Exploration of Existence of Optimal Solution for Truss Dynamical Topology Optimization

In this paper, under the condition of unchanged topology configuration of the truss, the theorem of the extremum existence of the natural frequency, which is the key constraint for the dynamic topology optimization, is demonstrated. Then the basic theory of solution existence for dynamic topology optimization of truss is clarfied from two aspects, when the design variables (section areas)are continuous and their bound are not imposed, if there is no frequency constraint, the optimal solution always exists for a given optimization problem and contrarily, when the frequency constraint is considered, the frequency will become the key constraint and also the existence of solution will be changed by the topology alteration. The numerical examples show that the proposed theory is correct and effective.