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摘要: 为了合理处理列车车体结构分析中典型的板梁偏心连接问题, 分别基于罚单元法和La-grange乘子法构造了板梁组合结构模型, 将组合结构中相关节点对之间通过偏心关系建立的约束方程引入到平衡方程中, 解决了梁单元因偏心连接而对组合结构总体刚度矩阵的贡献问题, 并编制了求解板梁组合结构静强度计算问题的有限元程序。实例计算表明不但两种计算方法的计算结果吻合, 而且其计算结果均与有限元分析软件ANSYS 9.0计算结果接近, 位移误差在1%以内, 应力误差在2%以内, 分析表明二者均是处理板梁偏心连接组合结构的有效方法。Abstract: In order to deal with the eccentric connection problems of plate and beam reasonably in the structural analysis of vehicle, the constraint equations to the correlative nodes of plate and beam were involved in their balance equations, based on the theories of penalty element method and Lagrange multiplier method, which can solve the contribution problem of the eccentric connection to unitary stiffness matrix.A finite element program was worked out to solve the static intensity calculation problem of composite structure.Numerical computation result shows that the results of the two methods are both close to those obtained by finite element software ANSYS 9.0, the maximum errors of displacement and stress are respectively less than 1% and 2%, it indicates that the two methods are effective on dealing with the composite structure of plate and beam.
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表 1 求解结果比较
Table 1. Comparison of analysis results
方法 v/mm u/mm w/mm θx/rad θy/rad 当量应力/MPa 罚单元法 -0.529 57×10-2 0.665 27×10-3 -1.509 7 -0.229 71×10-1 0.235 61×10-2 414.61 Lagrange法 -0.529 58×10-2 0.665 27×10-3 -1.509 7 -0.229 71×10-1 0.235 61×10-2 414.75 ANSYS 9.0 -0.525 39×10-2 0.690 55×10-3 -1.511 0 -0.229 89×10-1 0.237 47×10-2 409.52 
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