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摘要: 为了研究复杂载荷作用下薄板结构的受力, 基于离散Kirchhoff原理, 推导了三角形弯曲薄板单元的应变矩阵、刚度矩阵中的显式面积坐标积分方法, 根据变分原理构造了任意四边形弯曲单元DKQ, 引入对称及反对称畸变模式进行网格畸变敏感性分析, 将DKQ弯曲单元与平面应力单元组合, 得到了用于薄板分析的四边形平板单元, 并编制了有限元分析程序。计算结果表明: 相对偏移量从-0.18变化至0.18, 反对称畸变模式下挠度最大误差为1.83%, 而对称畸变模式下挠度最大误差为0.99%;对某地铁车体结构, 计算结果与ANSYS结果误差在3.5%之内, 这说明构造的DKQ弯曲单元对网格畸变不敏感, 具备良好的位移解收敛性和计算精度。Abstract: In order to analyze the states of thin-walled structures under complicated loads by discrete Kirchhoff principle, the strain matrix of triangle bending element and explicit area coordinate integral method were discussed in detail.According to variant principle, DKQ (Discrete Kirchhoff Quadrilateral) bending element was constructed.By introducing symmetric and antisymmetric mesh distortion modes, mesh distortion sensitivity analysis was carried out.Through combining DKQ element with planar stress element, quadrilateral plate element used for general thin-walled structures analysis was implemented by finite element program.Numerical test result indicates that when relative offset value varies from-0.18 to 0.18, the deflection maximum errors of antisymmetric and symmetric modes are 1.83% and 0.99% respectively.For a car-body of some subway vehicle, the differences between the analysis values and those obtained by ANSYS are less than 3.5%.The result shows that DKQ bending element is insensitive to mesh distortion and has good convergence capability and accuracy for displacement field.
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Key words:
- vehicle engineering /
- structure analysis /
- finite element /
- qudrilateral bending element
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表 1 C的数值解
Table 1. Numeric Solution of C
理论解[9] 简支: 0.011 60 固支: 0.005 61 N 数值解 数值解 2 0.012 063 0.005 979 3 0.011 833 0.005 822 4 0.011 744 0.005 745 5 0.011 698 0.005 704 
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表 2 结果比较
Table 2. Comparison of Analysis Results
当量应力/MPa X/mm Y/mm Z/mm ANSYS 135.595 -0.679 21 3.920 9 -4.021 8 本文方法 131.421 -0.655 59 3.863 8 -4.008 3
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