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总览 评价 葛威延 ， 何斌 * ， 安逸 ， 刘冬梅 （ 南京工业大学工程力学系，南京，211816； ） 摘要： 考虑一阶剪切影响的Mindlin板理论是板分析设计的重要方法。采用一阶Mindlin板理论，应用半解析有限条带法推导中间含有一根节线的高阶条单元控制方程；结
葛威延， 何斌*， 安逸， 刘冬梅
（
南京工业大学工程力学系，南京，211816； ）
摘要：
考虑一阶剪切影响的Mindlin板理论是板分析设计的重要方法。采用一阶Mindlin板理论，应用半解析有限条带法推导中间含有一根节线的高阶条单元控制方程；结合传递矩阵技术推导条单元的传递矩阵和传递方程，形成一种新的半解析有限条传递矩阵法分析矩形板的屈曲载荷和屈曲模态。采用该方法分析了不同厚度矩形板在不同边界条件下的屈曲载荷因子，并分析了四边简支带肋矩形板的屈曲载荷因子与长宽比的关系，数值结果与有限元法相吻合，验证了形成的方法在分析Mindlin板屈曲时是高效的。
关键词：
Mindlin板；屈曲；传递矩阵；有限条法；带肋板
Wei-Yan Ge， Bin He*， Yi An， Dong-Mei Liu
（
Department of Engineering Mechanics, Nanjing Tech University, Nanjing,211816； ）
Abstract：
The Mindlin plate theory that considers the effect of first-order shear deformation is an important method to analyze and design the structural plate. Based on first-order Mindlin plate theory, the semi-analytical finite strip method is used to deduce the control equation of high-order strip unit with a mid-nodal line. The transfer matrix technology is combined to deduce the transfer matrix and the transfer equation of the plate strip to form a new semi-analytical finite strip transfer matrix method, which is used to analyze the buckling coefficients and mode of the rectangular plate. Based on this method, the buckling coefficients of the rectangular plates with different thicknesses under different boundary conditions are analyzed, and the relationship between the buckling load factors and the length-width ratio of the ribbed rectangular plates of simply supported on four sides is also analyzed. The numerical results match with the finite element method. It is verified that the method is efficient to analyze the buckling of the Mindlin plate.
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