Stress-constrained topology optimization using the velocity field level set method

This paper proposes a stress-constrained structural topology optimization method in the velocity field level set framework. To avoid the strength failure in structures, the stress should meet certain strength criteria at all material points. This point-wise constraint brings great difficulty to topology optimization. Instead of using the traditional aggregation scheme, we propose a new stress constraint in the single domain integral form, which is mathematically equivalent to the point-wise stress limitation and enables the precise stress control throughout the entire material domain without introducing numerous constraints. Its simple expression with relatively low non-linearity facilitates the optimization formulation, the sensitivity analysis and the numerical implementation. Here, the velocity field level set method is used for the stress-constraint topology optimization. The implicit material representation by the level set model is combined with the body-fitted mesh, which provides a clear and smooth material boundary with high numerical calculation accuracy for the stress and the sensitivity. Moreover, the velocity field level set method maps the original boundary variation-based optimization problem from the functional design space into a finite-dimensional one by introducing the velocity field design variables. Thus, it allows using of the general mathematical optimization algorithms in the level set model, which provides an efficient and steady way to deal with the stress-constrained optimization problems.