Researches Into Topology Optimization Of Structure With Elastoplastic Deformation And Checkerboard Suppression Method

Topology optimization is a most effective method of determining materials’distribution in initial stage of structural design, and it can provide the product with initial concept design. Moreover, topology optimization can also determine the designed products’basic shape, and it is provided with a decisive meaning for the designed products’effectiveness. At present, the researches in topology optimization are mainly focused on linear materials, nevertheless, hardly being involved in nonlinearity materials’structures. However, when some structures in engineering bear the practical loads, whose materials will produce nonlinear deformation. For these structures, if only the linearly elastic topology optimization is carried on, ones wouldn’t obtain the optimal structures meeting practical using demands. Therefore, it is essential to further study the structural topology optimization with nonlinear materials.The evolutionary structural optimization (ESO) method is extended to the structural topology optimization with elasto-plastic material from elastic material, and the topology optimization model considering stress constraint and material’s elasto-plastic deformation is established in this work. Corresponding optimization designs are implemented by employing Ansys’s APDL language to program, and the comparison examples of elastic optimization and elasto-plastic optimization are shown. The comparison analysis based numerical examples’ results show that:Under the circumstances of the same design domain and load, the optimized topology configuration of elasto-plastic material’s structures are obviously different from linear elastic material; For linear elastic and elasto-plastic structural topology optimization, the material’s usage quantity W both gradually decreases with the increasing of the optimized structural stress constraint coefficient β, and a turning point exists on the W-β curve corresponding to the structural elastic limit, and near this point the rate of change of the right curve (taking the absolute value)is greater than the left, which sufficiently shows that the structural topology optimization considering material’s elasto-plastic character is fairly significant for saving material’s usage quantity.Checkerboard pattern often appears in the optimized structure which is gotten through topology optimization, which makes structural shape extraction and manufacture become rather difficult, and, therefore it ought to be avoided in the optimization process. Aiming at the calculation of elements’weight coefficients in the checkerboard filter technique and improving the checkerboard suppression method appearing in an existing reference, the more generalized and specific physical meanings’formulas are proposed in this work. The improved checkerboard suppression method is used for the structural topology optimization with elasto-plastic materials, and then authors employ ESO method to implement the optimization process. Two numerical examples are implemented by programming, and the obtained results show that the improved checkerboard suppression method in this work has enhanced the suppression effects, and the improved suppression method isn’t limited to the topology optimization of linear materials, and it is suitable for applying to the checkerboard suppression of nonlinearly structural topology optimization.Above-mentioned topology optimization examples are loaded in a force manner, and, nowadays, the topology optimization researches about structures with nonlinear materials (i.e., plasticity optimization design) are mainly concentrated on the situation with a force loading. However, for some structures, considering the displacement loading is more practical in applications, and also, convergence difficulty often emerges in the situation with a force loading, but, inversely, the drawback of convergence difficulty may be overcome through a displacement loading. Employing ESO method to optimization the nonlinear materials’ structures with a displacement loading, at the same time, the proposed improved checkerboard suppression method is applied to the situation with a displacement loading, and corresponding numerical examples are implemented by programming, further verifying the validity of the improved checkerboard suppression method in this work. Getting the changing relation of structural maximum equivalent stress and displacement loads, the reliability problem of afterwards optimized structures is analyzed.