有限位移理论的功的互等定理及其应用

提出了有限位移理论三维线弹性力学的功的互等定理.基于这一定理，导出了大挠度弯曲矩形板的功的互等定理.同时，应用简化矩形板的定理，直接得到了大挠度板条的功的互等定理.作为应用，计算了在均载作用下两端固定大挠度板条的弯曲和在均载作用下4边固定大挠度矩形板的弯曲.计算表明，根据弯曲薄板大挠度功的互等定理，大挠度弯曲矩形板可应用小挠度的相应基本解得以简单解决.

The Reciprocal Theorem for the Finite Displacement Theory and Its Applications

The reciprocal theorem of 3D linear elasticity for the finite displacement theory was proposed. On the basis of the theorem, the reciprocal theorem of rectangular plates in large defection was derived. Meanwhile, the reciprocal theorem of plate strips in large deflection was directly obtained through simplification of the theorem of the rectangular plates. For applications, the bending of a plate strip in large deflection with 2 ends fixed under uniformly distributed load and the bending of a rectangular plate in large deflection with 4 edges fixed under uniformly distributed load were calculated. The calculation shows, on the basis of the reciprocal theorem of bending thin plates in large deflection, the bending rectangular plates in large deflection can easily be sovled with the aid of the basic solution corresponding to the small deflection case.