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首页> 外文期刊>Journal of Computational Physics >Shape and topology optimization based on the phase field method and sensitivity analysis
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Shape and topology optimization based on the phase field method and sensitivity analysis

机译：基于相场法和灵敏度分析的形状和拓扑优化

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摘要

This paper discusses a structural optimization method that optimizes shape and topology based on the phase field method. The proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions. The advantage of the method is the simplicity of computation, since extra operations such as re-initialization of functions are not required. Structural shapes are represented by the phase field function defined in the design domain, and optimization of this function is performed by solving a time-dependent reaction diffusion equation. The artificial double well potential function used in the equation is derived from sensitivity analysis. The proposed method is applied to two-dimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem. The numerical examples provided illustrate the convergence of the various objective functions and the effect that perimeter control has on the optimal configurations.
机译：本文讨论了一种基于相场方法优化形状和拓扑的结构优化方法。所提出的方法具有与基于结合了周边控制功能的水平集方法的结构优化方法相同的功能。该方法的优点是计算简单，因为不需要额外的操作，例如功能的重新初始化。结构形状由在设计域中定义的相场函数表示，并且该函数的优化是通过求解与时间有关的反应扩散方程来进行的。方程中使用的人工双阱势能函数是从灵敏度分析中得出的。该方法适用于二维线性弹性和振动优化问题，例如最小柔度问题，柔顺机构设计问题和本征频率最大化问题。所提供的数值示例说明了各种目标函数的收敛性，以及周边控制对最佳配置的影响。

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