多场耦合及多相材料的柔顺机构拓扑优化研究
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摘要
随着科技的发展,多场耦合在实际工程及集成化产品中的作用变得越来越显著,甚至起主导作用。在对这些工程产品进行拓扑优化设计时,单一物理场下进行的拓扑优化设计方法已不能满足实际应用,迫切需要有效的方法来解决耦合问题。本文以多场耦合拓扑优化为研究对象,对多物理场中关联性最大的热场引发的结构散热、材料性能和结构的热可靠性等拓扑优化问题进行了系统地研究,主要研究内容如下:
(1)在考虑温度效应的作用下,进行刚性结构和柔顺机构的拓扑优化设计。论证了热固耦合分析的必要性,为多场耦合的拓扑优化设计提出一种新的思路和方法。首先,对热场进行有限元分析,在本构关系中计入了热应变,用虚功原理和有限元法推导了等效节点热载荷,并将热载荷转化为体力施加给弹性场,得到了结构的耦合控制方程。然后建立了热固耦合拓扑优化模型,得到了热固耦合结构与柔顺机构最优拓扑图。最后,对比和分析了不同温度下的拓扑结果。
(2)在热固耦合的基础上,提出了一种热电耦合的多目标拓扑优化方法,设计了一种电热驱动的柔顺机构。根据焦耳定理,电场将产生等效热量,机构在热的作用下将产生热应力和热应变,从而驱动机构产生输出位移。应用顺序耦合方法进行电-热-结构多物理场耦合分析,采用比值法权衡了多个目标之间的比例关系,用移动近似算法对优化问题进行迭代求解,为微机电系统中的电-热-结构材料一体化综合设计提供了一种新的方法。
(3)提出了一种在对流换热的边界条件下进行结构散热拓扑优化设计的方法。以最小散热弱度为目标,建立了相关模型,得到了与实际应用中的热交换器非常相似的散热拓扑图,以实例论证了忽略对流换热进行的散热结构拓扑优化是不完备的。此外,在均匀温度场的基础上提出了非均匀温度场的散热拓扑优化设计,应用叠加原理将非均匀温度场等效为一个均匀温度场与多个集中热源叠加而成,从而将非均匀温度场的散热拓扑优化设计转化为一个多目标的优化设计。
(4)根据不同的目标得到了各种材料微观结构拓扑图,并设计了由不同材料构成的柔顺机构。推导了多相材料等效弹性模量、离轴刚度与整体刚度矩阵,研究了不同材料主方向的微观结构,根据不同的功能需求,得到各种不同性能的多相复合材料;并进行了多相复合材料构成的柔顺机构拓扑优化设计研究,实现输入输出成非对应关系的多功能需求,从而充分发挥多相材料的性能。
(5)基于概率可靠性理论,探讨了如何减少温度环境、几何尺寸以及作用荷载等因素的不确定性而导致的机构性能下降的问题。用可靠度指标衡量各种随机因素的不稳定性,构建了以可靠性指标为约束条件的热固耦合拓扑优化数学模型,最后对比分析了可靠性与确定性拓扑结果,证明了进行可靠性拓扑优化能找到经济与性能的最佳结合点。在此基础上,给出了一种基于密度法的等高线边界轮廓拓扑图提取方法,并采用线切割加工工艺,研制了位移反向器原型,对位移反向器的位移性能及温度效应进行了试验测试。结果表明,考虑温度效应的位移反向器的试验测试结果与理论模型基本吻合,说明了理论模型的正确性。
With the development of technology, multi-field coupling play an increasingly significant role in the engineering and integrated product, even it plays a leading role. Therefore, topology optimization design methods under a single physical field cannot meet the practical application when design these engineering products using topology optimization method. There are urgent needs for effective ways to solve the coupling problem. In this paper, topology optimization in multi-field coupling is research object, the topology optimization problems such as structure cooling, material performance and reliability induced by thermal field.
(1) Considering the effect of temperature, the topology optimization of rigid structure and compliant structure were carried out. The need for thermal-mechanical-coupling analysis was demonstrated, and a novel method is proposed for topology optimization of multi-field coupling. First, the finite element analysis on thermal field is performed; the thermal strain is included in the constitutive relations. Virtual work principle and finite element method are used to derive equivalent nodal thermal load, and the thermal loads are converted into body forces and applied to the elastic fields, and the coupled control equations of structure are obtained. The thermal- mechanical -coupling topology optimization model is built, and the optimized topology diagrams of thermal- mechanical structure and compliant structure are obtained. Finally, comparison analyses of topology results at different temperatures were carried out.
