Optimality criteria-based topology optimization of a bi-material model for acoustic–structural coupled systems

This article investigates topology optimization of a bi-material model for acoustic–structural coupled systems. The design variables are volume fractions of inclusion material in a bi-material model constructed by the microstructure-based design domain method (MDDM). The design objective is the minimization of sound pressure level (SPL) in an interior acoustic medium. Sensitivities of SPL with respect to topological design variables are derived concretely by the adjoint method. A relaxed form of optimality criteria (OC) is developed for solving the acoustic–structural coupled optimization problem to find the optimum bi-material distribution. Based on OC and the adjoint method, a topology optimization method to deal with large calculations in acoustic–structural coupled problems is proposed. Numerical examples are given to illustrate the applications of topology optimization for a bi-material plate under a low single-frequency excitation and an aerospace structure under a low frequency-band excitation, and to prove the efficiency of the adjoint method and the relaxed form of OC.     

Compliant mechanism design with non-linear materials using topology optimization

In this paper, compliant mechanism design with non-linear materials using topology optimization is presented. A general displacement functional with non-linear material model is used in the topology optimization formulation. Sensitivity analysis of this displacement functional is derived from the adjoint method. Optimal compliant mechanism examples for maximizing the mechanical advantage are presented and the effect of non-linear material on the optimal design are considered.     

Definition of the kinetic equation form for damage under the plastic deformation

Plastic deformation of metals leads to the residual variation of the volume of the metal due to the appearance and growth of deformational defects. This process is known as ‘defect accumulation’. The intensity of this process depends on the metal properties and loading parameters. This work is concentrated first of all with experiments, used to set up the physically substantiated model of damage accumulation under complex stress states. A special technique allowed the loading of the specimens under various superimposed hydrostatic pressures (0.1–800 MPa) to simulate the process of damage accumulation under a wide range of stress states. The metal density was chosen as the characteristic of damage. The experiments support hypotheses of a linear dependence between the damage accumulation intensity and the controlling stress state index, and an inverse exponential dependence of the critical damage accumulation.     

材料塑性成形时敏感性分析研究现状

敏感性分析在材料塑性成形过程中的工艺优化设计及控制方面有重要的应用。综述了材料塑性成形时敏感性分析方法及各种方法在工艺优化设计中的应用,介绍了国内外学者基于敏感性分析在微观组织的优化控制、预成形优化设计、模具优化设计以及参数设计等方面所取得的研究进展。     

The continuous adjoint approach to the k–ω SST turbulence model with applications in shape optimization

In this article, the gradient of aerodynamic objective functions with respect to design variables, in problems governed by the incompressible Navier–Stokes equations coupled with the k–ω SST turbulence model, is computed using the continuous adjoint method, for the first time. Shape optimization problems for minimizing drag, in external aerodynamics (flows around isolated airfoils), or viscous losses in internal aerodynamics (duct flows) are considered. Sensitivity derivatives computed with the proposed adjoint method are compared to those computed with finite differences or a continuous adjoint variant based on the frequently used assumption of frozen turbulence; the latter proves the need for differentiating the turbulence model. Geometries produced by optimization runs performed with sensitivities computed by the proposed method and the ‘frozen turbulence’ assumption are also compared to quantify the gain from formulating and solving the adjoint to the turbulence model equations.     

基于水平集描述的结构拓扑与构件布局联合优化新方法

该文提出了一种结构拓扑与内嵌构件布局联合优化的新颖方法。这种方法突出的特点是利用水平集函数隐式地描述不规则的构件形状,因此可以非常方便地处理构件之间的互不覆盖约束条件。数值算例表明：较之文献中已有的方法,该文算法能够以更小的计算量有效地实现结构拓扑与内嵌构件布局的联合优化。     

The continuous adjoint approach to the k–ε turbulence model for shape optimization and optimal active control of turbulent flows

The continuous adjoint to the incompressible Reynolds-averaged Navier–Stokes equations coupled with the low Reynolds number Launder–Sharma k–ε turbulence model is presented. Both shape and active flow control optimization problems in fluid mechanics are considered, aiming at minimum viscous losses. In contrast to the frequently used assumption of frozen turbulence, the adjoint to the turbulence model equations together with appropriate boundary conditions are derived, discretized and solved. This is the first time that the adjoint equations to the Launder–Sharma k–ε model have been derived. Compared to the formulation that neglects turbulence variations, the impact of additional terms and equations is evaluated. Sensitivities computed using direct differentiation and/or finite differences are used for comparative purposes. To demonstrate the need for formulating and solving the adjoint to the turbulence model equations, instead of merely relying upon the ‘frozen turbulence assumption’, the gain in the optimization turnaround time offered by the proposed method is quantified.     

