Research On Stress-penalty-based Structural Topology Optimization Methods

With the development of science and technology,the structural optimization has been widely used in different areas,such as aerospace and automatic industry.As a method to achieve the structure with the optimal performances by adding,removing and redistributing materials,topology optimization can be conducted at the concept stage where the information of structural geometry and topology are unknown.Most of the works of topology optimization focus on the stiffness-based topology optimization.In the practical engineering,however,the stiffness is not the only design criteria.The strength should be also considered,and the requirement of strength is achieved by accomplishing the stress constraint.To deal with the numerical problems of the existing methods for the stress-constrained topology optimization,such as low computational efficiency and instability,this paper proposes some effective methods and uses them in the stress-constrained design of minimizing the structural volume and compliance,the stress-constrained multi-material design of continuum structures and the multi-material design of compliant mechanisms with stress constraints.The main research works of this paper are shown as follows:Firstly,the stress-penalty-based topology optimization model is proposed.In order to solve the stress-constrained topology optimization problem,the penalty of the stress is developed to control the local stress level,and an adaptive adjusting scheme of the stress penalty factor is proposed to improve its control ability.Then the parametric level set method is applied to establish the topology optimization model.Based on the shape derivative,the sensitivity analysis is conducted,and the optimization criterion method is used to solve the problem.Numerical examples are presented to illustrate the validity and effectiveness of the proposed model.Secondly,a method based on adaptive volume constraint and stress penalty is proposed.According to this method,the stress-constrained volume and compliance minimization topology optimization problem is transformed into a stress-penalty-based compliance minimization problem and a volume-decision problem.To solve the volume-decision problem,a combination scheme of the interval search and local search is proposed.Numerical examples are used to test the proposed method.Thirdly,the stress-penalty-based multi-material topology optimization method of continuum structure is proposed.The multi-material level set topology description model is adopted to describe the structural topologies,and the stiffness interpolation and separable stress interpolation schemes are provided for elastic stiffness and stress evaluation,respectively.With the parametric level set method,the stress-penalty-based multi-material optimization model of continuum structure is given.Two stress-constrained multi-material topology optimization problems are investigated,i.e.,the minimum compliance problem and the minimum global measure of stress problem.The sensitivity analysis is carried out,and the optimization criterion method is applied to solve the problems.Numerical examples are provided to demonstrate the applications of the method.Fourthly,a stress-penalty-based multi-material topology optimization method of compliant mechanisms is proposed.The weighted sum method is used to deal with the multi-objective optimization of the output displacement and compliance of compliant mechanisms.The penalty of stresses is considered to control the local stress level in different materials.The stress-penalty-based multi-material topology optimization model of compliant mechanisms is constructed.The sensitivity analysis is conducted,and the optimization criterion method is applied.Applications of the method are demonstrated by numerical examples.Finally,the conclusion of the paper and prospect of the research are given.