交叉梁系结构的矩阵分析法

Structural Analysis of Crossed Beam System by Matrix Method

通过寻求交叉梁系力法分析过程的规律,利用其结构本身的几何特点,引进矩阵运算,将求解多余力的正则方程及系数、各梁的弯矩和交叉点的位移表达成统一形式,使结构分析规范化,避免弯矩图的绘制和繁琐的计算,大大有利于计算机求解。与有限元法相比,方程阶数降低了一半以上。本法适于分析纵横梁正交、四角简支或某边简支的一般交叉梁系,能够求解多余力、各梁弯矩和交叉点位移。同时,对对称结构相应导出了更简单的计算公式。

Discussing the procedure of structural analysis of crossed beam systems byforce method, the normal equations for the redundant forces and their flexi-bility coefficients, the bending moments of beams and the displacements oftheir intersection points are thus expressed in utlified forms by use of matricesand by taking advantage of the geometries of the structure itself. In this waythe structural analysis will be normalized so as to avoid plotting bending mo-ment diagrams and tedious calculations. The new method is also superior toFEM in that the order of normal equation is reduced to half or less, so it isapplicable to computers, especially to the analysis of general crossed beamsystems whose beams are perpendicular to each other with simple sup-ports at the four edge points or along the sides. This method is available toredundant forces, bending moments of beams and displacements at intersectionpoints.Furthermore, more simplified computation formulae are derived to thesymmetrical structures.