Topology Optimization Design of Strut-and-Tie Model Based on Bi-Modulus Truss-Like Materials
Strut-and-tie model method is one of the standard methods for designing reinforcement in complex reinforced concrete structures.It is very important to construct the strut-and-tie model in complex stress regions using topology optimization.The algorithms of Solid Isotropic Microstructures with Penalization(SIMP)and Evolutionary Structural Optimization(ESO)have been widely used in such studies.These algorithms are optimized for isotropic perforated plates of unit thickness,the essence of which is to seek approximate solutions near the optimal solution.In addition,existing methods rarely consider the effect of different material tension-compression properties on the optimal topology due to the difficulties caused by the unsmooth character of the constitutive curve.A topology optimization algorithm based on a truss-like continuum with bi-modulus materials is proposed to construct the optimal topology of the strut-and-tie model.The density and orientation of the orthogonal trusses at each node are considered as the design variables.The material properties in the tension and compression regions are consistent with the tensile modulus of the reinforcement and the compression modulus of the concrete,respectively.A material substitution scheme is introduced to overcome the non-linearity caused by the bi-modulus,and a correction formula for stiffness matrix is given.The optimization is achieved through an iterative algorithm based on sensitivity information.Numerical examples show that differences in elastic modulus significantly affect the optimal topology.Compared to the density-based optimization methods,the proposed algorithm is able to accurately describe the optimal material distribution field under complex stress states,with the computational efficiency imporved by about 26％.Besides that,more details of the material distribution can be given.The algorithm is able to improve efficiency and accuracy while giving more design details.
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