The application of 2D base force element method (BFEM) to geometrically non-linear analysis

A 4-Mid-Node Plane Model of Base Force Element Method on Complementary Energy Principle

“…Substituting (20) into (28) and considering (19), (10), and (14), the explicit expression for displacement of nodes can be written as…”

“…A three-dimensional model of base force element method (BFEM) on complementary energy principle was proposed by Liu and Peng [18] for elasticity problems. The application of 2D base force element method (BFEM) to geometrically nonlinear analysis was proposed by Peng et al [19].…”

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]…”

“…A three-dimensional model of base force element method (BFEM) on complementary energy principle was proposed by Liu and Peng [36] for elasticity problems. A 4-mid-node plane element model of the BFEM on complementary energy principle was proposed by Peng et al [38] for geometrically nonlinear problem, which is derived by assuming that the stress is uniformly distributed on each edges of a plane element. In the paper [39], an arbitrary convex polygonal element model of the BFEM on complementary energy principle was proposed for geometrically nonlinear problem.…”

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].…”