Nonlinear reanalysis for structural modifications based on residual increment approximations
Nonlinear reanalysis for structural modifications based on residual increment approximations
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DOI：
10.1007/s00466-015-1209-3
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发表时间：
2016
影响因子：
4.1
通讯作者：
D. Materna;V. Kalpakides
中科院分区：
文献类型：
--
作者：
D. Materna;V. Kalpakides
本文提出了一种非线性问题的重分析方法。主要目标是预测由于给定的设计修改而导致的状态变量的变化，例如横截面、几何形状、材料参数等的变化。该方法基于残余增量近似，该近似在迭代算法中使用。重新分析方法只需要评估残差向量，可以非常快速且高效地完成。此外，通过使用有理逼近方法扩展了该方法的有效性。与基于变化刚度矩阵评估的其他现有再分析方法相比，仅需要计算和存储残差向量。该方法是通用的，可以应用于具有不同类型设计修改的线性和非线性问题。此外，所提出的重新分析方法很容易在现有有限元程序中实现，因为不需要关于设计变量的导数。通过非线性弹性的几个计算示例证明了所提出框架的能力。
This paper presents a reanalysis method for nonlinear problems. The main objective is to predict the changes in the state variables due to given design modifications, e.g. changes in the cross-sections, the geometry, material parameters etc. The approach is based on residual increment approximations, which are used within an iterative algorithm. The reanalysis method requires only the evaluation of residual vectors, which can be done very fast and efficient. Moreover, the validity of the approach is extended by using a rational approximation method. In contrast to other existing reanalysis methods, which are based on the evaluation of changed stiffness matrices, only residual vectors have to be computed and stored. The approach is general and can be applied to linear and nonlinear problems with different kind of design modifications. Furthermore, the proposed reanalysis method is easy to implement in existing finite element programs, because no derivatives with respect to the design variables are necessary. The capability of the proposed framework is demonstrated by means of several computational examples from nonlinear elasticity.