基于向量和矩阵运算的拱坝多拱梁法应力计算研究

Study on Stress Calculation of Arch Dam Multi-Arch Beam Method Based on Vector and Matrix Operation

拱梁分载法有着百余年的发展历史,目前仍是拱坝应力分析的基本方法。当代工程中多采用五向全调整多拱梁法分析拱坝应力,合理划分水平拱圈和竖向曲梁,按照拱、梁的节点位移相等的原则通过试算等方法确定拱、梁的分载,进而得到坝体应力。采用向量的形式来表述多拱梁法的荷载、内力和位移,通过矩阵分析手段来组织拱、梁分载运算,数学概念简洁、清晰,可方便地在面向对象的程序设计语言或数学软件平台上实现。

The arch-beam split-load method has a history of more than one hundred years,and it is still the basic method of arch dam stress analysis at present.In contemporary engineering,five-way full adjustment multi-arch beam method is often adopted to analyze arch dam stress,horizontal arch ring and vertical curved beam are reasonably divided,and the load sharing of arch and beam is determined by trial calculation and other methods according to the principle of equal node displacement of arch and beam,thus obtaining dam body stress.The load,internal force and displacement of the multi-arch beam method are expressed in the form of vectors,and the split-load operation of the arch and beam is organized by matrix analysis.the mathematical concept is concise and clear,which can be conveniently realized on the object-oriented programming language or mathematical software platform.