三維梁元素非線性分析之改進研究

Abstract

本文的目的在控扭轉角的形狀函數及內力、剛度矩陣之變形參九 的高次項對三維梁之非線性分析的精確性及平衡迭代之收斂性的影響。 本文中考慮了梁的翹曲剛度。本文中考慮了兩種扭轉角的形狀函 數，即Hermitian多項式及縣臂梁受端點扭矩的線性解析解。 本文以數值便題說明扭轉角的形狀函數對非線性分析效率的影響 並探討內力中變形參數的三次項對分析結果的影響及剛度矩陣中變形 參數的一次項對平衡迭代收斂性的影響。

The objective of this paper is to improve the efficiency of nonlinear analysis for 3-D beam. The effect of the shape functions of twist angle and higher order terms of nodal parameters of internal nodal force and stiffness matrix on the accuracy of nonlinear analysis and convergence of equilibrium iterations is investigated. The warping rigidity of beam is considered in this paper. Two kinds of shape functions are considered: Hermitian polynomials and the linear analytical solution of cantilever beam subjected end torque. Numerical examples are studied to demonstrate the effect of the shape function of twist angle on the efficiency of nonlinear analysis. The effect of the third order terms of internal nodal force on the accuracy of results and the effect of the second order terms of the stiffness matrix on the convergence rate of equilibrium iteration are also investigated.