一般杆系结构的非线性数值分析

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The Nonlinear Numerical Analysis Method for Frames

摘要: 本文在total-Lagrange坐标系下,对Kirchhoff梁给出了考虑几何非线性的两种梁单元刚度的显式表达式.一种是一般的非线性梁元,它既考虑了应变增量和位移增量间的二次项,又计及了刚体位移的影响,另一种是简化的非线性梁元,它只在线性梁的平衡方程中直接加入了轴力对弯曲的影响.非线性方程采用混合法求解,文中通过一些算例的数值计算,对两种单元作了比较详细的分析和评估.

Abstract: This paper gives the direct formulas of stiffness matrixes of two-kinds of Kirchhoff nonlinear elements under total-Lagrange coordinate. For the first one, it includes not only the quadric terms of increments of strain and displacement but also-the influence of rotations. For the second one, it is simplified and its nonlinear is considered by taking into account the influence of axial force on the equilibrium equation in the linear beam theory.The nonlinear equation obtained from both of the above-Said elements is solved by mixed Newton-Raphson method, and by comparing the results obtained from two kinds of nonlinear beam some important conclusions that we can know how to use them right are given in our paper.

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