Explicit relations for the solution of laminated plates modeled by a higher shear deformation theory: Derivation of exponential basis functions

• We present explicit relations for the governing equations in a HSDT.
• Relations for bases functions in laminates with general stacking sequence are given.
• Particularly a set of basis functions are obtained for (0°, 90°, 0°) laminates.
• We explain the way that the bases are to be used in a Trefftz approach.
• A solution with high accuracy is obtainable for laminates with irregular shape.

In this paper we present explicit operators needed for the solution of laminated plates using a higher-order shear deformation theory. Meanwhile we evaluate a set of bases satisfying the governing equations. Once the bases are found, they can be used in a Trefftz approach to solve a variety of laminated plate problems with high accuracy. For the first time we present explicit relations for the evaluation of the exponential basis functions (EBFs) for three-layer plates with (0°, 90°, 0°) stacking sequence while considering a wide range of ratios between the material properties of the layers. The operators needed for other cases are presented. The explicit EBFs and operators we present in this paper may be found vital by those who are interested in using a Zig-Zag theory for the solution of laminated plates in a mesh-free style.