基于SIMP法的变刚度结构拓扑优化研究

Research on Topology Optimization of Variable Stiffness Structures Based on SIMP Method

基于固体各向同性材料惩罚模型(Solid isotropic material with penalization,SIMP)是一种常用的拓扑优化模型,因其计算效率较高而应用广泛。在工程实际中,采用单一材料的结构往往难以满足较好地综合性能,而功能梯度材料结构能充分发挥其组成的各相材料的优点,在满足轻量化、高强度的要求的同时,达到良好的经济效益,在工程上应用广泛。然而,传统的SIMP法由于其预先设定材料属性,对功能梯度材料变刚度的结构体拓扑优化稍显不足,本文提出了一种基于有限元素法,采用功能梯度材料的变刚度改进方法,采用改进的SIMP法进行优化问题的求解,使得变刚度结构经过优化后其强度得到提高的同时,充分发挥功能梯度材料其各相组成材料的特性,合理分配材料使用进而降低成本。最后在MATLAB环境中以悬臂梁结构为算例模型验证了该方法的可行性,具有十分广阔的应用前景。

Solid isotropic material with penalization(SIMP)is a topology optimization model that used commonly,which is widely used because of its high computational efficiency.In engineering practice,the structure using a single material is often difficult to meet good comprehensive performance,while the functionally graded material structure can fully take advantage of its composition of each phase material,while meeting the requirements of light weight and high strength,achieve good economic benefits are widely used in engineering.However,due to the preset material properties of the traditional SIMP method,the topology optimization of the structure with variable stiffness of the functionally graded material is slightly insufficient.The improved SIMP method is used to solve the optimization problem.While the strength of the variable stiffness structure is improved,the characteristics of the phase composition materials of the functionally graded materials are fully utilized,and the material is allocated reasonably to reduce the cost.Finally,the feasibility of the method is verified by using a cantilever beam structure as a model in the MATLAB environment,and it has a very broad application prospect.