Using the concept of the base forces, a new finite element method (base force element method, BFEM) based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.
In order to study the mesomechanical properties of recycled aggregate concrete (RAC) under uniaxial tension, a numerical model of RAC with two different aggregate shapes (circular and convex) and five different replacement ratios of recycled aggregate (0, 30, 50, 70, and 100%) was established. A new finite element method-base force element method (BFEM) was used to derive the element strain and the element stiffness matrix with an explicit expression without Gauss integral. The two-dimensional numerical model of the RAC was simulated to study the effect of aggregate shape, replacement ratio of recycled aggregate, aggregate distribution and interfacial transition zone (ITZ) properties on mesomechanical properties of RAC. Simulation results demonstrated that once the first crack appeared, the peak stress and peak strain were reached. The first crack appeared in old ITZ, which was located in whether the upper part or the lower part of the large-size recycled aggregate. The continuous cracks were mainly around the recycled aggregate and the aggregate concentrated area. Comparing with natural concrete, when the replacement ratio of recycled aggregate was 100%, the elastic modulus decreased by 16~25%, the peak stress decreased by 12~15%, and the peak strain changed slightly. The ITZ had a significant influence on the mechanical properties of RAC and must be considered in the analysis.
The base force element method (BFEM) on potential energy principle is used to analyze recycled aggregate concrete (RAC) on mesolevel. The model of BFEM with triangular element is derived. The recycled aggregate concrete is taken as five-phase composites consisting of natural coarse aggregate, new mortar, new interfacial transition zone (ITZ), old mortar, and old ITZ on meso-level. The random aggregate model is used to simulate the mesostructure of recycled aggregate concrete. The mechanics properties of uniaxial compression and tension tests for RAC are simulated using the BFEM, respectively. The simulation results agree with the test results. This research method is a new way for investigating fracture mechanism and numerical simulation of mechanics properties for recycled aggregate concrete.
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