Free vibration solution of thick plate by using three-dimensional coupled thermoelastic theory

This paper reports on the free vibration solution of a thick plate by using three dimensional coupled thermoelastic theory. Many previously works reveal that the mechanical and thermal are coupled together, which mean that the deformation of the solid will produce temperature variation inside the solid. First, based on the three dimensional coupled thermoelastic theory, the governing equations of the thick rectangular plate for free vibration analysis are derived. Unlike the traditional first order or third order shear deformation theory with which the deformations along the thick direction are described by the deformations of the middle surface, a new form which use functions to describe the deformations along plate thick direction (the z direction) is presented in this paper. Galerkin method and Laplace transform are applied to convert the governing equations into a series of first order ordinary differential equations as well as the boundary conditions to obtain the closed solution of the coupled thermoelastic rectangular plate. The Newton iterative method is applied to solve the eigenfunction. Finally, a thick plate with four edges simply supported has been investigated by using the proposed method. Eigensolutions and the damping effects of the plate with thermoelastic coupling are investigated by numerical example

Nonlinear post-buckling of thin FGM annular spherical shells under mechanical loads and resting on elastic foundations

This paper presents an analytical approach to investigate the nonlinear buckling and post-buckling of thin annular spherical shells made of functionally graded materials (FGM) and subjected to mechanical load and resting on Winkler-Pasternak type elastic foundations. Material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and compatibility equations for annular spherical shells are derived by using the classical thin shell theory in terms of the shell deflection and the stress function. Approximate analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain closed-form of load-deflection paths. An analysis is carried out to show the effects of material and geometrical properties and combination of loads on the stability of the annular spherical shells

Thermal stresses in closed spherical shells

The purpose of this work is to discuss thermal stresses in closed spherical shells. This effort is further limited to linear thermoelastic stresses in thin shells. The basic concepts associated with three-dimensional continuum mechanics are presented in both direct and general tensor notation. The three-dimensional equations are reduced to the two-dimensional equations of shells under going finite displacements. These are subsequently reduced to those pertaining to spherical shells. A review of the recent literature associated with thermal stresses in spherical shells is included. An appendix is provided which reviews some of the basic elements of general tensors

On local strength of a spherical vessel with pits distributed along the equator

The effect of multiple shallow corrosion pits on the strength of a spherical vessel subjected to internal pressure is studied. The pits are considered both randomly and evenly distributed along the equator on the outer surface of the vessel. The dependencies of the stress concentration factor on the number of the pits are compared for linearly elastic and elastic-plastic material with hardening. The behavior of the vessels made of elastic and elastoplastic materials turns out to be qualitatively different. The approximation of periodic pits arrangement is discussed

Mechanics of Micro- and Nano-Size Materials and Structures

For this reprint, we intend to cover theoretical as well as experimental works performed on small scale to predict the material properties and characteristics of any advanced and metamaterials. New studies on mechanics of small-scale structures such as MEMS/NEMS, carbon and non-carbon nanotubes (e.g., CNTs, Carbon nitride, and Boron nitride nanotubes), micro/nano-sensors, nanocomposites, macrocomposites reinforced by micro-/nano-fillers (e.g., graphene platelets), etc., are included in this reprint