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A new general third-order zigzag model for asymmetric and symmetric laminated composite beams

机译：用于非对称层压梁的新的三阶Z字形模型

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摘要

This paper proposes a new third-order zigzag model for asymmetric and symmetric laminated composite beams. In the framework of a general displacement form, a new zigzag shear strain shape function with layer-wise coefficients corresponding to constant, linear, quadratic and cubic terms is proposed. By comparing transverse shear stress fields obtained by constitutive and equilibrium equations respectively, layerwise constants of quadratic and cubic terms are determined. With further consideration of interlaminar continuity and free stress conditions on traction free surfaces, other coefficients are achieved. As interlaminar continuity and dissimilar characteristics between layers are fully considered, the present model which has only three unknowns can accurately describe zigzag effects and provide C-z(0) quadratic distribution results of transverse shear stress field by constitutive equations directly. Characteristics and advantages of the present model are discussed by comparing with other classical theoretical models. Moreover, governing equations are formulated using the principle of minimum potential energy, and analytical and finite element solutions for static analysis of laminated beams are presented. Lastly, numerical validations are presented, and comparisons with exact solutions, other theoretical models and high-fidelity finite element models well demonstrate accuracy and effectiveness of the present model for laminated beams with different features.
机译：本文提出了一种新的非对称和对称层压复合梁的三阶Z字形模型。在一般位移形式的框架中，提出了一种新的Zigzag剪切应变形状，其具有对应于恒定，线性，二次和立方术语的层性系数。通过分别比较通过组成型和平衡方程获得的横向剪切应力场，确定二次和立方术语的层常数。随着对无牵引表面上的间隔连续性和自由应激条件的进一步考虑，实现了其他系数。作为层间连续性和层之间的不同特性被完全考虑，目前具有三个未知数的本模型可以准确地描述Zigzag效果并直接通过组成型方程提供横向剪切应力场的C-Z（0）二次分布结果。通过与其他古典理论模型进行比较讨论本模型的特征和优点。此外，使用最小势能原理配制了控制方程，并提出了用于层叠光束的静态分析的分析和有限元解。最后，提出了数值验证，以及精确解决方案的比较，其他理论模型和高保真有限元模型良好地证明了本发明模型的具有不同特征的层压光束的准确性和有效性。

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