板壳有限变形精确理论及有限元列式  

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

作　　者：詹福良[1] 李明瑞[2] 杨嘉陵[1] 黄文彬[2] 

机构地区：[1]北京航空航天大学固体力学研究所,北京100083 [2]中国农业大学东校区工程基础科学部,北京100083

出　　处：《固体力学学报》2001年第4期343-350,共8页Chinese Journal of Solid Mechanics

摘　　要：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 。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.

关 键 词：有限变形 非线性有限元 板壳 有限转动 TL算法 位移型退化壳理论 大步长加载 平方收敛效率 几何非线性 

分 类 号：O343.5[理学—固体力学]