板壳有限变形精确理论及有限元列式

以位移型退化壳理论为基础,提出了板壳模型的有限变形精确理论.该理论引入转动伪矢量概念,充分发挥刚性线段的运动学模型和有限转动矩阵的作用,精确表达非线性位移-应变关系,抛弃以往的小位移、小应变、小转动增量乃至小加载步长等各种简化假设,并严格遵循能量共轭关系建立有限元平衡方程,能够可靠和有效地用于板壳结构的大位移、大转动分析.算例表明,该文列式在弹性范围内具明显的平方收敛效率,并且计算结果与加载步长无关.由于不受小加载步长、小转动增量等的限制,实现了板壳几何非线性问题的大步长加载 .

THE FINITE DEFORMATION THEORY AND FINITE ELEMENT FORMULATION OF PLATE AND SHELL

A finite deformation theory that can precisely describe the nonlinear geometric behavior of plate and shell structures is proposed. By taking full advantage of the kinematic model of a rigid line and finite rotation matrix, the simplification assumptions such as small displacement, small normal or shearing strain, small rotation, as well as small loading step etc. are abandoned. The finite element formulation of this theory is deduced with TL method. Numerical examples show the validity of the theory. With the presented formula, quadratic convergence ratio can always be observed durine elastic simulation and the computed results are independent of loading steps. Being free from constraints of small strain, small rotation increments etc., large loading steps can be adopted for geometrically nonlinear shell problems.