Effects of higher-order global–local shear deformations on bending, vibration and buckling of multilayered plates

In this paper, the effects of higher-order shear deformations on bending, natural frequencies and buckling loads of multilayered plates are studied. Based on the power series expansion of displacement components along thickness coordinate z and the double-superposition hypothesis proposed by Li and Liu [Li XiaoYu, Liu D. Generalized laminate theories based on double superposition hypothesis. Int J Numer Meth Eng 1997;40:1197–212], the mth-order global–local theory which satisfies the free surface conditions and the geometric and transverse shear stress continuity conditions at interfaces is presented. A refined four-node quadrilateral element is proposed for the numerical modeling of the global–local theory. In the process of finite element implementation, both the first and the second derivatives of transverse displacement w appear in the strain components. Transverse displacement functions satisfying C0 and C1 weak-continuity between elements are derived based on the refined element methods. Numerical results show that the transverse shear stress of multilayered plates, the natural frequency and the buckling loads of soft-core sandwich plates predicted by the proposed models of higher-order shear deformation are more accurate in comparison with the results based on the third-order global local theory and other lower order theories.