Base force element method (BFEM) on potential energy principle for elasticity problems

A Brief Review on Polygonal/Polyhedral Finite Element Methods

“…This is because the deformation field in conventional FEM is complex and discontinuous near nonlinear regions and, in the case of large strain problems, the steep gradients of deformation cannot be represented accurately by the conventional shape functions [159]. BFEM has been later extended to polygonal elements based on the complementary energy principle [160] and potential energy principle [161]. Figure 14 shows an example of a BFEM element.…”

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]…”

“…Based on the concept of the base forces, precise expressions for stiffness and compliance matrices for the FEM were obtained by Gao [52]. The applications of the stiffness matrix to the plane problems of elasticity using the plane quadrilateral element and the polygonal element were researched by Peng et al [37]. Using the concept of base forces as state variables, a three-dimensional formulation of base force element method (BFEM) on complementary energy principle was proposed by Peng and Liu [35] for geometrically nonlinear problems.…”

Application of Base Force Element Method to Mesomechanics Analysis for Concrete

“…Over the past 50 years, numerous efforts techniques have been proposed for developing finite element models [12][13][14][15] and some other improvement and alternative methods have been proposed and developed, such as boundary element methods [16,17] and meshless methods [18,19]. In recent years, a new type of finite element method, the base force element method (BFEM), has been developed by Peng et al [20][21][22][23][24][25] based on the concept of the base forces by Gao [26]. Further, the base force element method (BFEM) on potential energy principle was used to analyze recycled aggregate concrete on mesolevel [27].…”