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A simplified geometric stiffness in stability analysis of thin-walled structures by the finite element method

机译:薄壁结构稳定性有限元分析的简化几何刚度

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ABSTRACT Vibration analysis of a thin-walled structure can be performed with a consistent mass matrix determined by the shape functions of all degrees of freedom (d.o.f.) used for construction of conventional stiffness matrix, or with a lumped mass matrix. In similar way stability of a structure can be analysed with consistent geometric stiffness matrix or geometric stiffness matrix with lumped buckling load, related only to the rotational d.o.f. Recently, the simplified mass matrix is constructed employing shape functions of in-plane displacements for plate deflection. In this paper the same approach is used for construction of simplified geometric stiffness matrix. Beam element, and triangular and rectangular plate element are considered. Application of the new geometric stiffness is illustrated in the case of simply supported beam and square plate. The same problems are solved with consistent and lumped geometric stiffness matrix, and the obtained results are compared with the analytical solution. Also, a combination of simplified and lumped geometric stiffness matrix is analysed in order to increase accuracy of stability analysis.
机译:摘要薄壁结构的振动分析可以使用一致的质量矩阵进行,该质量矩阵由用于构造常规刚度矩阵的所有自由度(d.o.f.)的形状函数确定,也可以使用集总质量矩阵进行。以类似的方式,可以使用一致的几何刚度矩阵或具有集中屈曲载荷的几何刚度矩阵来分析结构的稳定性,该几何刚度矩阵仅与旋转d.o.f有关。近来,利用平面内位移的形状函数构造用于板偏转的简化质量矩阵。在本文中,相同的方法用于构造简化的几何刚度矩阵。考虑了梁单元以及三角形和矩形板单元。在简单支撑梁和方板的情况下,说明了新几何刚度的应用。使用一致且集中的几何刚度矩阵可以解决相同的问题,并将获得的结果与解析解进行比较。而且,分析了简化的和集总的几何刚度矩阵,以提高稳定性分析的准确性。

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