An enhanced global–local higher-order theory for the free edge effect in laminates

According to the double-superposition hypothesis proposed by Li and Liu [Li XY, Liu D. Generalized laminate theories based on double superposition hypothesis. Int J Numer Methods Eng 1997;40:1197–212], an enhanced global–local higher-order theory (EGLHT-mn) is developed to analyze the edge-effect problems in laminates. The in-plane displacement field consists of mth-order (9 ⩾ m ⩾ 3) polynomial in global coordinate z along the thickness direction and order 3 power series in local coordinate ζ within each layer whereas the transverse deflection is represented by a nth-order (9 ⩾ n ⩾ 3) polynomial of global coordinate z. By imposing the free surface conditions and the geometric and the stress continuity conditions at interfaces, the number of variables of the higher-order theory is independent of the number of layers of the laminates. As an improvement to the global–local theory proposed by Li and Liu (1997), the present higher-order theory takes into account all the effects of shear and normal stresses. A three-node triangular element satisfying the requirement of C1 weak-continuity conditions between elements is also presented. Comparing to previous published results, it is found that the present higher-order theory is capable of treating free-edge problems in symmetric and unsymmetric laminates under extension, bending and thermal loading. Other characteristic of the present theory is that transverse shear stresses can be accurately computed directly from the constitutive equations without smoothing. However, to determine transverse normal stresses, the local equilibrium equation approach has to been adopted.