均布载荷下变形受约束悬臂梁弹性大变形分析

建立了分析均布载荷作用下受约束悬臂粱的弹性大变形三阶段模型。模型的第1阶段为悬臂梁变形不受约束的阶段：第2阶段为悬臂梁自由端和其下面的约束相接触时的变形阶段，此时，在接触处有一支反力作用：第3阶段为悬臂梁和其下面的约束有一定接触范围时的变形阶段，此时在接触范围内，粱的挠度和转角是固定的。给出了各个阶段弹性大变形梁的边界条件，提出了各阶段求解梁弹性大变形的三重二分法。实例中，对于梁在各阶段的弹性大变形问题进行了分析计算，并和小变形理论的计算结果进行了比较。结果表明，在梁变形的第1阶段，小变形理论的相对误差随着初始间隙的增大而迅速增大；在梁变形的第2阶段，在给定的初始间隙范围内，小变形理论的相对误差变化不大；在梁变形的第3阶段，小变形理论的相对误差随着接触范围的增大也迅速增大。

Analysis to Large Deflections of Elastic Cantilever Beam with Constraint under Uniformly Distributed Load

A model for analyzing the large deflection of an elastic cantilever beam with constraint under uniformly distributed load was established. In the model,the deflection of the beam was divided into three stages：the first was a cantilever beam subjected to the uniformly distributed load without any constraint ;the second was a beam subjected to the load with a constraint at the free end,i.e, the beam was subjected to an extra reaction at the free end besides the uniformly distributed load ;the third was a beam subjected to the uniformly distributed load and the reaction with given deflection and angle of rotation over a part of the beam. The boundary conditions of the beam at every stage were given and the three-fold method of bisection was used to solve for the large deflection of the beam at every stage. In the example, the large deflections of the elastic beam at every stage were calculated and the results were compared with those obtained by small deflection theory. It is proven that at the first stage,the relative error by the small deflection theory increases quickly with the increase of the initial gap;at the second stage,the relative error by the small deflection theory has a few increase on the given initial gap; at the third stage, the relative error by the small theory increases quickly with the increase of contact region .