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CONTENTS
Volume 9, Number 6, December 2020
 

Abstract
The effect of porosity on the thermo-mechanical behavior of simply supported functionally graded plate reposed on the Winkler-Pasternak foundation is investigated analytically in the present paper using new refined hyperbolic shear deformation plate theory. Both even and uneven distribution of porosity are taken into account and the effective properties of FG plates with porosity are defined by theoretical formula with an additional term of porosity. The present formulation is based on a refined higher order shear deformation theory, which is based on four variables and it still accounts for parabolic distribution of the transverse shearing strains and stresses through the thickness of the FG plate and takes into account the various distribution shape of porosity. The elastic foundation is described by the Winkler-Pasternak model. A new modified power-law formulation is used to describe the material properties of FGM plates in the thickness direction. The closed form solutions are obtained by using Navier technique. The present results are verified in comparison with the published ones in the literature. The results show that the dimensionless and stresses are affected by the porosity volume fraction, constituent volume fraction, and thermal load.

Key Words
FGM plate; porosity; thermo-mechanical behavior; Winkler-Pasternak foundations

Address
Benferhat Rabia, Hassaine Daouadji Tahar and Rabahi Abderezak: Departement de Genie Civil, Universite Ibn Khaldoun Tiaret; BP 78 Zaaroura, Tiaret, Algerie; Laboratoire de Geomatique et Developpement Durable, Universite de Tiaret, Algerie

Abstract
The present study is concerned with the thermoelastic interactions in a two dimensional homogeneous, transversely isotropic thermoelastic solid with new modified couple stress theory without energy dissipation and with two temperatures in frequency domain. The time harmonic sources and Hankel transform technique have been employed to find the general solution to the field equations. Concentrated normal force, normal force over the circular region, thermal point source and thermal source over the circular region have been taken to illustrate the application of the approach. The components of displacements, stress, couple stress and conductive temperature distribution are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. Numerically simulated results are depicted graphically to show the effect of angular frequency on the resulted quantities.

Key Words
transversely isotropic; thermoelastic; time harmonic source; Hankel transform; new modified couple stress theory; two temperature

Address
Parveen Lata and Harpreet Kaur: Department of Basic and Applied Sciences, Punjabi University, Patiala, Punjab, India

Abstract
In this paper the linear elastic coupling between a 2 degree of freedom shear-type frame system and a rigid block is analytically and experimentally investigated. As demonstrated by some of the authors in previous papers, it is possible to choose a coupling system able to guarantee advantages, whatever the mechanical characteristics of the frame. The main purpose of the investigation is to validate the analytical model. The nonlinear equations of motion of the coupled system are obtained by a Lagrangian approach and successively numerically integrated under harmonic and seismic excitation. The results, in terms of gain graphs, maps and spectra, represent the ratio between the maximum displacements or drifts of the coupled and uncoupled systems as a function of the system's parameters. Numerical investigations show the effectiveness of the nonlinear coupling for a large set of parameters. Thus experimental tests are carried out to verify the analytical results. An electro-dynamic long-stroke shaker sinusoidally and seismically forces a shear-type 2 d.o.f frame coupled with a rigid aluminium block. The experimental investigations confirm the effectiveness of the coupling as predicted by the analytical model.

Key Words
elastic coupling; rigid block; gain coefficients and maps; experimental investigation

Address
Stefano Pagliaro, Angelo Aloisio, Rocco Alaggio and Angelo Di Egidio: DICEAA - University of L'Aquila, via G. Gronchi, 18-67100 L'Aquila, Italy

Abstract
Dynamic responses of a laminated composite cantilever beam under a harmonic are investigated in this study. The governing equations of problem are derived by using the Lagrange procedure. The Timoshenko beam theory is considered and the Ritz method is implemented in the solution of the problem. The algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of dynamic problem, the Newmark average acceleration method is used in the time history. In the numerical examples, the effects of load parameter, the fiber orientation angles and stacking sequence of laminas on the dynamic responses of the laminated beam are investigated.

Key Words
dynamic analysis; laminated composite beams; Ritz method

Address
S.D. Akbas: Department of Civil Engineering, Bursa Technical University, 16330, Bursa, Turkey

Abstract
Equilibrium equations of a porous FG plate resting on Winkler-Pasternak foundations with various boundary conditions are derived using a new refined shear deformation theory. Different types of porosity distribution rate are considered. Governing equations are obtained including the plate-foundation interaction. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The novel rule of mixture is proposed to describe and approximate material properties of the FG plates with different distribution case of porosity. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature. Effects of variation of porosity distribution rate, boundary conditions, foundation parameter, power law index, plate aspect ratio, side-to-thickness ratio on the deflections and stresses are all discussed.

Key Words
functionally graded materials; refined plate theory; various boundary conditions; imperfect plates; effect of porosity distribution rate

Address
Kablia Aicha: Laboratory of Geomatics and Sustainable Development, University of Tiaret, Algeria; Department of Mechanical Engineering, University of Tiaret, Algeria
Benferhat Rabia: Laboratory of Geomatics and Sustainable Development, University of Tiaret, Algeria; Department of Civil Engineering, University of Tiaret, Algeria
Tahar Hassaine Daouadji: Laboratory of Geomatics and Sustainable Development, University of Tiaret, Algeria; Department of Civil Engineering, University of Tiaret, Algeria
Ahmed Bouzidene: Department of Mechanical Engineering, University of Tiaret, Algeria


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