【作者】 何杰；

【导师】 任毅如； 钱战森；

【作者基本信息】 湖南大学 ， 机械工程（专业学位）， 2019， 硕士

【摘要】 目前,拓扑优化已经广泛地应用于汽车、船舶、航空航天、机械装备、建筑结构等工程领域,通过节省材料或者提高结构性能的方式为我们创造了巨大的经济效益。随着人们需求的提升,固定载荷作用下的结构拓扑优化和单一材料的结构拓扑优化已经无法满足需求人们日益苛刻的需求。因此,设计依赖载荷作用下的拓扑优化和多材料拓扑优化发展了起来。对于设计依赖载荷作用下的拓扑优化,已经有惯性载荷、表面压力、热载荷、电磁力等设计依赖载荷作用下的结构拓扑优化方面的研究。对于多材料拓扑优化,也已经有相对密度法、水平集法、ICM独立连续映射法、块坐标下降法等方法来解决多材料的结构拓扑优化问题。然而,设计依赖载荷作用下的多材料结构拓扑优化的研究非常少,国内外目前还没有惯性载荷作用下的多材料结构拓扑优化方面的研究。工况与材料是结构的两个重要维度,惯性载荷作用下的结构拓扑优化需要对应的优化方法,多材料的结构拓扑优化也需要对应的优化方法,惯性载荷作用下的多材料结构拓扑优化更需要一种特殊的优化方法来同时解决拓扑优化的设计依赖载荷的问题和多材料的问题。本文致力于研究惯性载荷作用下的多材料结构拓扑优化方法。以结构刚度最大为目标,以结构质量为约束先后研究了惯性载荷作用下的单材料、多材料结构拓扑优化方法,并用算例验证方法的正确性。本文主要从以下几个方面进行研究:1.提出基于导重法和块坐标下降法进行自重载荷作用下的多材料结构拓扑优化方法。建立对应的数学模型,用块坐标下降法分解多材料优化问题,然后用导重法求解自重载荷作用下的块变量拓扑优化问题,最后用简支梁、悬臂梁、L型梁、挖孔结构等进行数值验证与比较分析。2.提出离心载荷作用下以及离心载荷与惯性载荷同时作用下的多材料结构拓扑优化方法。建立对应的数学模型,用块坐标下降法分解多材料优化问题,然后用导重法求解离心载荷作用下或者离心力与重力同时作用下的块变量拓扑优化问题,最后用悬臂梁模型进行数值验证与比较分析。3.提出RAMP插值模型和施加质量点的方法解决中间密度单元和模糊结构的问题。用有理近似插值模型RAMP替换传统的SIMP插值模型来表达密度与弹性模量间假定的非线性函数关系,很好地解决了优化结果中存在大量中间密度单元的问题。对于悬臂梁的优化结果中末端存在模糊结构的问题,提出施加质量点的方法改善优化效果。更多还原

【Abstract】 At present,topology optimization has been widely used in automotive,marine,aerospace,mechanical equipment,building structures and other engineering fields,creating huge economic benefits by saving materials or improving structural performance.As people’s demands increase,structural topology optimization under fixed loads and structural topology optimization of single materials have been unable to meet the increasingly demanding needs of people.Therefore,topology optimization and multi-material topology optimization under the design-dependent load have been developed.For the topology optimization under the design-dependent load,there are already researches on structural topology optimization under the influence of design load such as inertial load,surface pressure,thermal load and electromagnetic force.For multi-material topology optimization,there are also methods such as relative density method,level set method,ICM independent continuous mapping method and block coordinate descent method to solve the problem of structural topology optimization of multi-materials.However,there are very few studies on topology optimization of multi-material structures under design-dependent loads.At present,there is no research on topology optimization of multi-material structures under inertial loads.Working conditions and materials are two important dimensions of structure.Structural topology optimization under inertial loads requires corresponding optimization methods.Structural optimization of multi-materials also requires corresponding optimization methods.Multi-material structural topology optimization under inertial loads is more A special optimization method is needed to solve both the topology-optimized design-dependent load problem and the multi-material problem.This thesis is devoted to the study of multi-material structure topology optimization method under the action of inertial load.Taking the maximum structural stiffness as the goal and the structural quality as the constraint,the single material and multi-material structure topology optimization methods under inertial load are studied successively,and the correctness of the method is verified by an example.This paper mainly studies from the following aspects:1.A multi-material structure topology optimization method based on guide-weight method and block coordinate descent method under self-weight load is proposed.The corresponding mathematical model is established,and the multi-material optimization problem is decomposed by the block coordinate descent method.Then the guide-weight method is used to solve the block variable topologyoptimization problem under self-weight load.Finally,the simply supported beam,cantilever beam,L-beam and digging structure are used for numerical verification and comparative analysis.2.A multi-material structure topology optimization method under the action of centrifugal load and centrifugal load and inertial load is proposed.The corresponding mathematical model is established,and the multi-material optimization problem is decomposed by the block coordinate descent method.Then the guide-weight method is used to solve the block variable topology optimization problem under the action of centrifugal load or centrifugal force and gravity.Finally,the cantilever beam model is used for numerical verification and comparative analysis.3.The RAMP interpolation model and the method of applying mass points are developed to solve the problem of intermediate density element and fuzzy structure.The rational approximation interpolation model RAMP is used to replace the traditional SIMP interpolation model to express the nonlinear function relationship between density and elastic modulus,which solves the problem of a large number of intermediate density units in the optimization results.For the problem that the fuzzy structure exists at the end of the cantilever beam,the method of applying the mass point is proposed to improve the optimization effect.更多还原