No 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.

Abstract:Recycle Aggregate Concrete (RAC) is a common "green" product used for a variety of purposes, although the durability and strength of the material still need more research to adequately determine influences on these parameters. The failure pattern, punching bearing capacity, and deflection variation of wallboard of both ordinary concrete and RAC with various rebar reinforcement diameters and spacing were analyzed. Based on experimental data, the ABAQUS finite element analysis of the thin wallboard was performed, and the calculated results are in good agreement with the experimental results. The results show that the failure characteristics of ordinary concrete wallboards and RAC wallboards are similar, but the brittleness of the RAC specimens is more significant. Under the same reinforcement ratio, concrete material, whether new or recycled, had little effect on the punching bearing capacity of the specimens. In the case of a low reinforcement ratio, increasing the reinforcement ratio (decreasing the spacing of steel bars) can effectively improve the bearing capacity of the wallboard. Under the same reinforcement ratio, the wallboard with larger diameter and larger spacing has a higher bearing capacity and less deformation after failure.