基于U.L列式的带刚臂平面梁元非线性分析

Non-linear Analysis of Plane Beam Element with Rigid Arms Based on U.L Formulation

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,基于U.L法推导出两端带任意刚臂的平面梁元的切线刚度矩阵表达式,指出已有文献在推导过程中省略了单元已有内力对切线刚度矩阵附加项的影响,有可能出现在非线性程度较高的时候计算不收敛的问题,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;利用本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.

A U. L formulation was proposed for the nonlinear analysis of plane beam element with rigid arms. According to the characteristics of the motion and the deformation of a rigid-ended plane beam ele- ment, an explicit expression of non-linear tangent stiffness matrix was derived by U. L procedure. The de- ficiency of the reference that neglects the effects of element inner-force on additional term of the tangent stiffness matrix was improved to solve the divergence for strong nonlinear problems. An accurate deforma- tion algorithm was presented,and a detailed calculation procedure was provided. A computer program was developed to analyze the geometrical nonlinear behavior of the plane beam with and without rigid arm. The results have demonstrated that the proposed innovative element and algorithm are efficient and accurate with satisfied convergence, and have promising applications in practical engineering projects.