On variational sensitivity analysis and configurational mechanics

This contribution is concerned with the application of variational design sensitivity analysis in the context of structural optimization and configurational mechanics. In both disciplines we consider variations of the material configuration and we use techniques from variational sensitivity analysis in order to solve these problems. We derive the physical and material residual problem in one step by using standard optimization procedures. Furthermore, we investigate the sensitivity of the physical as well as the material residual problem and obtain the coupled saddle point problem based on these sensitivities. Both problems are coupled by the pseudo load operator, which plays an important role by the solution of structural optimization problems. By means of computational examples from mesh optimization and shape optimization, we demonstrate the capability of the proposed theoretical framework.     

Structural shape and topology optimization based on level-set modelling and the element-propagating method

This article introduces the element-propagating method to structural shape and topology optimization. Structural optimization based on the conventional level-set method needs to solve several partial differential equations. By the insertion and deletion of basic material elements around the geometric boundary, the element-propagating method can avoid solving the partial differential equations and realize the dynamic updating of the material region. This approach also places no restrictions on the signed distance function and the Courant–Friedrichs–Lewy condition for numerical stability. At the same time, in order to suppress the dependence on the design initialization for the 2D structural optimization problem, the strain energy density is taken as a criterion to generate new holes in the material region. The coupled algorithm of the element-propagating method and the method for generating new holes makes the structural optimization more robust. Numerical examples demonstrate that the proposed approach greatly improves numerical efficiency, compared with the conventional level-set method for structural topology optimization.     

基于人工材料的结构拓扑渐进优化设计

首先,提出了一种在结构边界和孔洞周围附加人工材料的思路。在此基础上,结合ESO方法和应力灵敏度,建立了结构有限单元增、删的准则, 给出了一种新的拓扑优化算法。算例表明该方法能采用固定有限元网格中不同的初始优化结构就可获得优化拓扑。由于其概念上的简洁性和应用上的有效性,该方法具有一定的工程应用价值。     

Variational design sensitivity analysis in the context of structural optimization and configurational mechanics

Variational design sensitivity analysis is a branch of structural optimization. We consider variations of the material configuration and we are interested in the change of the state variables and the objective functional due to these variations. In the same manner in configurational mechanics we are interested in changes of the material body. In this paper, we derive the physical and material residual problem by using standard optimization procedures and we investigate sensitivity relations for the physical and material problem. These sensitivity relations are used in order to solve the coupled physical and material problem. Both problems are coupled by the pseudo load operator, which play an important role for the solution of structural optimization problems. Furthermore, we derive explicit formulations for the variations of the physical and material problem and propose different solution algorithms for the coupled problem.     

塑性损伤的发展与应用

本文介绍了塑性损伤的机制和建立塑性损伤模型的一般方法;系统地分析比较了基于连续介质力学、细观力学、连续损伤力学等多种损伤理论,推导了它们之间的内在联系;综述了三轴度、应变路径、组织等对塑性损伤的影响,重点阐述了损伤-塑性流变的耦合分析;还介绍了电阻测量、统计与定量表征、有限元等塑性损伤的分析方法;并且分析了目前塑性损伤...     

柔度和应力约束下连续体结构可靠性拓扑优化

强度和刚度作为衡量工程结构的力学性能的重要指标,一直是工程优化领域重点关注的对象。另外,工程结构在服役过程中存在的不确定性因素对结构性能也影响较大。鉴于此,针对不确定载荷下同时考虑应力和柔度可靠性要求的结构设计问题,该文提出一种基于多项式混沌展开式代理模型的可靠性拓扑优化方法。利用Kieisselmeier-Steinhauser函数聚合最大应力和柔度,构建结构的极限状态函数。引进多项式混沌展开式,建立极限状态函数关于载荷随机变量的显式的代理模型,简化可靠性分析目标性能函数对随机变量的求导过程。详细推导了目标性能函数关于设计变量的导数,采用移动渐进线算法进行设计变量的更新,最后采用2个典型算例及蒙特卡洛仿真模拟验证了所提方法的准确性和有效性,数值结果表明所提方法可以给出同时满足应力和柔度可靠性要求的设计。