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Vertex assigned morphing for parameter free shape optimization of 3-dimensional solid structures

机译：顶点为三维固体结构的可用形状优化分配了变形

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摘要

In the past the Vertex Morphing method has mainly been used in the context of optimization of thin walled shell structures or fluid mechanical problems. In this paper an extension of this parameter free shape optimization method to 3-dimensional solid structures based on the free Finite Element code CalculiX is presented. Key element of the whole process is an efficient adjoint sensitivity analysis that can handle many design variables providing gradient information for the response functions of interest, e.g. stresses and mass. Typically, parameter free shape optimal designs result in non-smooth geometries and suffer from mesh dependencies. To avoid these phenomena an intermediate filter operation in combination with several post processing steps of the raw sensitivities is added. In the optimization, the filter size is also used as an additional design parameter controlling the curvature of the optimal shape. In many engineering optimization applications constraints have to be considered. These restrictions are included in the optimization problem by the use of Rosen's gradient projection method. For the successive shape update a pseudo linear-elastic static Finite Element analysis with multiple point constraints and a varying Young's modulus is performed in every design iteration. Finally, the capabilities of the extended Vertex Morphing method are demonstrated for an academic example and a geometrically complex part from aerospace industry. (C) 2019 Elsevier B.V. All rights reserved.
机译：在过去，顶点变形方法主要用于优化薄壁壳结构或流体机械问题的背景下。在本文中，提出了基于自由的有限元码计算的三维实体结构的这种参数自由形状优化方法的扩展。整个过程的关键要素是有效的伴随灵敏度分析，可以处理许多设计变量，为感兴趣的响应函数提供梯度信息，例如，压力和质量。通常，参数自由形状最佳设计导致非平滑几何形状并遭受网格依赖性。为了避免这些现象，中间滤波器操作与原始敏感度的若干后处理步骤组合。在优化中，滤波器大小也用作控制最佳形状曲率的附加设计参数。在许多工程优化应用中，必须考虑约束。通过使用Rosen的梯度投影方法，这些限制包括在优化问题中。对于连续的形状更新，在每个设计迭代中执行具有多点限制的伪线性弹性静态有限元分析和不同的杨氏模量。最后，对来自航空航天工业的学术典范和几何复杂部分进行了演示的扩展顶点变形方法的能力。 （c）2019 Elsevier B.v.保留所有权利。

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