A review of the analysis of sandwich FGM structures

On the finite element analysis of functionally graded sandwich curved beams via a new refined higher order shear deformation theory

In the present work, an attempt has been made to carry out the bending analysis of sandwich FGM beams under combined hygro-thermo-mechanical loadings. Temperature and moisture-dependent material pr...

Hygro-thermo-mechanical based bending analysis of symmetric and unsymmetric power-law, exponential and sigmoidal FG sandwich beams

This research work is focused on the buckling analysis of functionally graded (FG) curved sandwich beams using an effective and simple three-unknown refined shear theory. Unlike the first shear deformation theory and higher-order shear deformation theory, this theoretical formulation only has three unknowns. This feature makes the formulation computationally faster to solve. It also provides a clear advantage over the classical plate theory since it considers the shear deformation effect in spite of having three unknowns. The present theory accounts for a new parabolic distribution of transverse shear stress through thickness direction and satisfies the traction-free boundary conditions needless of any shear correction factor. In this present study, the FG modeling encompasses a single layer and two kinds of sandwich beams: one composed of a homogeneous core with FG face sheets, and another made up of homogeneous face sheets with FG core. On the basis of the proposed kinematic model, a new efficient Hermite–Lagrangian finite element formulation is successfully developed to determine accurately the critical buckling loads of FG curved sandwich beams. The governing equations are derived by employing the principle of virtual works and solved by means of the finite element method. The accuracy and effectiveness of the proposed model are demonstrated by comparing the present results with those available in the literature. The results indicate that the developed finite element model is promising in terms of accuracy and fast rate of convergence for both thin and thick FG sandwich beams. Moreover, a detailed numerical study is carried out to examine the effects of the boundary conditions, power-law index, radii of curvature, length-to-height ratio and face-core-face thickness ratio on the buckling response of FG sandwich beams. Such parametric analysis can serve as a basis for engineering solutions in the context of FG sandwich curved beams.

A three-unknown refined shear beam element model for buckling analysis of functionally graded curved sandwich beams

This article presents the static analysis of FG sandwich beams curved in elevation. Navier-type semi-analytical solutions are obtained based on polynomial type fifth order shear and normal deformation theory. The beam has FG skins and isotropic core. Material properties of FG skins are graded in z-direction according to the power-law distribution. The present theory accounts for a fifth-order distribution of axial displacement and fourth-order distribution of transverse displacement. The present theory considers the effect of thickness stretching and gives a realistic variation of transverse shear stress through the thickness of the beam. The governing equations are obtained within the framework of the principle of virtual work. Semi-analytical static solutions for the simply supported FG sandwich beams curved in elevation are obtained using Navier’s technique. The beam is subjected to uniformly distributed load. The non-dimensional numerical values for displacements and stresses are obtained for various power-law index and thickness of the core. The present results are found in good agreement with previously published results.

On the static deformation of FG sandwich beams curved in elevation using a new higher order beam theory

This article presents Navier type closed-form solutions for static bending, elastic buckling and free vibration analysis of symmetric functionally graded (FG) sandwich beams using a hyperbolic shear deformation theory. The beam has FG skins and isotropic core. Material properties of FG skins are varied through the thickness according to the power law distribution. The present theory accounts for a hyperbolic distribution of axial displacement whereas transverse displacement is constant through the thickness i.e effects of thickness stretching are neglected. The present theory gives hyperbolic cosine distribution of transverse shear stress through the thickness of the beam and satisfies zero traction boundary conditions on the top and bottom surfaces of the beam. The equations of the motion are obtained by using the Hamilton’s principle. Closed-form solutions for static, buckling and vibration analysis of simply supported FG sandwich beams are obtained using Navier’s solution technique. The non-dimensional numerical results are obtained for various power law index and skin-core-skin thickness ratios. The present results are compared with previously published results and found in excellent agreement.

http://jsm.iau-arak.ac.ir/article_664227_008bb7e3e1a8208dd0730276194d4920.pdf

On Static Bending, Elastic Buckling and Free Vibration Analysis of Symmetric Functionally Graded Sandwich Beams

Due to the availability of limited literature on functionally graded porous circular beams, the static deformation and free vibration analysis of simply supported functionally graded porous circular beams considering the effects of even and uneven porosities are presented in this paper. The Navier type closed-form solutions are obtained for both static and vibration problems within the framework of the higher-order hyperbolic circular beam theory. The theory considers the effects of transverse shear deformation and rotary inertia. The theory satisfies the transverse shear-stress free boundary conditions at the upper and lower surfaces of the beam. The circular beam is made up of the functionally graded material in which material characteristics vary across the thickness direction using the power-law technique which has been adjusted to approximate the porosity effects with even and uneven distributions. A dynamic version of the virtual work principle is employed to derive the governing differential equations of motion, which are then solved analytically using the Navier solution technique. The non-dimensional values of displacements, stresses, and fundamental frequencies are presented for various values of the power-law index ( p i ), the radius of curvature ( R ), porosity volume fraction (α), and type of porosity distribution (even and uneven). The present results are compared in few problems with existing literature and found in good agreement with those. This study also highlights some new results for the reference of future researchers, especially on circular beams. 

Pravin V. Avhad

Papers

On the static deformation of FG sandwich beams curved in elevation using a new higher order beam theory

On Static Bending, Elastic Buckling and Free Vibration Analysis of Symmetric Functionally Graded Sandwich Beams

On the static deformation and frequency analysis of functionally graded porous circular beams

Static analysis of functionally graded composite beams curved in elevation using higher order shear and normal deformation theory

On the deformation of laminated composite and sandwich curved beams