Structural Optimization Method Of Structure Subject To Impact Loads

The optimization of structures subject to impact attracted the widespread attention of researchers and engineers. For many structures, the response under impact will directly affect its performance. Structural optimization can effectively improve the structural performance under impact. However, in comparison with other structural optimization problems, the workes of structural optimization under impact are relatively less. This is because that, the structural optimization under impact often needs additional consider time factor and nonlinear effects, such as material nonlinearity and geometric nonlinearity. These troubles make the structural analysis difficult and time-consuming, and also make sensitivity difficult to calculate. Thus, optimization of structures subject to impact is one of the most challenging optimization problems.This paper works on the optimization of structures subject to impact and proposed several methods for overcoming the difficulties of structure optimization under impact as mentioned in previous. We consider two kinds of structures optimization under impact in this paper. One is the minimization of residual vibration response of structures subject to impact, and the other is crashworthiness topology optimization.In the research of minimization of residual vibration response of structures subject to impact, a quadratic integral function is used to elevate the residual vibration response, which can globally measure the structural performance. However, the integral function needs time-consuming iterative calculation. By Lyapunov’s second method, the quadratic integral function can be simplified into matrix forms and the calculation of residual vibration response can be also simplified greatly. If the initial excitations of residual vibration stage are dependent on design variables, the calculation of sensitivity of residual vibration response with respect to design variables will become difficult. Thus, in this paper, the structural optimization problem of minimization of residual vibration response of structures subject to impact are divided into two kinds of the structural optimization problem, one is for the residual vibration generate by initial excitations and the other is for the residual vibration generate by impact load.Firstly, minimization of residual vibration response of structures subject to initial excitations is considered. In this work, an adjoint sensitivity analysis scheme is proposed to calculate the sensitivities of residual vibration response with respect to design variables. By the adjoint method, no matter how many design variables in the optimization problem, only two Lyapunov equations need to be solved for obtaining all sensitivities. Thus, by the Lyapunov equations and adjoint sensitivity analysis schemes, minimization of residual vibration response of structures subject to initial excitations can be solved efficiently. Based on the proposed methods, topology optimization is used to considered optimal distributions of dampers (or damped springs) and layout of material in plate structures for minimization of residual vibration.Secondly, minimization of residual vibration response of structure subject impact is considered. For impact, the initial excitations of residual vibration are dependent on design variables. For this case, the second adjoint sensitivity analysis scheme is proposed, which combined the first method proposed in previous and the method proposed by Arora. The second method can obtain high accuracy sensitivities when initial excitations of residual vibration dependent on design variables, which greatly broadens the scope of application of proposed methods. By the second method, this paper studies the optimal distributions of damping material on plate structure subject to impact.Next, the paper considers minimization of residual vibration response of the free-free structure. Lyapunov method can not be applied to the structure which is not fully constrained, due to the singularity of the stiffness matrix of free structure makes the Lyapunov equation do not have the unique solution. In this work, two methods are proposed, which can eliminate the singularity of stiffness matrix without changing the elastic modes of the structure. By the proposed method, the residual vibration of free structure can be elevated by Lyapunov equation and the sensitivity analysis schemes proposed in previous can also be applied. In the research, a single resonators microstructure system is considered, which is equivalent to a lumped mass with negative mass. Optimal parameters and distributions of the single resonators system for minimization of residual vibration response are studied by structural optimization.Finally, we study the structural crashworthiness topology optimization problem. Crashworthiness problems often contain a variety of nonlinear effects, which makes crashworthiness optimization very difficult, especially crashworthiness topology optimization. For obtaining the topologically optimized design of crashworthiness, a hybrid method is proposed, which combines the equivalent static load optimization method and hybrid cellular automata method. The proposed hybrid method transforms the nonlinear dynamic optimization problem to nonlinear static optimization by equivalent static analysis based on inertia forces and revised the nonlinear static analysis model in optimization process by a double iterative algorithm. In the inner loop, the hybrid cellular automata method is used to update the design variables of the nonlinear static optimization problem. In the outer loop, the nonlinear dynamic analysis is performed to test the performance of optimized design and update the equivalent static analysis model. By numerical example, the proposed hybrid method is compared with hybrid cellular automata method. Results show that these two methods obtain very similar results, but the CPU time of the former is much less than the later. At last, the study considers crashworthiness topological optimized design of a vehicle body model.