Structural topology optimization under inertial loads

Structural topology design optimization under inertial loads is studied in the paper. Based on the sensitivity scheme of structural compliance, the non-monotonous feature of the objective function is described. Due to the design-depedent effects of loads and element stiffness, various material penalization models are investigated to show their influences on the optimization results and iteration processes. Subsequently, an improved RAMP model with variable parameter is proposed and validated. For the problem with inequality volume constraint under self-weight loading, the optimal solution is obtained in stable convergence way for the first time, also to approach the theoretic solution associated with a void structure without material. Theoretical and numerical results showed that the compliance sensitivity remains no longer to be negative due to the the design-dependent effect of inertial loads. This means that the objective function is non-monotonous. As a result, the inequality volume constraint is not always active at the optimum solution. In other words, less material may lead to a stiffer structure for an optimum material layout. Besides, it is shown that the integration of a proper RAMP model with the BESO method can improve greatly the result so that both BESO and MP methods become consistent for self-weight design problem whereas previously existing optimization results obtained by BESO and MP methods are quite different.