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Optimization of geometrically nonlinear structures based on a multi-point approximation method and adaptivity

机译：基于多点逼近法和自适应性的几何非线性结构优化

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摘要

Presents an approach for optimal design of geometrically non-linear structures, using adaptive mesh refinement (AMR). The optimization technique adopted is based on the multi-point approximation method. The finite element method is used for the structural analysis. Reformulation of the optimal design problem is applied to circumvent complications caused by the non-linear behaviour of the structure. The latter may lead to bifurcations, limit points and/or significant reduction of the structural stiffness for individual intermediate designs generated by an optimization algorithm. Discretization errors are controlled using AMR. To reduce computational costs, the requested global and local discretization errors are not taken as fixed values but are specified on the basis of the current status of the optimization process. In the beginning relatively large errors are accepted, while as the process progresses discretization errors are reduced. The method is applied to thin-walled structures with geometrically non-linear behaviour.
机译：提出了一种使用自适应网格细化（AMR）进行几何非线性结构优化设计的方法。采用的优化技术基于多点逼近法。有限元法用于结构分析。重新设计最佳设计问题可避免结构的非线性行为引起的复杂情况。对于优化算法生成的各个中间设计，后者可能导致分叉，极限点和/或结构刚度的显着降低。离散化错误是使用AMR控制的。为了降低计算成本，所请求的全局和局部离散误差不作为固定值，而是根据优化过程的当前状态指定。在开始的时候，可以接受相对较大的误差，而随着过程的进行，离散误差会减少。该方法适用于几何非线性行为的薄壁结构。

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