基于计算机快速求解梁弯曲内力的一体化积分法  

作　　者：金蓉 李银山[2] 崔春义 

机构地区：[1]大连海事大学交通运输工程学院,辽宁大连116026 [2]河北工业大学机械工程学院,天津300401

出　　处：《科技创新与应用》2022年第17期59-63,共5页Technology Innovation and Application

摘　　要：介绍一种简洁的一体化积分法,只需要确定梁的分布载荷函数,通过计算机积分,在很短的时间内就可以解决复杂载荷作用下梁的弯曲内力问题。对于静定梁,由弯矩、剪力、载荷集度间的微分方程和力边界条件,两次积分求解弯曲内力;对于超静定梁,由挠度、转角、弯矩、剪力、载荷集度间的微分方程、力和位移的边界条件,四次积分求解弯曲内力。一体化积分法求解梁的内力是固体力学边值问题的具体应用,它与计算机编程结合可快速求得梁内力的解析解,并绘出剪力图和弯矩图。该方法具有规范化、程式化、高效率、高可靠性、较好的交互性等优点。对复杂载荷作用下的静定梁和超静定梁等工程问题,具有显著的优越性,可广泛应用于教学和工程实践。This paper introduces a simple integrated integration method,which only needs to determine the distributed load function of the beam,and through computer integration,the bending internal force of the beam under complex load can be solved in a very short time.For the statically indeterminate beam,the bending internal force is solved by the differential equation among moment,shear force,load concentration and force boundary condition,while for the statically indeterminate beam,the bending internal force is solved by the differential equation among deflection,rotation angle,bending moment,shear force and load concentration,and the boundary conditions of force and displacement.The solution of the internal force of the beam by the integrated integral method is a specific application of the boundary value problem of solid mechanics.Based on computer programming,the analytical solution of the internal force of the beam can be quickly obtained,and the shear force diagram and moment diagram can be drawn.This method has the advantages of standardization,stylization,high efficiency,high reliability,good interaction and so on.It has remarkable advantages for engineering problems such as statically indeterminate beam and statically indeterminate beam under complex load,and can be widely used in teaching and engineering practice.

关 键 词：弯曲内力 超静定梁 边界条件 复杂分布载荷 一体化积分法 

分 类 号：O342[理学—固体力学]