Abstract
In this paper the special higher-order global–local theories including the mth-order polynomial of global thickness coordinate z and 1, 2-3 order power series of local thickness coordinate ζ k are studied. These theories satisfy the free surface conditions and the geometric and stress continuity conditions at interfaces. Moreover, the number of unknowns is independent of the layer numbers of the laminate. Main aim of this paper is to study the relationship between the order of the global component in mth-order theory and the accuracy of solution. Numerical solutions show the third-order global–local higher-order theory (namely 1, 2-3 double-superposition theory called by Li and Liu [Li X, Liu D. Generalized laminate theories based on double-superposition hypothesis. Int J Numer Meth Eng 1997;40:1197–212] will encounter difficulties when accurately predicting transverse shear stresses as the number of layers of laminated plates is more than five. In particular, the accuracy of this theory drops when used for non-symmetric multilayered plates. However, other higher-order global–local theories can present reasonable in-plane stresses and transverse shear stresses by the direct constitutive equation approach. Neglecting transverse normal strains in the present global–local theories, the transverse normal stresses can be only predicted from equilibrium equation approach.
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