多因素耦合影响下的杆系结构几何非线性分析

通过分析横向剪切对梁单元的影响、轴心力的二次影响以及约束扭转时翘曲引起的二次剪应力效应 ,引入了翘曲函数及三次多项式的扭转模式 ,得出了 7个自由度的杆系结构精确模型 .在几何非线性分析中 ,考虑了轴向荷载、平面弯曲、剪切、约束扭转翘曲以及荷载 -变形各效应的耦合 ,基于此建立了变形状态几何非线性分析的切线刚度矩阵 .利用建立于弧长法基础上的球面显式迭代 -增量法 ,进行了空间结构的几何非线性全过程分析 .

Geometric Nonlinear Analysis of Space Bar Structure Based on Diversified Coupling Factors

Through analyzing the action of the transverse shear to the beam,and the secondary influence of the axial force and quadratic shear stress effect of the warping caused by restrained torsion,an accurate analysis model of 7 freedom degrees of space beam is obtained by introducing the warping function and the torsion mode of tri-polynomial.Owing to the geometric nonlinearity,the structure of elastic material also shows nonlinear property.Based on these, a second order nonlinear model is put forward and the tangent stiffness matrix of the geometric nonlinear analysis during deforming is derived considering the coupling influence of the axial load,bending,shear,constrained torsion,warping and loading-deformation effect.Through the arc-length orthogonality method,the spherical surface apparently pattern iterative programming is worked out and can follow the tracks of the whole process of the structural deformation.