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 (pi), 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.
Abstract Plenty of research articles are available on the static deformation analysis of laminated straight beams using refined shear deformation theories. However, research on the deformation of laminated curved beams with simply supported boundary conditions is limited and needs more attention nowadays. With this objective, the present study deals with the static analysis of laminated composite and sandwich beams curved in elevation using a new quasi-3D polynomial type beam theory. The theory considers the effects of both transverse shear and normal strains, i.e. thickness stretching effects. In the present theory, axial displacement has expanded up to the fifth-order polynomial in terms of thickness coordinates to effectively account for the effects of curvature and deformations. The present theory satisfies the zero traction boundary condition on the top and bottom surfaces of the beam. Governing differential equations and associated boundary conditions are established by using the Principal of virtual work. Navier’s solution technique is used to obtain displacements and stresses for simply supported beams curved in elevation and subjected to uniformly distributed load. The present results can be benefited to the upcoming researchers.
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.
In this paper, a polynomial type fifth-order curved beam theory is developed and applied to investigate the bending response of laminated composite, sandwich, and functionally graded beams curved in elevation under the temperature load changing linearly through the thickness. The theory developed herein considered the effects of both transverse shear strain (γxz≠0) and transverse normal strain (εz≠0) along with the curvature effects (1+z/R). Governing equations and boundary conditions of the curved beams are derived with the help of the principle of virtual work. Navier's method is used to get the analytical solutions of simply supported curved beams under the action of thermal load. The numerical results are obtained for various (h/L) and (R/L) ratios along with the different values of the power-law exponent in the case of functionally graded beams. The numerical results obtained using the present theory for laminated composite, sandwich, and functionally graded straight beams are compared with previously published results and then the formulation and computer codes are extended to derive the numerical results corresponding to curved beams. The authors have presented many useful results in the present paper on curved beams which can be serving as a benchmark for further studies.
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