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This paper presents prediction of static behavior of composite beams with arbitrary anisotropic materials. The procedure is based on decomposing a 3-D nonlinear elasticity problem into a 2-D analysis of cross section and a 1-D analysis across the beam length. This is accomplished by assuming that magnitude of strain is small compared to unity and cross section size is small relative to wave length of deformation, inherent to beam-like structures. In 2-D cross sectional analysis warping functions are calculated in terms of 1-D strain parameters and finally, fully coupled classical stiffness constants are derived which include extension, torsion and bending in two directions. 1-D analysis is modeled by Finite Element Method through calculating beam strain energy. In this article warpings are derived using Rayleigh-Ritz method. The great advantage of using Rayleigh-Ritz is simplifying cross sectional analysis in contrast with the mesh generation in FEM of similar procedures. Different cross section stiffnesses are investigated for ply orientation angle. Calculated results for symmetric and anti-symmetric composite box beams correlate well with 3-D FEM using Abaqus software as well as experimental results. The present solution has more accurate results for anti-symmetric composite box beam. According to costly use of 3-D FEM analysis, the present procedure with high speed and acceptable accuracy, is truly sufficient for preliminary and optimization problems.

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In this paper, elastic-plastic symmetrical buckling of a thin solid circular plate of variable thickness, under uniform edge pressure, is investigated, based on both Incremental Theory (IT) and Deformation Theory (DT). Two kinds of simply supported and clamped boundary conditions have been considered. A power-law function was assumed for thickness variation. To minimize the integral uniqueness criterion, based on Rayleigh-Ritz method, transversal displacement was approximated by a test function which includes some unknown coefficients and satisfies geometric boundary conditions. Substituting the test function in the stability criterion and minimizing with respect to the unknown coefficients results in a homogeneous algebraic set of equations in terms of unknown coefficients. For non-trivial solution, the determinant of coefficient matrix should be equated to zero. Using this equation, critical buckling load is determined. The results of present study were compared with existing analytical solutions for circular plate of constant thickness and a good agreement was observed. This clearly shows the validity of presented analysis. Then the effect of thickness variation and boundary conditions type on the critical buckling load was investigated, for commercial aluminum and steel 1403 materials. The results show that when the thickness of circular plate center is 10% greater than its edge thickness the buckling load may increase up to 40% comparing with the circular plate for which the center thickness is 10% less than its edge thickness.

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This paper, presents the static analysis of composite beams with transverse shear effects using polynomials based dimensional reduction method. In dimensional reduction method, a three dimensional elasticity problem is split into a two dimensional cross section analysis and a one dimensional beam analysis. FEM is commonly used to analyze beam cross section in the literature. In this study, polynomial functions and Rayleigh-Ritz method are used to present an analytical procedure for two dimensional cross section analysis. Variational Asymptotic Method (VAM) is employed considering shear stiffnesses of composite beam cross section. VAM, asymptotically generates fully coupled cross section stiffness matrix. VAM benefits small parameters, related to characteristic length of cross section, to find stationary values of beam energy functional. By minimizing the energy functional with respect to warpings, in and out of plane warping functions are acquired. In this article, isotropic beams with different cross section geometries and symmetric as well as anti-symmetric composite box beams are investigated. Presented results show appropriate correlation of the present study with theoretical and experimental results, as well as 3D Finite Element analysis. Using dimensional reduction method reduces the computing time and empowers researchers to design and optimize composite beam-like structures.

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In this paper, elastic-plastic buckling of a thick rectangular plate has been investigated based on both Incremental (IT) and Deformation (DT) plasticity theories. Uniform biaxial edge traction was assumed as the plate loading while simply supported as the boundary conditions. Integral uniqueness criterion has been minimized to determine the critical buckling traction. Based on Rayleigh-Ritz method, a linear combination of polynomial base functions, which satisfy the geometrical boundary conditions, has been used as the trial functions for rotations and transverse deflection. To validate the analysis, the results for the Mindlin plate theory have been compared with the previously published results and a very close agreement has been observed. Then the effects of thickness ratio, aspect ratio and also different biaxial traction ratios on the buckling traction have been investigated. The results show that for the problem considered here, very close critical buckling traction is predicted by the both Mindlin and sinusoidal plate theories. This implies that Mindlin plate theory is sufficiently accurate to predict critical buckling traction in this problem. Moreover when the loading is gradually changed from biaxial into uniaxial compression or when the thickness-ratio is increased, the difference between the two theories is also increased. Also for compression-tension loading case, the critical buckling traction predicted by deformation theory is much less than the incremental theory.

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In this paper, the longitudinal vibration of nanorod based on Eringen’s nonlocal elasticity theory was studied using Rayleigh-Ritz method. A non-uniform nano-rod with variable cross-sectional area, density and Young’s modulus were considered. In the present work, boundary polynomials with orthogonal polynomials were used as shape functions in the Rayleigh-Ritz method which causes the vibrational analysis to be computationally efficient and imposing of boundary conditions to be easier. Using the mentioned polynomials the convergence rate of the obtained results was increased. All of the equations used in this study were made to have no dimensional to reduce the number of effective parameters in the solution. The influence of the nonlocal and in-homogeneity parameters on the vibrational behavior of nanorod was investigated. The results were compared to available results in the literature and a good agreement has been achieved. The results showed that nanorod frequencies were depended to the small scale effect, non-uniformity, and boundary conditions. For instance, an increase in frequency ratio causes the scale coefficient in all vibration modes to be increased, especially in higher modes. In addition, the frequencies were increased by increasing in the length of the nanorod.

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In this paper, thermal and vibration response of cross-ply bi-stable composite laminated plates were studied using semi-analytical, finite element and experimental method. In order to evaluate the semi-analytical and finite element results, a bi-stable composite plate was manufactured using a special procedure. Next, geometrical characteristics and displacement of different paths on the plate were measured experimentally at room temperature. In semi-analytical approach, the two stable states and the first natural frequency of cross-ply laminates are calculated based on Rayleigh–Ritz approach combined with Hamilton’s principle. In this study, a modified shape function was introduced that allows the curvatures to vary in both longitudinal and transverse directions. Using the modified shape function, the displacement of the plate in its stable configuration and the first natural frequency of the plate can be more accurately predicted in compared to the Hyer’s shape functions. The obtained results from the proposed shape function are in good agreement with the finite element and experimental data. The proposed shape functions can also be used in dynamic and vibration analysis to determine the snap-through load of the cross-ply laminates.

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This paper presents an study and analysis of acoustic wave scattered and radiated from a truncated conical shell excited by an time-harmonic constant amplitude acoustic wave arriving from infinity by specified angle of incidence. The shell immersed in unbounded air and inner face has in-vacuo condition. Donnel-mushtari theory of shell displacement field proposed to investigate the kinetic and potential energy of shell and Hamilton principal is employed to extract the shell dynamic equation. Incident sound wave is considered as plane wave which is an incoming wave solution of reduced homogenous wave equation. The Helmholtz integral equation is use to model the scattered and radiated sound by shell. Boundary element method (BEM) is employed to relate the surface nodal pressure to nodal displacement. Then by combination of BEM and Rayleigh-Ritz method, the coupled structural-acoustic problem is solved and the sound pressure in any point of medium and shell surface is obtained. The final result has been compared with Finite Element – Boundary Element (FE-BE) method and result shows that the analytical result is in good agreement with the numerical FE-BE method. Also the bahaivor of medium fluid is studied by considering air and water as two case of fluid medium