Applications Of Topology Optimization In Structures And Compliance Mechanisms

Structural optimization is to replace traditional design method with systematic and target-oriented mathematical programming method to obtain lower cost and better performance structures under certain constraints.Structural optimization is divided into three broad categories: size optimization,shape optimization and topology optimization,among which topology optimization is the research focus of nowadays.Topology optimization is to find the structural optimal topology configuration under the constraints of limited materials.At present,many methods have been developed for topology optimization,among which the variable density topology optimization method is widely used due to its simple concept and easy programming.Based on the variable density method,the application of topology optimization in compliance mechanisms,heat conduction structures and the load sickness problems possibly encountered in structural topology optimization are studied,the main contents of this paper are as follows:(1)Introduce the common methods of topology optimization,the interpolation models and optimization algorithms commonly used in variable density method.This paper also introduces the numerical instability and the corresponding solutions,as well as load sickness problems and the solutions in literatures.(Chapter 2)(2)Introduce a density interpolation model,namely SR interpolation model,which can balance the advantages of SIMP(Solid Isotropic Microstructures with Penalization)model and RAMP(Rational Approximation of Materia1 Properties)model.The SR interpolation model is modified by referring to the measures to avoid matrix singularity of the SIMP model and then extended to the field of compliant mechanisms and heat conduction structures.In addition,it is pointed out that because the value of the objective function calculated by different interpolation models for the same topology configuration varies greatly,directly comparing the value of the objective function calculated by each model is meaningless.Therefore,the concept of equivalent objective function is proposed to overcome it.Both two-dimensional and three-dimensional examples have been presented to show that the modified SR model is suitable for the application of compliant mechanisms and heat conduction problems.(Chapter 3 and Chapter 4)(3)Introduce the "load sickness" problem,which occurs when there is huge difference in values of the maximum load and the minimum load of the structure.The "load sickness" will cause the transfer path of the small load unclear or even disappearing completely.On the basis of summarizing the existing methods,a modified hierarchical sensitivity filtering optimization strategy is proposed for load sickness problems.By introducing the structural strain energy as the weighting coefficient,the dependence of the coefficient values on a specific problem is avoided.And by adopting different filtering radius to filter the elements on the path of large and small load respectively,the results are more accordant with the actual loading condition.The effectiveness and efficiency of this method are verified by several examples.(Chapter 5)...