Topology Optimization Of Structure And Cellular Microstructure With Respect To Dynamic Stress Response Under Random Excitations

The structures in aerospace engineering are developing toward the characteristics of precise and lightening,and subjected to increasingly harsh vibration environments.Traditionally,most works were focused on the stiffness problems under dynamic loads,such as displacement and complaisance.While few works has been devoted to the strength design problems,leading to the restriction of the topology optimization in the application of engineering design.In order to solve the strength requirement of lightweight design in engineering application,the topology optimization methods for typical structures considering dynamic stress requirements under random excitations are studied in this paper.The main achievements and contributions of this paper are as follows:(1)A methodology for maximizing dynamic stress response reliability of continuum structures involving multi-phase materials is established.The topology optimization model is built based on a material interpolation scheme with multiple materials.The objective function is to maximize the dynamic stress response reliability index subject to volume constraints on multi-phase materials.To solve the defined topology optimization problems,the sensitivity of the dynamic stress response reliability with respect to the design variables is derived for updating the structural topology.Subsequently,an optimization procedure based on the bi-directional evolutionary structural optimization(BESO)method is developed.Finally,several numerical examples are presented to demonstrate the effectiveness of the proposed approach.(2)A methodology for the topology optimization of continuum structures subject to dynamic stress response constraints under random excitations is proposed.The topology optimization model is built based on the rational approximation for material properties(RAMP),with the structural weight as the objective function,and structural dynamic stress response constraints.In order to greatly reduce the computational cost of dynamic stress responses,the P-norm aggregation function is adopted to replace the dynamic stress response constraints.To solve the defined topology optimization problem,a method with varying dynamic stress response limits is presented,and the sensitivity of the equivalent dynamic stress response constraints with respect to the reciprocal design variables is derived so as to form the explicit approximate functions for structural equivalent dynamic stress response constraints.Then,based on dual theory,an algorithm by using nonlinear programming method with simple trust regions is introduced to solve the optimization problem.Finally,the results of several numerical examples are given to demonstrate the validity and effectiveness of the proposed approach.(3)A new layout optimization method is proposed to consider high-cycle dynamic fatigue constraints which are caused by periodic random dynamic loads.Being incorporated with the rational approximation for material properties(RAMP),the optimization model is built,where the objective function is the structural weight,and the dynamic fatigue failure constraints are applied in the structure.According to the Crossland’s criterion,the dynamic fatigue constraints can be formulated by the peak value of the period fluctuating dynamic stress that never exceed the threshold.Then,the Kreisselmeier–Steinhauser(KS)aggregation function is introduced to reduce the number of dynamic fatigue failure constraints.Moreover,a constraint-limit-variant method is adopted to obtain stable convergent topologies.The sensitivity of the dynamic fatigue constraints with respect to the design variables is derived so as to form the approximate functions for the dynamic fatigue constraint functions.Finally,based on the sensitivity and dual theory,the defined optimization problem is solved.The results of several numerical examples are given to demonstrate the validity and effectiveness of the proposed approach.(4)A concurrent topology optimization method of macrostructural material distribution and periodic microstructure considering dynamic stress response under random excitations is proposed.The optimization model is built to minimize the dynamic stress response of the macro structure subject to volume constraints in both macrostructure and microstructure.To ensure the safety of the macrostructure,a new relaxation method is put forward to establish a relationship between the dynamic stress limit and the mechanical properties of microstructure.The sensitivities of the dynamic stress response with respect to the design variables in two scales,i.e.,macro and micro scales,are derived.Then,the aforementioned optimization problem is solved by the BESO method.Finally,several numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method.