(2) On the basis of the thermal- mechanical coupling model, a multi-objective thermal-electrical-coupling topology optimization method was proposed, and a thermal-and-electrical-driven compliant mechanism was designed. According to Joule theorem, the electric field will produce the equivalent heat, the mechanism will generate thermal stress and deformation under the thermal field, and thus it drives the mechanism to obtain output displacements. Sequential coupling method is applied to perform the analysis of electric-thermal-structural-coupling multi-physics, and the ratio method is used to balance the proportional relation between multiple objectives, and the optimization problem is solved by using MMA approximation algorithm. Thus, it provides a theoretical foundation for the electricity-thermal-structure-material integrated and comprehensive design of MEMS system.
(3) A topology optimization method for structure cooling based on convection heat transfer in the boundary conditions was proposed. The optimization model is built using minimum weak degree of heat as optimized object, and the topology results of cooling structure similar to the practical heat exchanger were obtained, thus it illustrates the idea and the model proposed in the paper is correct. And examples have demonstrated that the neglect of heat convection for topology optimization is not entirely correct. In addition, the topology optimization of cooling structure under the non-uniform temperature field is proposed on the basis of uniform temperature field, and the non-uniform temperature field is treat as the superposition of a number of uniform temperature fields and concentrated heat sources by using the superposition principle, and thus the topology optimization problem of cooling structure under non-uniform temperature field is converted into a multi-objective optimal design.
(4) Topology results of a variety of material microstructure were obtained according to different objects, and the compliant mechanisms consisting of different materials were designed. The equivalent elastic modulus, off-axis stiffness and overall stiffness matrix of multiphase materials are derived, and the microstructures of main directions of different materials are studied. The multiphase composites of a variety of different properties are obtained according to different functional requirements. The topology optimization of compliant mechanisms based on multiphase composite is studied to achieve multi-functional needs of correspondence between input and output in order to maximize the performance of multiphase materials.
(5) Based on probability reliability theory, we study how to reduce the effect of uncertain of temperature environment, geometry and loading. The reliability index is used to quantitatively measure the various random uncertain factors, and the thermal-solid-coupling topology optimization model is built using the reliability index as constraint conditions. By comparing the topology results by using reliability method and deterministic one, it proved that the best combination of economy and performance point can be found by using reliability topology optimization. On the basis of the above study, we presented a method of topology extraction based on density contour boundary contour. And the displacement reverser was machined by wire cutting technology, and its displacement performance and the temperature effect was tested. The test showed the results from test are consistent one from theoretical model, and it illustrated the correctness of the theoretical model.
(1)在考虑温度效应的作用下,进行刚性结构和柔顺机构的拓扑优化设计。论证了热固耦合分析的必要性,为多场耦合的拓扑优化设计提出一种新的思路和方法。首先,对热场进行有限元分析,在本构关系中计入了热应变,用虚功原理和有限元法推导了等效节点热载荷,并将热载荷转化为体力施加给弹性场,得到了结构的耦合控制方程。然后建立了热固耦合拓扑优化模型,得到了热固耦合结构与柔顺机构最优拓扑图。最后,对比和分析了不同温度下的拓扑结果。
(2)在热固耦合的基础上,提出了一种热电耦合的多目标拓扑优化方法,设计了一种电热驱动的柔顺机构。根据焦耳定理,电场将产生等效热量,机构在热的作用下将产生热应力和热应变,从而驱动机构产生输出位移。应用顺序耦合方法进行电-热-结构多物理场耦合分析,采用比值法权衡了多个目标之间的比例关系,用移动近似算法对优化问题进行迭代求解,为微机电系统中的电-热-结构材料一体化综合设计提供了一种新的方法。
(3)提出了一种在对流换热的边界条件下进行结构散热拓扑优化设计的方法。以最小散热弱度为目标,建立了相关模型,得到了与实际应用中的热交换器非常相似的散热拓扑图,以实例论证了忽略对流换热进行的散热结构拓扑优化是不完备的。此外,在均匀温度场的基础上提出了非均匀温度场的散热拓扑优化设计,应用叠加原理将非均匀温度场等效为一个均匀温度场与多个集中热源叠加而成,从而将非均匀温度场的散热拓扑优化设计转化为一个多目标的优化设计。
(4)根据不同的目标得到了各种材料微观结构拓扑图,并设计了由不同材料构成的柔顺机构。推导了多相材料等效弹性模量、离轴刚度与整体刚度矩阵,研究了不同材料主方向的微观结构,根据不同的功能需求,得到各种不同性能的多相复合材料;并进行了多相复合材料构成的柔顺机构拓扑优化设计研究,实现输入输出成非对应关系的多功能需求,从而充分发挥多相材料的性能。
(5)基于概率可靠性理论,探讨了如何减少温度环境、几何尺寸以及作用荷载等因素的不确定性而导致的机构性能下降的问题。用可靠度指标衡量各种随机因素的不稳定性,构建了以可靠性指标为约束条件的热固耦合拓扑优化数学模型,最后对比分析了可靠性与确定性拓扑结果,证明了进行可靠性拓扑优化能找到经济与性能的最佳结合点。在此基础上,给出了一种基于密度法的等高线边界轮廓拓扑图提取方法,并采用线切割加工工艺,研制了位移反向器原型,对位移反向器的位移性能及温度效应进行了试验测试。结果表明,考虑温度效应的位移反向器的试验测试结果与理论模型基本吻合,说明了理论模型的正确性。
With the development of technology, multi-field coupling play an increasingly significant role in the engineering and integrated product, even it plays a leading role. Therefore, topology optimization design methods under a single physical field cannot meet the practical application when design these engineering products using topology optimization method. There are urgent needs for effective ways to solve the coupling problem. In this paper, topology optimization in multi-field coupling is research object, the topology optimization problems such as structure cooling, material performance and reliability induced by thermal field.
