基于一种简化Green应变的薄壳大挠度方程

LARGE DEFLECTION EQUATIONS OF THIN SHELLS BASED ON THE SIMPLIFIED GREEN STRAIN

将正交曲线坐标下的格林应变张量引入到薄壳大变形分析,通过建立恰当的基本假设,直接导出了用格林应变张量表示的壳体变形几何方程,将该方程代入到本构方程,由能量原理得到了小应变非线性变形平衡方程、内力方程和边界条件,在此基础上提出了大应变变形的简化分析方法.文中导得的方程涵盖薄板壳大、小变形的全部方程,推导过程简捷、系统,所得结果规则、清晰,与此前有关分析方法的结果完全吻合.

By introducing reasonable fundamental assumptions and the Green strain in orthogonal curvilinear coordinates, geometric equations expressed by the Green strain tensor for solving thin shells with large deformation are derived in this paper. Applying energy principle, the equations of equilibrium and physical equations as well as boundary conditions of shells with nonlinear deformation at small strain are obtained. The equations can result in all the governing equations of thin plates and shells with nonlinear or linear deformation. The results obtained in this paper agree well with the previous results.