基于能量变分剪切效应空间梁单元刚度矩阵及荷载列阵推导

DERIVATION OF ELEMENT STIFFNESS MATRIX AND LOAD ARRAY FOR SPACE BEAM WITH SHEAR EFFECT BASED ON ENERGY VARIATION

为了系统研究空间梁单元考虑剪切变形影响时的刚度矩阵及荷载列阵,将能量变分原理应用于空间梁的单元分析。建立了考虑剪切效应的空间梁单元位移函数,利用最小势能原理导出了这种空间梁单元的刚度矩阵和荷载列阵的表达式,显式积分得到单元刚度矩阵,同时计算了平面内部分非节点荷载作用下的等效节点荷载,修正了相关文献中的部分错误。计算结果表明:该方法所得到的单元刚度矩阵与相关文献中其他方法的计算结果完全一致,为编制空间巨型结构的有限元程序奠定基础,对推算其他类型单元刚度矩阵及其荷载列阵也具有理论意义和应用价值。

In order to study systematically the stiffness matrix and load array of space beam element with the impact of shear deformation, the element was analyzed by the energy variation principle. The displacement functions for space beam element with shear deformation effect were put forward, and then expressions of element stiffness matrix and load array for this beam were deduced strictly by the minimum potential energy principle. Explicit integration was carried out for the element stiffness matrix and the equivalent nodal loads under some forms of no-node load within a plane were calculated as well, which had revised the mistakes in relevant reference. Results show that the element stiffness matrix computed by the method is consistent with those in related documents calculated by other methods, which makes a foundation for compiling the finite element procedure for space mega frame structure. Which has a good theoretical and practical value in the calculation of the element stiffness matrixes and load arrays for other elements as well.