论连续体有限变形的位移协调条件

On the Compatibility Condition of Displacement Field for Finite Deformation of Continuum

有限变形的协凋条件在文献中常以Riemann-Christoffel张量等于零表达.水文应用Cesaro方法和作者的非线性应变-转动张量分解定理证明上述条件仅是必要的,尚不充分保证位移场的单值性与连续;文中导出新的一般有限变形的位移协调条件.当应变与转动微小时,它化为Saint-Venant方程。

The vanishing of Riemann-Christoffel tensor is usually adopted as the compatibility condition of finite deformation. However, we prove in this paper by the method of Cesaro that this condition is necessary but not sufficient for the guarantee of single-valued, continuous displacement field. A new general compatibility condition,based on theorem of strain-rotation decomposition (Chen [4]) is derived The displacement compatible condition reduces to Saint-Venant s condition when strain and rotation are infinitesimal.