摘要
集中力和集中力偶广泛存在于实际力学问题中,但在推导载荷集度、剪力和弯矩间的微分关系时所截取的微段并不包含集中量.求解内力方程和弯曲变形时需人为地将梁分段,求解过程异常繁琐.本文通过引入奇异函数将集中量转化为分布量,并给出任意载荷作用下的载荷集度方程.通过微积分关系求出内力、转角和挠度方程.本方法便于学生理解微分关系推导时截取微段仅含分布载荷的力学模型,求解弯曲变形时也无需对梁进行分段,计算过程大大简化且便于计算机编程.
Abstract
The concentration of force and moment is widespread in practical mechanical problems.However,when deriving the differential relationships between load intensity,shear force,and bending moment,the differential segments extracted do not include concentrated loads.Solving the equations for internal forces and bending deformations often requires artificial segmentation of the beam,making the solution process exceptionally intricate.This paper introduces singular functions to transform concentrated loads into distributed loads and provides load intensity equations under any loading conditions.Through calculus relationships,equations for internal forces,rotations,and deflections are derived.This approach enhances students'comprehension of a mechanical model in which,during the derivation of differential relationships,the differential segments solely consist of distributed loads.The solution to bending deformations also eliminates the need for beam segmentation,significantly simplifies the calculation process and makes it suitable for computer programming.
基金项目
深圳技术大学教学改革项目(20241006)
深圳技术大学教学改革项目(20221003)
深圳市科技计划项目(29853M-kCJ-2023-002-09)
NETL
NSTL
万方数据