Optimal structural topology design using the homogenization method with multiple constraints

In applications of the homogenization method for optimal structural topology design the solution is obtained by solving the optimality conditions directly. This reduces the computational burden by taking advantage of closed-form solutions but it restricts the optimization model to having only one constraint. The article develops a generalized class of convex approximation methods for mathematical programming that can be used for the optimal topology homogenization problem with multiple constraints included in the model, without substantial reduction in computational efficiency. A richer class of design models can be then addressed using the homogenization method. Design examples illustrate the performance of the proposed solution strategy.