Murakami's Zig-Zag Function in conjunction of Green-Lagrange Strain- and Second-Piola Kirchhoff Stress-tensors and Generalized Unified Formulation are introduced for the first time to present a class of Zig-Zag theories for composite structures. Transverse strain effects are retained and modeled, making the present approach also suitable for thick structures. Each displacement variable is independently represented with user-selected order of expansion. The stress recovery is achieved with a special procedure in which combination of deformation gradient and Second-Piola Kichhoff transverse stresses are integrated along the thickness of the undeformed geometry. Comparison with available data and commercial codes indicate the effectiveness of the proposed framework for variable kinematics Zig-Zag theories in the presence of large displacements.

首次引入了村上隆的Zig-Zag函数，结合了Green-Lagrange应变和第二Piola Kirchhoff应力张量以及广义统一公式，提出了一类用于复合结构的Zig-Zag理论。保留并建模了横向应变效应，从而使本方法也适用于厚结构。每个位移变量都由用户选择的扩展顺序独立表示。应力恢复是通过特殊的过程实现的，其中将变形梯度和Second-Piola Kichhoff横向应力的组合沿未变形几何形状的厚度积分。与可用数据和商业代码的比较表明，在存在大位移的情况下，所提出的可变运动学之字形理论框架的有效性。