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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Asymptotic decomposition in the problem of joined elastic beams
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Asymptotic decomposition in the problem of joined elastic beams

机译：弹性梁连接问题的渐近分解

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摘要

The analysis of problem of joined elastic beams is presented in comparison with the engineering and asymptotic approaches. Our analysis is based on three-dimensional elasticity theory model and recently developed method of local perturbation (Gaudiello and Kolpakov, 2011), which seems to be an effective tool for analysis of fields in the vicinity of joint. We demonstrate that the method of local perturbation developed in (Gaudiello and Kolpakov, 2011) for scalar Laplace equation can be modified for vectorial elasticity theory problem. We demonstrate that the elasticity theory problem in joined domains of small diameter can be decomposed into one-dimensional problem describing global deformation of a system of joined beams and three-dimensional problems describing local deformation of singular joints in uniform fields. The first problem is the classical one, which ignores individual properties of joint absolutely. The second problem initiates reminiscence about the cellular problem of the homogenization theory for periodic structure. In spite of some similarities, the mentioned problems differ significantly. In particular, the joint of normal type (the joint similar in dimensions and material characteristics to the joined beams) does not manifest itself on global level. Due to the strong localization of perturbation of solution, computation of local strains and stresses in the vicinity of joint can be realized with standard FEM software.
机译：与工程方法和渐近方法相比较，分析了连接弹性梁的问题。我们的分析基于三维弹性理论模型和最近开发的局部扰动方法（Gaudiello和Kolpakov，2011），这似乎是分析关节附近场的有效工具。我们证明，在（Gaudiello和Kolpakov，2011）中针对标量拉普拉斯方程开发的局部摄动方法可以针对矢量弹性理论问题进行修改。我们证明，小直径连接域中的弹性理论问题可以分解为描述连接梁系统整体变形的一维问题和描述均匀场中奇异节点局部变形的三维问题。第一个问题是经典问题，它绝对地忽略了接头的各个属性。第二个问题引起人们对周期性结构同质化理论中细胞问题的怀念。尽管存在一些相似之处，但上述问题仍存在很大差异。特别是，普通类型的接头（尺寸和材料特性与所连接梁相似的接头）不会在整体上显现出来。由于溶液扰动的局部性强，因此可以使用标准的FEM软件来计算接头附近的局部应变和应力。

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