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Error control and adaptive methods for the sensitivity error for large geometry changes based on exact variational formulations

基于精确变分公式的大几何变化灵敏度误差的误差控制和自适应方法

基本信息

批准号：
210321696
负责人：
Professor Dr.-Ing. Daniel Materna
金额：
--
依托单位：
Fachbereich 3 - Bauingenieurwesen und Wirtschaftsingenieurwesen Bau
依托单位国家：
德国
项目类别：
Research Fellowships
财政年份：
2012
资助国家：
德国
起止时间：
2011-12-31 至 2014-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/210321696?language=en
关键词：
Error control adaptive methods sensitivity

项目摘要

Structures can nowadays be efficiently designed on the basis of the technological progress and improved production methods. An important role plays the optimization of the geometry of components in order to reduce the weight and to save material resources. Sensitivity analysis is a central part for the solution of optimization problems as well as parameter studies. It yields a prediction for thechange in the structural response due to the change of input parameter (design changes). The accuracy of sensitivity information has an important influence on the convergence speed and efficiency of optimization processes. Almost exclusive first order sensitivity relations are used, which yield for large design changes just a rough approximation for the true change of the structural response. Furthermore,sensitivity analysis is nowadays performed based on numerical solution methods, such as the finite element method. Therefore, two important error sources have to be considered within the sensitivity analysis for large design changes: 1. approximation error (error due to approximation of first order) and 2. discretization error (error due to discretization and solution with numerical methods). The goal is the development of efficient and reliable error estimators for the sensitivity errorfor large geometry changes, which is the combination of both error sources. Furthermore, the sensitivity error is to be minimized by using adaptive methods. The accuracy and reliability of sensitivity information shall be quantified and improved. The improved sensitivity information shall be used in order to increase the efficiency and convergence speed of optimization processes.

如今，根据技术进步和改进的生产方法，可以有效地设计结构。优化零部件的几何形状对减轻重量、节约材料资源起着重要作用。灵敏度分析是优化问题求解和参数研究的核心部分。对输入参数变化(设计变化)引起的结构响应变化进行了预测。灵敏度信息的准确性对优化过程的收敛速度和效率有重要影响。采用了几乎排他的一阶灵敏度关系，对于较大的设计变化，只能粗略地近似反映结构响应的真实变化。此外，目前的灵敏度分析是基于数值解方法，例如有限元方法。因此，在大型设计变化的灵敏度分析中必须考虑两个重要的误差源：1.近似误差(一阶近似误差)和2.离散化误差(离散化和数值方法求解的误差)。我们的目标是开发高效、可靠的误差估计器，用于对两种误差源组合的大型几何变化的灵敏度误差进行估计。此外，采用自适应方法使灵敏度误差达到最小。应量化和提高敏感性信息的准确性和可靠性。为了提高优化过程的效率和收敛速度，应使用改进的灵敏度信息。