Abstract In the present research, a unified semi-analytical solution that incorporates influence of the auxeticity (negative Poisson ratio) of the material into elastic responses of the variable thickness functionally graded conical and cylindrical shells and circular/annular plates is developed. The top or bottom layers of the shell/plate may be subjected to general non-uniform normal and shear tractions. The mentioned material and loading complexities have not been investigated before and consequently, the presented comprehensive results are quite new. The proposed unified formulation is developed using the principle of minimum total potential energy and solved using Taylor’s transform, for some combinations of the simply supported, clamped and free edge conditions. Accuracy of results of the proposed unified solution is verified by results of the three-dimensional theory of elasticity extracted from the ABAQUS finite element analysis code. Finally, a comprehensive parametric study including evaluation of individual/simultaneous effects of the auxeticity, structure configuration, shear/normal traction, thickness variability, and boundary conditions on the resulting lateral deflection and in-plane stress distributions of the considered shell and plate structures is accomplished.

Abstract Effects of viscoelastic substrates on the sandwich structures oscillations are examined in this paper. In this regard, dynamic response of sandwich annular panels with FG polar orthotropic face sheets resting on viscoelastic substrate is presented. Young’s modulus in the radial and circumferential direction, shear modulus and density of each face sheet may be varied continuously in the radial direction. The viscoelastic substrate is modeled as Kelvin-Voigt foundation. To describe more accurately response of sandwich structures, the governing dynamical equations are derived based on the layerwise theory and five systems of second order coupled partial differential equations are obtained. The effects of the stiffness and damping coefficients of the foundation on the dynamic behavior of sandwich plate are investigated for various transient loads and boundary condition. Since no available results may be found in literature to demonstrate the efficiency and accuracy of the obtained results, the obtained results are verified by comparison with finite element results based on the three dimensional theory of elasticity for some special cases.

AbstractThe available shear correction factors have mainly been proposed for single-layer rectangular plates with zero shear tractions and isotropic homogenous materials. The present analytical shear factors are especially suitable for the first-order zigzag or layerwise theories of circular sandwich plates with functionally graded cores/face sheets and simultaneous normal and shear tractions. Although the present layerwise correction factors are general, they are evaluated for the modal analyses where effects of the shear correction are more remarkable than those of the stress analyses. It is the first time that the concept of the local shear correction factor is introduced. To present more accurate results, the Mori-Tanaka micromechanical-based material properties model is used instead of the traditional rule of mixtures. The governing equations are solved using the analytical Taylor transform method. Comparisons made among results associated with the known shear correction factors, present results, and results of the three-dimensional theory of elasticity reveal that significant enhancements may occur through using the proposed analytical shear correction factors.