(1) Considering the effect of temperature, the topology optimization of rigid structure and compliant structure were carried out. The need for thermal-mechanical-coupling analysis was demonstrated, and a novel method is proposed for topology optimization of multi-field coupling. First, the finite element analysis on thermal field is performed; the thermal strain is included in the constitutive relations. Virtual work principle and finite element method are used to derive equivalent nodal thermal load, and the thermal loads are converted into body forces and applied to the elastic fields, and the coupled control equations of structure are obtained. The thermal- mechanical -coupling topology optimization model is built, and the optimized topology diagrams of thermal- mechanical structure and compliant structure are obtained. Finally, comparison analyses of topology results at different temperatures were carried out.
(2) On the basis of the thermal- mechanical coupling model, a multi-objective thermal-electrical-coupling topology optimization method was proposed, and a thermal-and-electrical-driven compliant mechanism was designed. According to Joule theorem, the electric field will produce the equivalent heat, the mechanism will generate thermal stress and deformation under the thermal field, and thus it drives the mechanism to obtain output displacements. Sequential coupling method is applied to perform the analysis of electric-thermal-structural-coupling multi-physics, and the ratio method is used to balance the proportional relation between multiple objectives, and the optimization problem is solved by using MMA approximation algorithm. Thus, it provides a theoretical foundation for the electricity-thermal-structure-material integrated and comprehensive design of MEMS system.
(3) A topology optimization method for structure cooling based on convection heat transfer in the boundary conditions was proposed. The optimization model is built using minimum weak degree of heat as optimized object, and the topology results of cooling structure similar to the practical heat exchanger were obtained, thus it illustrates the idea and the model proposed in the paper is correct. And examples have demonstrated that the neglect of heat convection for topology optimization is not entirely correct. In addition, the topology optimization of cooling structure under the non-uniform temperature field is proposed on the basis of uniform temperature field, and the non-uniform temperature field is treat as the superposition of a number of uniform temperature fields and concentrated heat sources by using the superposition principle, and thus the topology optimization problem of cooling structure under non-uniform temperature field is converted into a multi-objective optimal design.
(4) Topology results of a variety of material microstructure were obtained according to different objects, and the compliant mechanisms consisting of different materials were designed. The equivalent elastic modulus, off-axis stiffness and overall stiffness matrix of multiphase materials are derived, and the microstructures of main directions of different materials are studied. The multiphase composites of a variety of different properties are obtained according to different functional requirements. The topology optimization of compliant mechanisms based on multiphase composite is studied to achieve multi-functional needs of correspondence between input and output in order to maximize the performance of multiphase materials.
(5) Based on probability reliability theory, we study how to reduce the effect of uncertain of temperature environment, geometry and loading. The reliability index is used to quantitatively measure the various random uncertain factors, and the thermal-solid-coupling topology optimization model is built using the reliability index as constraint conditions. By comparing the topology results by using reliability method and deterministic one, it proved that the best combination of economy and performance point can be found by using reliability topology optimization. On the basis of the above study, we presented a method of topology extraction based on density contour boundary contour. And the displacement reverser was machined by wire cutting technology, and its displacement performance and the temperature effect was tested. The test showed the results from test are consistent one from theoretical model, and it illustrated the correctness of the theoretical model.
引文
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