Stability analysis of hyper symmetric skeletal structures using group theory
Stability analysis of hyper symmetric skeletal structures using group theory
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DOI：
10.1007/s00707-008-0022-x
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发表时间：
2008-05
期刊：
影响因子：
2.7
通讯作者：
A. Kaveh;M. Nikbakht
中科院分区：
文献类型：
--
作者：
A. Kaveh;M. Nikbakht
本文的主要目的是开发一种方法，有效地计算具有高阶对称性的框架结构的屈曲载荷，以减少其相关的特征值问题的大小。这是通过使用对称群的表示将对称模型的二阶刚度矩阵分解为子矩阵来实现的，通过逐步的方法。所得到的子矩阵的物理解释显示为子结构（因素），然后进一步分解的可能性，研究每个构建的子模型。由于变换的相似性，构造的子矩阵包含主结构矩阵的特征值。整个结构的屈曲载荷是通过计算其系数的屈曲载荷来获得的。本文的方法提供了一个数学基础和逻辑手段来处理对称性，而不是寻找各种边界条件施加的对称结构，在传统的方法。提供实例来说明本方法的简单性和效率。
The main objective of this article is to develop a methodology for the efficient calculation of buckling loads for frame structures having high-order symmetry properties in order to reduce the size of their associated eigenvalue problems. This is achieved by decomposing the second-order stiffness matrix of a symmetric model into submatrices using a representation of its symmetry group, via a step-by-step approach. The physical interpretation of the resulting submatrices is shown as substructures (factors), and the possibility of further decomposition is then investigated for each of the constructed submodels. Due to the similarity in transformation, the constructed submatrices contain the eigenvalues of the main structural matrix. The buckling load of the entire structure is obtained by calculating the buckling loads of its factors. The methods of the present paper provide a mathematical foundation and a logical means to deal with symmetry instead of looking for various boundary conditions to be imposed for symmetric structures, as in the traditional methods. Examples are provided to illustrate the simplicity and efficiency of the present method.