Exact and Accurate Reanalysis of Structures for Geometrical Changes
Exact and Accurate Reanalysis of Structures for Geometrical Changes
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DOI：
10.1007/s366-001-8302-9
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发表时间：
2001-12
影响因子：
8.7
通讯作者：
U. Kirsch;P. Papalambros
中科院分区：
文献类型：
--
作者：
U. Kirsch;P. Papalambros
提出了结构系统中几何变化的重新分析方法。求解过程基于组合近似方法，其中二项式级数项用作简化基近似中的基向量。计算基于单次精确分析的结果，不需要计算导数，并且每次重新分析都需要少量的计算工作。该方法易于实现，可与一般的有限元程序结合使用。对于几何中的低阶修改，可以有效地获得精确解。在基向量接近线性相关的情况下，可以获得准确的解。当表示初始设计和修改设计的两个向量之间的角度较小时，也可以针对接近比例的几何形状实现此类解决方案。数值示例证明了使用少量基向量即可实现高精度
A reanalysis approach for geometrical changes in structural systems is presented. The solution procedure is based on the combined approximations method, where the binomial series terms are used as basis vectors in reduced basis approximations. The calculations are based on results of a single exact analysis, calculation of derivatives is not required, and each reanalysis involves a small computational effort. The method is easy to implement, and can be used with general finite element programs. Exact solutions are obtained efficiently for low-rank modifications in the geometry. Accurate solutions are achieved in cases where the basis vectors come close to being linearly dependent. Such solutions are also achieved for nearly scaled geometries, when the angle between the two vectors representing the initial design and modified design is small. Numerical examples demonstrate the high accuracy achieved with a small number of basis vectors