A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams

This paper presents a nonlocal sinusoidal shear deformation beam theory for the bending, buckling, and vibration of nanobeams. The present model is capable of capturing both small scale effect and transverse shear deformation effects of nanobeams, and does not require shear correction factors. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion as well as the boundary conditions of the beam are derived using Hamilton’s principle. Analytical solutions for the deflection, buckling load, and natural frequency are presented for a simply supported beam, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory. The comparison firmly establishes that the present beam theory can accurately predict the bending, buckling, and vibration responses of short nanobeams where the small scale and transverse shear deformation effects are significant

Bending and vibration of functionally graded material sandwich plates using an accurate theory

In this paper, the bending and the free flexural vibration behaviour of sandwich functionally graded material (FGM) plates are investigated using QUAD-8 shear flexible element developed based on higher order structural theory. This theory accounts for the realistic variation of the displacements through the thickness. The governing equations obtained here are solved for static analysis considering two types of sandwich FGM plates, viz., homogeneous face sheets with FGM core and FGM face sheets with homogeneous hard core. The in-plane and rotary inertia terms are considered for vibration studies. The accuracy of the present formulation is tested considering the problems for which three-dimensional elasticity solutions are available. A detailed numerical study is carried out based on various higher-order models to examine the influence of the gradient index and the plate aspect ratio on the global/local response of different sandwich FGM plates.Comment: 28 pages, 6 figures, 9 table

Hygrothermal analysis of heterogeneous piezoelectric elastic cylinders

The analytical solutions of hygrothermal effects in heterogeneous piezoelectric solid and hollow cylinders are obtained. The interaction of electric displacement, electric potentials, and elastic deformations is discussed. The present cylinder is subjected to a mechanical load at its lateral surfaces as well as an electric potential. The displacement, stresses and electric potentials in the heterogeneous piezoelectric cylinders are determined. The material properties coefficients of the present cylinder are assumed to be changed in the radial direction. The hygrothermoelastic responses of piezoelectric heterogeneous hollow and solid circular cylinders are presented. Numerical application examples for both cylinders are displayed. The significant of influence of material inhomogeneity, initial temperature, final moisture, and the pressure load and electric potential ratios are investigated. Suitable discussions and conclusions are presented

A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates

A new sinusoidal shear deformation theory is developed for bending, buckling, and vibration of functionally graded plates. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed sinusoidal shear deformation theory contains only four unknowns and has strong similarities with classical plate theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton’s principle. The closed-form solutions of simply supported plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the bending, buckling, and vibration responses of functionally graded plates

Nonlocal thermoelastic vibrations for variable thermal conductivity nanobeams due to harmonically varying heat

This article constructs a new model of nonlocal thermoelasticity beam theory with phase-lags considering the thermal conductivity to be variable. A nanobeam subjected to a harmonically varying heat is considered. The nonlocal theories of coupled thermoelasticity and generalized thermoelasticity with one relaxation time can be extracted as limited and special cases of the present model. The effects of the variable thermal conductivity parameter, the nonlocal parameter, the phase-lags and the angular frequency of thermal vibration on the lateral vibration, the temperature, the displacement, and the bending moment of the nanobeam are investigated

Free vibration analysis of doubly convex/concave functionally graded sandwich beams

This paper presents the highly accurate analytical investigation of the natural frequencies for doubly convex/concave sandwich beams with simply-supported or clamped-supported boundary conditions. The present sandwich beam is made of a functionally graded material composed of metal and ceramic. The properties are graded in the thickness direction of the two faces according to a volume fraction power-law distribution. The bottom surface of the bottom face and the top surface of the top face are both metal-rich material. The core is made of a fully ceramic material. The thickness of the sandwich beam varies along its length according to a quadratic-law distribution. Two types of configuration with doubly convex and doubly concave thickness variations are presented. The governing equation and boundary conditions are derived using the dynamic version of the principle of minimum of the total energy. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effect of configurations of the constituent materials on the frequencies. Natural vibration frequencies of sandwich beams versus many parameters are graphically presented and remarking conclusions are made

Effects of Porosity, Rotation, Thermomagnetic, and Thickness Variation on Functionally Graded Tapered Annular Disks

This paper presents a study on porous functionally graded piezoelectric (FGP) annular disks. The paper discussed the magneto-electric-hygrothermal effects on rotating variable thickness porous FG annular disks. Material properties coefficients and magnetic permeability are changed in a power function of radius. The disk is subjected to various loading of a uniform magnetic field, hygrothermal effect, and variation of electric potentials and mechanical pressure on the disk. A semi-analytical technique is used to get the mathematical solution of the rotating annular disk. Numerical outcomes are provided to examine the porosity factor and grading index on the rotating of the disk by different four sets of boundary conditions. The results offered a comparison between the porous and non-porous annular disks with various boundary conditions. Finally, the mathematical solution is beneficial to the planning and manufacture of a rotating porous disk influenced by complex loading and conditions

Axiomatic/asymptotic evaluation of multilayered plate theories by using single and multi-points error criteria

AbstractThis paper deals with refined theories for multilayered composites plates. Layer-Wise (LW) and Equivalent Single Layer (ESL) theories are evaluated by means of axiomatic–asymptotic approach. Theories with forth order displacement fields in the thickness layer/plate direction z are implemented by referring to the Unified Formulation by Carrera. The effectiveness of each term of the made expansion is evaluated by comparing the related theories with a reference solution. As a result a reduced model is obtained which preserve the accuracy of the full-model (model that include the whole terms of the z-expansion) but it removes the not-significant terms in the same expansion (those terms that do no improve the results according to a given error criteria). Various single-point and multi-point error criteria have been analyzed and compared in order to establish such an effectiveness: error localized in an assigned point along z, error localized at each interface, error located at the z-value corresponding to the maximum value of the considered variables, etc. Applications are given in case of closed form solutions of orthotropic cross-ply, rectangular, simply supported plates loaded by bisinusoidal distribution of transverse pressure. Symmetrically and unsymmetrical laminated cases are considered along with sandwich plates. It is found the reduced model is strongly influenced by the used localized error and that in same case the reduced model which is obtained by of single point criteria can be very much improved by the use of multi-point criteria

Bending of inhomogeneous sandwich plates with viscoelastic cores

This article presents the bending analysis of an inhomogeneous composite sandwich rectangular plate with viscoelastic core. The sinusoidal plate theory as well as other familiar shear deformation plate theories is used. Different types of intermediate plates are considered according to the thickness of all layers and the symmetry of the plate. Illyushin's approximation and the effective moduli methods are used to treat the governing equations of sandwich plates that reinforced with inhomogeneous fibers. Various results for deflections of and some stresses in such plates are presented. A comparison study is made to investigate the effect of time, inhomogeneity, and constitutive parameters as well as the effect of span-to-thickness and aspect ratios on the bending response of the sandwich plates