Study On Structural Optimization And Its Application Based On Plastic Limit And Shakedown Analysis

The direct method of plastic limit and shakedown analysis can be used to obtain the non-failure external load region where the load bearing is greater than the elastic limit and less than the plastic limit,without considering the loading history,which allows the structure to be further lightened or optimized for design loads.Combining it with dimensional optimization can be a good solution to solve the parameter optimization interval considering structural fatigue under complex loading conditions;its combination with topology optimization method can make the spatial distribution of strength margin of structural "redundancy" controlled between safety and finite mass to achieve higher structural light weighting.Therefore,the main research work of this thesis is:(1)Based on the plastic limit and shakedown analysis,a characterization method of structural strength margins under dual loads considering the kinematic hardening characteristics of the structure is established.This chapter firstly solves the problem of reflecting both alternating plastic failure and incremental failure under the improved numerical solution framework of plastic limit shakedown analysis,and realizes the solution under two independent loads.Based on the above two algorithms,a strength margin method is proposed to characterize the strength margin of the final configuration during the iterative process of topology optimization and its final configuration,and the shakedown strength margin of the final configuration with the maximum stiffness as the goal is analyzed and verified by a three-dimensional Michell cantilever beam as an example.(2)A multi-parameter joint optimization method based on plastic limit and shakedown analysis is proposed.For the structural size and parameter optimization problems,two types of problems are established: optimal design of structural parameters in the optimal shakedown domain under mass constraint,and design of lightweight parameters of the structure under shakedown strength constraint.Due to the unknown concavity of the optimization problem,a genetic algorithm is introduced to find the optimal global space,and a joint genetic-internal point hybrid algorithm is used to solve the problem.The established multi-parameter double-layer nested optimization algorithm achieves the solution of the above optimization problems,while taking into account the local search advantage of the interior point method and the global search capability of the genetic algorithm.A standard load test calibration analysis model of the cast aluminum beam is used to obtain the structural dimension’s results of its shakedown optimization in complex and unknown rail line load conditions.(3)A joint approximation method of combining plastic limit/shakedown analysis and topology optimization is proposed.The lower shakedown limit theorem is integrated into the topology optimization framework,and the ’effective’ and ’ineffective’ elements in the topology optimization are redefined by the shakedown strength,and the influence of the self-equilibrium residual stress field is considered at the element level,and the traditional elastic equivalent effect is replaced by the total shakedown stress.The results of the threedimensional L-shaped bracket show that after the 50% weight reduction,the approximation of the maximum value of the total shakedown stress only increases 17.20%compared with the initial value,and by compared with the topological configuration obtained by the stiffness and equivalent elastic stress,the configuration designed by the total shakedown stress is higher in the shakedown limit.The results are 2.01% and 9.82%higher in the shakedown limits,respectively,and the design results of the total shakedown stress level indicate that a 2.01% increase in the shakedown strength can be obtained at the expense of 2.24% of the structural stiffness.(4)Light-weight optimization design and analysis of metal airtight module.The structural optimization method under the two types of problems built above is applied to the design of a manned air-tight cabin of a spacecraft.Different structural optimization methods were selected for the different types of problems applicable to the three regions:top part of the docking frame,the connection part between cabin wall panels and the docking frame and the connection frame.The results show that the elastic limit,shakedown limit and plastic limit of the top of the docking frame sub-model are improved by 39.3%,37.77% and 37.77%,respectively,compared with the initial design,while these three parameters are-14.45%,+35.80% and +47.48% for the sub-model of the connection part between cabin wall panels and the docking frame;compared with the topology optimization results based on the elastic equivalent stress,for sub-model of top of the docking frame,the elastic limit,shakedown limit and the plastic limit increased by14.71%,13.60% and 13.60% respectively,for sub-model of the connection part between cabin wall panels and the docking frame,the data is +3.81%,+3.81% and +13.15%;the re-evaluation of the overall optimization of the airtight module shows that after the weight reduction of 16.15%,the elastic limit,shakedown limit and the plastic limit are sacrificed by 9.23%,8.46% and 1.54%,respectively,and the shakedown limit is still greater than the actual load bearing by 19%,which means the structure is still in the non-failing external load region.