试用有限变形几何场论分析小变形理论的近似性

Study on the Approximation of Small Deformation Theory by Rational Mechanics

一般认为弹性小变形几何方程的近似性是由于忽略了变形的高阶小量而产生的。事实上,用有限变形理论可以揭示小变形几何方程的近似性来自两个方面,即忽略转动和变形高阶小量的影响。

In this paper, the approximations of small elastical deformation theory have been discussed by finite deformation theory. Generally speaking, the approximation of small elastical deformation theory comes from neglecting high-order small quatity. In fact, the rotation effect which is neglected in small deformation theory is also an important approximation for this theory.