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为解决平面梁元在相交处可能存在的刚性连接问题,根据带刚臂平面梁元在受力后的运动和变形特点,该文基于共旋坐标法推导出两端带任意刚臂的平面梁元的切线刚度矩阵显式表达式,给出了不平衡力的精确全量算法,并提供了详细的计算步骤。利用该文的研究成果编制了程序,对无刚臂和有刚臂的平面梁结构进行了几何非线性分析。计算结果表明:这种非线性单元列式的正确性和非线性求解过程的收敛性,实用价值较强。
In order to solve the rigid connection problem of planar beam element at the intersection, according to the motion and deformation characteristics of beam element with rigid arm after being stressed, a planar beam with arbitrary rigid arms at both ends is derived based on co-rotating coordinate method Element tangential stiffness matrix explicit expression, given the exact amount of unbalance force algorithm, and provides detailed calculation steps. Using the research results of this paper, a program was developed to analyze the geometric nonlinearity of the planar beam structure without arms and with arms. The calculation results show that the correctness of the nonlinear element formulation and the convergence of the nonlinear solution process are of great practical value.