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

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 layerwise 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 Cz0 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.


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