Optimized sinusoidal higher order shear deformation theory for the analysis of functionally graded plates and shells

The optimization of the sinusoidal higher order shear deformation theory (HSDT) for the bending analysis of functionally graded shells is presented in this paper for the first time. The HSDT includes the stretching effect and their shear strain shape functions (sin(mz) and cos(nz)) contain the parameters “m” and “n” that need to be selected by providing displacements and stresses which produce close results to 3D elasticity solutions. The governing equations and boundary conditions are derived by employing the principle of virtual work. A Navier-type closed-form solution is obtained for functionally graded plates and shells subjected to transverse load for simply supported boundary conditions. Numerical results of the optimized sinusoidal HSDT are compared with the FSDT, other quasy-3D hybrid type HSDTs, reference solutions, and 3D solutions. The key conclusions that emerge from the present numerical results suggest that: (a) the optimization procedure is beneficial in terms of accuracy; and (b) it is possible to gain accuracy keeping the unknown's constant by performing the optimization procedure shown in this paper.