一种准确预测层合梁结构层间剪应力的新锯齿理论

层合梁是航空航天领域典型的承力构件，而过大的层间剪应力（层间处的横向剪应力）是导致其分层失效的主要原因。针对常见的层数较多的复合材料层合梁以及材料属性差异较大的三明治夹层梁，现有的理论模型仍然无法准确预测其横向剪应力。通过构造一个新的线性分段锯齿函数，提出了一种能够准确预测层合梁结构横向剪应力的新锯齿理论模型。几个典型的数值算例表明，本文提出的新锯齿理论模型在计算层数较多和材料属性差异较大的层合梁时，具有较高的计算精度，能够准确预测层合梁的分层。另外，该模型预先满足横向剪应力层间连续条件，无需三维平衡方程后处理就能够准确预测层合梁的横向剪应力。位移场中未知量个数少，不含横向位移的一阶导，便于C⁰梁单元的构造。

A new zig-zag theory for accurately predicting interlaminar shear stress of laminated beam structures

Laminated beams are typical bearing members in the aerospace industry. Excessive interlaminar shear stress (transverse shear stress at the interlayer) is the main cause of delamination failure. The existing laminated beam models can not accurately predict the transverse shear stress for the composite laminated beams with large number of layers and sandwich beams with large differences in material properties. In this study, a new zig-zag theoretical model that can accurately predict the transverse shear stress of laminated beams is proposed by constructing a new linear piecewise zig-zag function. Several typical numerical examples show that the new zig-zag theoretical model has higher calculation accuracy for the composite laminated beams with large number of layers and sandwich beams with large differences in material properties, and can predict the delamination of laminated beams. In addition, the model fulfills a priori the interlaminar transverse shear stress continuous condition at the interfaces and can accurately predict the transverse shear stress of laminated beam without the post-processing of three-dimensional equilibrium equation. The number of unknown variables of this model in displacement field is small. Without the first derivatives of transverse displacement in the displacement field, this model is well suited for developing C⁰ elements.