for the base force element method (BFEM) on complementary energy principle
(1) The calculation results of the BFEM on complementary energy principle show that the numerical results of the present method coincide with the theoretical solution, the results of conventional quadrilateral isoparametric element (Q4 model) and quadrilateral reduced integration element (Q4R model)

Summary

Introduction

The finite element method (FEM) has been playing a very important role in solving various problems in engineering and science. 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. Some scholars still adhere to explore the finite element method based on complementary energy principle [48,49,50,51]. These methods have not been widely applied in engineering

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