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A dislocation solution to evaluate the mode III stress intensity factors (SIFs) of the crack tips, torsional rigidity and the hoop stress around the cavities in an infinite rectangular cross-section bar coated by an FG layer under torsion is developed based on the Saint–Venant theory. The solution of the rectangular cross section with the FG coating weakened by a screw dislocation under torsion was first obtained in terms of the dislocation density function. Then, the problem is transformed into a group of Cauchy integral equations in the rectangular cross-section bar with the FG coating layer via the distributed dislocation approach. The singular integral equations are reduced to a set of algebraic equations to evaluate them numerically. After solving the integral equations, the SIFs of the crack tips, the hoop stresses around the cavities and the torsional rigidity of the entire domain are found. The obtained solution is validated by performing comparison studies in multiple cases. It is shown that the interaction between the cracks, the cracks length, variation of the shear module of the FG coating layer and distance of the crack tips from stress-free surfaces can significantly affect the SIFs of crack tips and torsional rigidity of the rectangular cross-section bar coated by an FG layer.

A nonlinear finite element model based on the modified strain gradient theory (MSGT) in combination with the first-order shear deformation theory (FSDT) of shells for the free vibration of multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) toroidal micropanels is developed. The nine-noded shell elements with five degrees of freedom per node are used to accurately simulate thin as well as moderately thick toroidal micropanels without shear locking phenomena. In addition to initial thermal stresses, the influences of nonlinear elastic foundation and the elastic rotational springs at the micropanel edges are considered. The formulation and corresponding computer codes are validated by performing convergence study and doing comparison studies with some existing results in the literature. Then, the impacts of amplitude ratio, geometric parameters, ratio of thickness-to-material length scale parameter (MLSP), temperature rise, coefficients of elastic foundation and rotational springs, and different GPLs distribution patterns on the nonlinear vibrational behaviors of the multilayer FG-GPLRC toroidal micropanels are investigated. The results show that the size dependence of material properties increases the impact of geometric nonlinearity on the vibrational behavior of the micropanels. In addition, it affects the nonlinear vibrational behavior more than the linear one in a widespread range of thickness-to-MLSP ratio.

Large deformation of a horizontally uniform cantilevered Euler-Bernoulli beamshell subjected to its own weight is studied. The governing equation for the first time is analytically solved using the analytical technique for nonlinear problems Homotopy Analysis Method (HAM). A series solution is presented that can be used for the analysis of beamshells undergoing large deformations with wide range of weight, material/cross section properties and lengths. The results obtained by HAM are compared with the results reported in the previous works, and good agreement is found. Finally, the load-displacement characteristics of a uniform cantilever beamshell under different load conditions, dimensionless weight parameter are presented.