Study On Topogy Optimization Design Of Continuum Structure Based On ICM Method

Structural optimization design replaces the traditional design by means of systematic and target-oriented process and approaches in order to make the structural materials more economic and the stress distribution more reasonable.Topology optimization,the high level of structural optimization,is dedicated to improving the structural performance and reducing the weight of the structure and thus brings huge economic benefits by means of enhancing the topological structure.In recent decades,topology optimization has gained rapid development and has been widely applied in construction,machinery,aviation,aerospace,marine engineering and shipbuilding,etc.It is now the most challenging research subject in the field of structural optimization.In terms of subjects,the topology optimization can be divided into discrete topology optimization and continuum topology optimization.Compared to discrete topology optimization,the continuum topology optimization problem is a more difficult issue in the field of structural optimization.Therefore,it is of great significance and promising to carry out researches on it.Most of the conventional continuum topology optimizations are based on the minimum degree of compliant,constrained by its volume.However,in practical construction,it is necessary to meet the requirements of strength and stiffness of engineering structures.Therefore,it is of practical significance to research the optimization of the minimum weight of the continuum structure under the constraint of stress and displacement.In this paper,the continuum structure is taken as the subject of study.Based on the topology optimization of ICM(Independent-Continuous-Mapping),a topology optimization model of continuum structure under multi-conditions is established with the minimum weight as the target,separately constrained by the stress and displacement as well as jointly constrained by both of stress and displacement.Secondly,this paper makes full use of the strong capability of ANSYS finite element calculation,the flexibility of MATLAB programming and its powerful toolbox so as to improve computational efficiency.Based on MATLAB and ANSYS co-simulation method,this paper focuses on applying ICM topological optimization algorithm to practical engineering design optimization,which provides a more mature technology foundation for the design optimization of similar engineering structures.In this paper,the relevant theories and applications are thoroughly and systematically researched as follows:(1)The establishment,solution and application of topology optimization model of continuum structure under the constraint of stress are carried out.A new iterative convergence criterion is proposed to improve the ICM method.Based on the improved solution,the topology optimization of continuum structure constrained by stress with the minimum weight as the target under multi-conditions is worked out.With calculations and analysis on two and three dimensional numerical examples,radius filter selection and topology design under multi-working conditions are discussed.(2)Modeling,solution and application of topology optimization of continuum structure under the constraint of displacement are carried out.Based on Moore theorem,the method of transforming the displacement constraint to the explicit constraint of design variable is proposed to greatly improve calculation efficiency.Then,the topology optimization model under the constraint of displacement is derived.This model is translate into dual problem by dual programming,and the dual objective function is transformed into quadratic programming problem,which is solved by the algorithm of sequential quadratic programming.This paper discusses the selection of filter radius and multi-condition topology design by two dimensional numerical examples.Finally,the convergence and feasibility of ICM solution are further verified by three-dimensional examples.(3)The establishment,solution and application of the topology optimization model of continuum structure under the joint constraint of stress and displacement are carried out.Firstly,the stress constraint is proposed to be transformed into overall strain energy constraint in order to overcome the sensitivity analysis of stress constraint as well as the difficulty of working out the huge amount of calculation.The strain energy constraint and displacement constraint are non-dimensionalized to reduce the calculation difference between values derived from magnitude of different physical quantities so as to establish the model that contains two types of non-dimensional constraints.Then the model ist ranslate into dual programming model,which is solved by the algorithm of sequential quadratic programming.The examples of two dimensional and three dimensional show the effects of different filter functions.The different methods of solving the numerical instability are also discussed.(4)With MATLAB and ANSYS as co-simulation development platforms,this study uses APDL programming language,adopts ICM algorithm and conducts topological optimization design of practical engineering structures.The results of numerical examples indicate that optimized results meet the stress and displacement need in practical engineering.In addition,the optimization greatly reduces the weight of the structure and saves cost,which provides technical support for the topological optimization design of more complex practical engineering structures.