在大跨度空间结构、高层建筑和桥梁等工程中，隔震橡胶支座端部的柔性约束或倾斜对其力学性能和稳定性有着显著影响。基于支座两端有任意转角和相对位移的理论，并结合固端约束条件下的试验结果进行非线性响应分析。研究发现：在特定状态下支座水平位移的理论解和试验结果高度一致。继而，通过在四种边界条件下对支座进行对比分析，进一步探讨了支座在最不利边界条件下的力学性能。分析表明：随着顶部转角的增大，支座顶部弯矩由抗倾覆变为倾覆弯矩。此外，支座P-Δ（轴压-水平位移）效应为：随着轴压的增加，支座倾覆临界角增加。然而，无论是顶部转角还是轴压增加，均会导致支座内力增大、变形加剧以及水平刚度下降，尤其是底部弯矩的显著增加，容易引起支座内部橡胶局部破裂，从而导致支座整体的失稳。

In the engineering of large-span space structures, high-rise buildings and bridges, the flexible restraint or tilt of the end of the seismic isolation rubber bearing has a significant effect on its mechanical properties and stability. Based on the theory that the two ends of the bearing have arbitrary turning angle and relative displacement, and combined with the test results under the solid end constraint condition for nonlinear response analysis. It is found that the theoretical solution and the test results are highly consistent with the horizontal displacement of the bearing in a specific state. Following that, the mechanical properties of the bearing under the most unfavourable boundary conditions are further explored by comparing the bearing under four boundary conditions. The analyses show that the top moment of the bearing changes from anti-tilting to tilting moment with the increase of the top turning angle. In addition, the bearing P-Δ effect is that the critical angle of bearing overturning increases with the increase of axial pressure. However, both the increase of top angle and axial pressure will lead to the increase of internal force, deformation and decrease of horizontal stiffness of the bearing, especially the significant increase of the bottom bending moment, which will easily cause the local rupture of rubber inside the bearing, thus leading to the instability of the bearing as a whole.