Nonlinear stability of advanced sandwich cylindrical shells comprising porous functionally graded material and carbon nanotube reinforced composite layers under elevated temperature

The nonlinear stability of sandwich cylindrical shells comprising porous functionally graded material(FGM) and carbon nanotube reinforced composite(CNTRC)layers subjected to uniform temperature rise is investigated. Two sandwich models corresponding to CNTRC and FGM face sheets are proposed. Carbon nanotubes(CNTs) in the CNTRC layer are embedded into a matrix according to functionally graded distributions. The effects of porosity in the FGM and the temperature dependence of properties of all constituent materials are considered. The effective properties of the porous FGM and CNTRC are determined by using the modified and extended versions of a linear mixture rule, respectively. The basic equations governing the stability problem of thin sandwich cylindrical shells are established within the framework of the Donnell shell theory including the von K’arm’an-Donnell nonlinearity. These equations are solved by using the multi-term analytical solutions and the Galerkin method for simply supported shells.The critical buckling temperatures and postbuckling paths are determined through an iteration procedure. The study reveals that the sandwich shell model with a CNTRC core layer and relatively thin porous FGM face sheets can have the best capacity of thermal load carrying. In addition, unlike the cases of mechanical loads, porosities have beneficial effects on the nonlinear stability of sandwich shells under the thermal load. It is suggested that an appropriate combination of advantages of FGM and CNTRC can result in optimal efficiency for advanced sandwich structures.

Nonlocal isogeometric analysis for bidirectional functionally graded porous curved microbeams with arbitrary boundary conditions

This research aims to analyze the static bending and free vibration behaviors of bidirectional functionally graded porous(BFGP)curved microbeams with elastic boundary conditions resting on a Pasternak’s elastic foundation in a hygro-thermal environment.Isogeometric analysis based on non-uniform rational B-splines,first-order shear deformation theory,nonlocal elasticity theory combined with the modified strain gradient theories,modified Timoshenko beam theory are formulated to depict bending and shear deformations of BFGP curved microbeams.Especially,because using the modified Timoshenko beam theory,this study removes the requirement for a shear correction factor and describes shear stress by zero at the upper and lower cross-sectional sites of the BFGP curved microbeam.Different from traditional boundary conditions,where the beginning and end positions of a curved beam are connected by an elastic system of straight and torsion springs.This allows for greater flexibility in controlling the stiffness of the springs to obtain arbitrary boundaries.To assess the accuracy and convergence of the proposed approach,validation numerical examples were conducted in the various examples.

Free vibration analysis of functionally graded porous curved nanobeams on elastic foundation in hygro-thermo-magnetic environment

Herein,a two-node beam element enriched based on the Lagrange and Hermite interpolation function is proposed to solve the governing equation of a functionally graded porous(FGP)curved nanobeam on an elastic foundation in a hygro–thermo–magnetic environment.The material properties of curved nanobeams change continuously along the thickness via a power-law distribution,and the porosity distributions are described by an uneven porosity distribution.The effects of magnetic fields,temperature,and moisture on the curved nanobeam are assumed to result in axial loads and not affect the mechanical properties of the material.The equilibrium equations of the curved nanobeam are derived using Hamilton’s principle based on various beam theories,including the classical theory,first-order shear deformation theory,and higher-order shear deformation theory,and the nonlocal elasticity theory.The accuracy of the proposed method is verified by comparing the results obtained with those of previous reliable studies.Additionally,the effects of different parameters on the free vibration behavior of the FGP curved nanobeams are investigated comprehensively.

A deep energy method for functionally graded porous beams

We present a deep energy method(DEM)to solve functionally graded porous beams.We use the EulerBernoulli assumptions with varying mechanical properties across the thickness.DEM is subsequently developed,and its performance is demonstrated by comparing the analytical solution,which was adopted from our previous work.The proposed method completely eliminates the need of a discretization technique,such as the finite element method,and optimizes the potential energy of the beam to train the neural network.Once the neural network has been trained,the solution is obtained in a very short amount of time.