Research On Continuum Structural Topology Optimization Method Based On The Feasible Domain Adjustment

Structural optimization design,lightweight materials and advanced manufacturing technology play an important role in vehicle lightweight design.Topology optimization design is the most potential structural optimization design method,which can improve the material utilization rate and reduce the weight of the structure.It is an important research topic to develop topological optimization technology for vehicle lightweight engineering.In this thesis,according to the engineering requirements of vehicle lightweight,the structural topology optimization method based on feasible domain adjustment are investigated in order to enrich and develop the structural topology optimization theory and method,focusing on the iteratve solving robustness problem of structural topology optimization and multi-load cases,multi-objective,multi-constraints,multi-phase materials and stress-constrained topology optimization design problem.It is expected to promote the development and application of vehicle lightweight technology.(1)To solve the topology optimization problem of structure volume minimization under multi-displacement constraints,an approximate binary solution method is proposed.A distribution feature of constraint displacement derivatives is investigated.By using variable displacement constraint,a new approximate optimization model with tight displacement constraint and monotonic variation feasible domain is formed.Based on the KKT condition,the design variable set is decomposed into four sub-sets to form a design variable interval-limited adaptive adjustment scheme.The approximate optimization model is solved by adopting a smooth dual algorithm.Typical numerical examples and the automobile frame optimal example show that the proposed method can effectively reduce the weight of the structure and obtain a series of topologies with clear 0/1 distribution during an optimization process.(2)To solve the topology optimization problem of structural compliance under multi-load cases,a new solution method is proposed.Based on the Rational Approximation for Material Properties(RAMP)and the Method of Moving Asymptotes(MMA),the sensitivity calculation of the structure compliance is carried out.Being referred to the bound formulation method,original multiple objective functions dealing with structural compliance under multi-load cases are transferred to multiple constraints by using a bound variable,and a novel quadratic function of the bound variable is treated as a new objective function.At the same time,being integrated with a varied volume limit scheme,a novel and equivalent approximate topology model is constructed.The approximate..optimization model is solved by adopting a smooth dual algorithm.The proposed method has a stable convergence process and good robustness.It is concluded from given examples that the proposed method is higher efficient for generating a same optimal topology,or may obtain a more optimal topology than the existed methods.At the same time,the proposed method can also solve the topology optimization problem with ill-load cases.(3)For the multi-phase material structural compliance topology optimization problem and the existence of multiple local optimization solutions,a new solution method is proposed,and the ability of the proposed method to get multiple local optimization solutions and to find a better optimization solution are investigated.Based on the Rational Approximation of Material Properties(RAMP)model,the varied volume limit scheme is introduced to construct a model for the multi-phase material structural topology optimization problem and its approximate model.A modified alternating active-phase scheme is proposed,in which the multi-phase material topology optimization problem is divided into some two-phase topology optimization sub-problems,which may include two real material volume constraints.And the sub-problems are solved by the smooth dual algorithm.Compared with the existed methods,the proposed method can obtain a different local optimal topology starting from a different initial topology,and can also obtain a better local optimal multi-phase material topology by using various initial topologies.And the proposed work gives a valuable idea and a multiple design approach to solve the multi-material topology optimization problem.(4)To solve the topology optimization problem of structural volume minimization under stress constraint,a new method based on stress gradient and stress constraints aggregation functions is proposed.Based on the Rational Approximation of Material Properties(RAMP)and the trust region scheme,a new equivalent approximation optimization model is constructed by using the qp stress relaxation approach,stress gradient aggregation function,stress-constrained aggregation function and weighting aggregation stress constraint functions.A set of stress quadratic explicit approximations are constructed,based on stress sensitivities and the Method of Moving Asymptotes,and the original aggregation functions are substituted by the approximate expansion expressions.And,being integrated with a varied stress constraint limit,an equivalent approximate topology model is constructed.The second derivative of the constraint function is added to the objective function by using the Lagrange multiplier calculated by the previous iteration step to construct an equivalent approximate quadratic programming model,and the smooth dual algorithm is used to solve it.Numerical examples show that the proposed method can better solve the stress singularity,effectively control the stress concentration and obtain better structural topology.