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Stress-constrained level set topology optimization for compliant mechanisms

机译：压力约束的水平集拓扑优化，用于兼容机制

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This work presents a level set-based topology optimization procedure to design compliant mechanisms subject to local stress constraints. A classical technical difficulty related to the design of compliant mechanisms is the emergence of non-realistic flexible joints (hinges) subject to unfeasible strain and stresses. A natural way to overcome this occurrence is the inclusion of stress constraints within the formulation. This approach brings, on the other hand, particular difficulties associated with the local nature of stress constraints. To deal with this issue, stress constraints are included in the present work using an augmented Lagrangian mathematical programming technique. A level set approach defines the design of the mechanical part and a reaction-diffusion equation is used to update the level set function towards the optimized state. A natural extension of the velocity field provided for the reaction-diffusion equation allows for hole nucleation during the design updating. The joining of an augmented Lagrangian approach and level set implicit boundaries to handle local stress constraints in order to obtain hinge-free compliant mechanisms is the novelty of this paper. Several two-dimensional numerical examples show the efficacy of the proposed procedure. In particular, an example analyzes the influence of the weak material in the design of compliant mechanisms. Level set designs enable that final solutions are validated in commercial finite element codes without any post-processing procedure. (C) 2019 Elsevier B.V. All rights reserved.
机译：这项工作提出了一个基于级别集的拓扑优化程序，以设计受局部压力约束的兼容机制。与顺应性机构设计相关的经典技术难题是出现了不切实际的挠性接头（铰链），该挠性接头承受不可行的应变和应力。克服这种情况的自然方法是在配方中加入应力限制。另一方面，这种方法带来了与压力约束的局部性质相关的特殊困难。为了解决这个问题，使用增强的拉格朗日数学编程技术将压力约束包括在当前工作中。水平集方法定义了机械零件的设计，并且使用反应扩散方程式将水平集函数更新为最佳状态。为反应扩散方程式提供的速度场的自然扩展允许在设计更新期间产生孔核。增强拉格朗日方法和水平集隐式边界的结合以处理局部应力约束，以获得无铰链的顺应性机制是本文的新颖之处。几个二维数值示例表明了所提出程序的有效性。特别是，一个示例分析了柔韧性材料在顺应机构设计中的影响。水平集设计使最终解决方案可以通过商业有限元代码进行验证，而无需任何后处理程序。 （C）2019 Elsevier B.V.保留所有权利。

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