中文摘要：

研究了具有点间隙约束的两端不可移弹性梁在湿热载荷作用下的后屈曲行为.基于轴向可伸长Euler-Bernoulli梁的几何非线性理论和线性湿热膨胀假设,建立了湿热环境中工作的弹性梁在点间隙约束下的后屈曲大变形控制方程.其中包含了变形后的轴线弧长、轴线的位移、横截面转角、等效内力和弯等七个基本未知函数.假设点间隙约束位于梁的中点附近,并且间隙值是在梁的湿热后屈曲变形范围之内.分别考虑了两端不可移简支（pinned-pinned）和两端固定（fixed-fixed）两种边界条件.采用打靶法数值求解所得强非线性两点边值问题,获得了均匀湿热载荷下梁的湿热后屈曲响应.着重分析了梁的中心点挠度达到给定间隙值而受到点约束后的湿热后屈曲变形和内力的变化特性,给出了与中点约束力相关的平衡构形和平衡路径曲线.

英文摘要：

Post-buckling behavior of elastic beams with immovable ends and a point space-constraint under hygrothrrmal loadings were studied.Based on the geometrically nonlinear theory and linear hygrathermal strain-temperature and humidity relation for the axial extensional Euler-Bernoulli beams,governing equations for large post-buckling deformation of the elastic beams with a point space-constraint and subjected to temperature and humidity rising were formulated,in which seven basic unknown functions,such as the arc length of the deformed axial line,the line displacement components,the rotational angle of the cross-section,the internal resultant forces and moment,were included.It is assumed that the point-space constraint be around the middle point of the beam and the space value be in the range of hygrothermal post-buckling deformation.Boundary conditions at the two ends of the beam were considered to be immovably simply supported（pinned-pinned） and fixed（fixed-fixed）,respectively.By using shooting method to solve the above mentioned strong nonlinear two-point boundary value problem numerically,hygrothermal post-buckling response of the beam under uniform increment both in temperature and humidity were obtained.Especially,changes in the characteristics of the hygrothermal post-buckling deformation and the internal forces of the beam after its middle point deflection reaches the gap value and at the same time the constraint force arises.Curves of equilibrium paths and configurations of the beams depending on the middle point space-constraint force were presented.