摘要：This paper presents the problem of volume minimization of two-dimensional continuous structures with compliance and stress constraints. Problems are solved by a topology optimization technique, formulated as finding the best material distribution into the design domain. Discretizing the geometry into simpler pieces and approximating the displacement field, equilibrium equations are solved through the finite element method. A material parametrization method is used to represent the fictitious constant material distribution into each finite element. Sequential Linear Programming is used to solve the optimization problem. For both compliance and stress constrained problems, an analytical sensitivity analysis for elastic behavior is derived, and for this last problem, Von Mises equivalent stress is the failure criteria considered. A first neighborhood filter was implemented to minimize the effects of checkerboard patterns and mesh dependency, two common problems associated to topology optimization. Stress constrained problems have a further difficulty, the stress singularity, which may prevent the algorithm to reach a feasible solution. To overcome this problem, the feasible domain is modified using a mathematical perturbation technique, the epsilon-relaxation.
其他摘要：This paper presents the problem of volume minimization of two-dimensional continuous structures with compliance and stress constraints. Problems are solved by a topology optimization technique, formulated as finding the best material distribution into the design domain. Discretizing the geometry into simpler pieces and approximating the displacement field, equilibrium equations are solved through the finite element method. A material parametrization method is used to represent the fictitious constant material distribution into each finite element. Sequential Linear Programming is used to solve the optimization problem. For both compliance and stress constrained problems, an analytical sensitivity analysis for elastic behavior is derived, and for this last problem, Von Mises equivalent stress is the failure criteria considered. A first neighborhood filter was implemented to minimize the effects of checkerboard patterns and mesh dependency, two common problems associated to topology optimization. Stress constrained problems have a further difficulty, the stress singularity, which may prevent the algorithm to reach a feasible solution. To overcome this problem, the feasible domain is modified using a mathematical perturbation technique, the epsilon-relaxation.
