中文摘要：

基于Euler—Bernoulli梁的精确几何非线性理论，考虑轴线可伸长的条件下，两端固支弹性杆件受纵向均布荷载作用的几何非线性静平衡控制方程，并将其化为无量纲的微分方程组，应用打靶法数值分析了杆的非线性弯曲和轴线上各质点位移变化问题。给出了杆轴线各质点位移、杆端转角、轴线伸长以及中心截面的轴力随均布载荷和杆长细比变化的特性曲线，分析和讨论了这些参数对杆变形的影响以及参数间的关系。数值结果表明：在固端到反弯点范围，由于轴线的伸长杆上各质点的水平移动移向反弯点方向，移动趋势先增大再减小呈对称型，而在反弯点到杆中范围内，随着轴线伸长逐渐加大，杆上各质点的水平移动方向相反，也逐渐先增大再减小呈对称型。杆的挠曲线反弯点位置约在杆的1／5处，不随杆的长细比或荷载的变化而改变。在杆半跨范围内，杆端转角曲线并非对称。

英文摘要：

Based on Euler-Bernoulli beam precise geometric nonlinear theory of extensible rods, the static equilibrium equations of elastic rods clamped at both ends were established under vertical uniformly distributed load and turned into dimensionless differential equations. By using a shooting method, the problems about nonlinear bending of rods and displacement of each particle were analyzed numerically. Characteristic curves of displacement of each particle on the axis, rod end angle, axial elongation and the force of the axial center section under different uniform load and slenderness ratio were plotted. The influence of these parameters on the deformation of rods and the relationship between these parameters were analyzed and discussed. The numerical results show that as a result of the axial elongation, stem horizontal displacement of each particle first moves to rod inflection point between fixed end and the rod inflection point, the moving trend increases first and then decreases in a symmetrical type, while with the increase of axial elongation, each particle of the rods between rod inflection point and the middle of the rods moves back to the rod inflection point, also gradually increases first and then decreases in a symmetrical type. The rod inflection point of deflection curve is at about 1/5 of the rod, the rod inflection point does not vary with changes of slenderness ratio and load. Within the scope of the rod and a half across, rod end rotation curve is not symmetrical. In half cross-rod, the rod end angle curve is not symmetrical.