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基于增强型整体-局部高阶理论,构造了四节点四边形单元并分析复合材料自由边拉伸问题。本理论预先满足层合板面内位移和层间应力连续条件及层合板上下自由表面条件,未知变量个数不依赖于层合板的层数。精化四节点四边形单元满足单元间C1弱连续性条件。数值结果表明,基于增强型整体-局部高阶理论构造的四边形单元能够精确分析自由边拉伸问题。层间横向剪切应力能够直接从本构方程中计算得出,而横向法应力则需在一个单元内使用局部三维平衡方程。
Based on the enhanced whole-local high-order theory, a four-node quadrilateral element is constructed and the free edge stretch of the composite is analyzed. The theory pre-satisfies the in-plane displacement and interlaminar stress continuous condition and the upper and lower free surface conditions of the laminate. The number of unknown variables does not depend on the number of layers of the laminate. Refinement of four-node quadrilateral elements satisfies the condition of weak continuity between cells C1. The numerical results show that the quadrilateral elements constructed based on the enhanced whole-local high-order theory can accurately analyze the free edge stretching problem. The lateral shear stress between layers can be calculated directly from the constitutive equation, whereas the transverse stress requires the use of a local three-dimensional equilibrium equation within one cell.