Topology Optimization And Response Analysis Of Elastic-plastic Structures Under Impact Load

Topology optimization is an effective measure to realize the design of lightweight structure.The mechanical response of a structure under impact load is one of the standards to evaluate its performance,but most of the topology optimization is still under the static load rather than dynamic load.The nonlinear effects of load and material considered in structural optimization design under the impact load increase the difficulty of structural analysis and make it complicated to calculate the dynamic response.This paper introduces the theory of Equivalent Static Load Method(ESL)and Bi-directional Evolutionary Structural Optimization(BESO).Based on these methods,the article overcomes the difficulties which are mentioned above,and then the topology optimization under impact load is realized.The main tasks were as follows:(1)Taking the minimum compliance as objective and the volume fraction as the constraint condition,the optimization procedure of soft-kill BESO method integrated at Abaqus-Matlab platform was derived carefully.The optimization examples with three types of different initial models were given,which were two-dimensional model with its mesh size of 0.4mm,twodimensional model with slot hole and three-dimensional model,respectively.The result shows that: evolutionary histories of volume fraction and compliance of these conditions existed in iteration process are smooth,which proves the validity and rationality of topology optimization algorithm realized in double platform.(2)The basic theory and implementation flow of construction of static load based on inertia forces were introduced and the elastic structure under rigid body impact with initial velocity of 50m/s was optimized.Under the rigid body impact with different initial velocity,the maximum deflections at the center point of upper panel and lower panel of impact load optimization configuration were compared with static load optimization configuration and monolithic beam.The results show that no matter what initial velocity is,the maximum deflection at the center point of upper panel of dynamic load optimization configuration is smaller than other structures.The maximum deflection at the center point of lower panel of dynamic load optimization configuration is the smallest in all structures when the initial velocity used in optimization is not reached.When the initial velocity used in optimization is arrived,the maximum deflection at the center point of lower panel of impact load optimization configuration is larger than static load optimization configuration.(3)The hard-kill BESO method and the equivalent static load method were extended to the multi-objective optimization problem.The evaluation function of objectives was established based on linear weighted method,and the topology optimization for periodic porous sandwich structure under impact load was realized,with its maximum energy absorption and minimum volume fraction as objective functions and displacement as constraint.The effects of the cell numbers along transverse and longitudinal direction and the setting value of displacement constraint were studied.The finite element models of sandwich structure with optimum core layer,trapezoidal core layer,rectangular core layer and random voronoi core layer were established.The deformation failure modes of sandwich structures with different core layer under the impact load were studied.The mechanical properties of above structures under the rigid body impact with different initial velocities and impulse loads were compared.The results show that: considering the deflection at the center point of upper panel and lower panel,specific energy absorption,the ratio of energy absorption of core layer and mean impact force comprehensively,sandwich structure with optimum core layer has better energy absorption capability and anti-impact performance than other structures.(4)The hard-kill BESO method and the equivalent static load method were extended to the multi-constraint optimization problem.Based on Karush-Kuhn-Tucker conditions(KKT),the connection between objective function and constraints was established by introducing the Lagrange multiplier.The topology optimization for elastic-plastic structure under impact load was realized,with its minimum volume fraction as objective functions and displacement and specific energy absorption as constraints.The deformation failure modes of impact load optimization configuration,static load optimization configuration and monolithic beam under the impact load were studied.The mechanical properties of above structures under the rigid body impact with different initial velocities were compared.The results show that: the load condition used in optimization should be selected reasonably in order to obtain the optimum structure with better energy absorption and anti-impact performance in prescribed application range.