• Structural Engineering and Mechanics
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• v.7 no.5
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• pp.473-484
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• 1999

In the present study, the thermal buckling analysis of thick anisotropic laminated composite plates is carried out using the finite strip method based on the higher-order shear deformation theory. This theory accounts for the parabolic distribution of the transverse shear strains through the thickness of the plate and for zero transverse shear stresses on the plate surfaces. Therefore, this theory yields improved results over the Mindlin plate theory and eliminates the need for shear correction factors in calculating the transverse shear stiffness. The critical temperatures of simply supported rectangular cross-ply and angle-ply composite laminates are calculated. The effects of several parameters, such as the aspect ratio, the length-to-thickness ratio, the number of plies, fibre orientation and stacking sequence, are investigated.

• Earthquakes and Structures
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• v.13 no.3
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• pp.255-265
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• 2017

In this paper, an efficient shear deformation theory is developed for wave propagation analysis in a functionally graded beam. More particularly, porosities that may occur in Functionally Graded Materials (FGMs) during their manufacture are considered. The proposed shear deformation theory is efficient method because it permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents; but the rule of mixture is modified to describe and approximate material properties of the functionally graded beams with porosity phases. The governing equations of the wave propagation in the functionally graded beam are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded beam is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions, the depth of beam, the number of wave and the porosity on wave propagation in functionally graded beam are discussed in details. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded beam.

• Steel and Composite Structures
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• v.49 no.3
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• pp.293-306
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• 2023

This article focuses on the study of the buckling behavior of two-dimensional functionally graded (2D-FG) nanosize tubes, including porosity, based on the first shear deformation and higher-order theory of the tube. The nano-scale tube is simulated using the nonlocal gradient strain theory, and the general equations and boundary conditions are derived using Hamilton's principle for the Zhang-Fu's tube model (as a higher-order theory) and Timoshenko beam theory. Finally, the derived equations are solved using a numerical method for both simply-supported and clamped boundary conditions. A parametric study is performed to investigate the effects of different parameters, such as axial and radial FG power indices, porosity parameter, and nonlocal gradient strain parameters, on the buckling behavior of the bi-dimensional functionally graded porous tube. Keywords: Nonlocal strain gradient theory; buckling; Zhang-Fu's tube model; Timoshenko theory; Two-dimensional functionally graded materials; Nanotubes; Higher-order theory.

• Advances in nano research
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• v.6 no.2
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• pp.93-112
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• 2018

An analytical solution of the buckling governing equations of functionally graded piezoelectric (FGP) nanobeams obtained by using a developed third-order shear deformation theory is presented. Electro-mechanical properties of FGP nanobeam are supposed to change continuously in the thickness direction based on power-law model. To capture the small size effects, Eringen's nonlocal elasticity theory is adopted. Employing Hamilton's principle, the nonlocal governing equations of a FG nanobeams made of piezoelectric materials are obtained and they are solved using Navier-type analytical solution. Results are provided to show the effect of different external electric voltage, power-law index, nonlocal parameter and slenderness ratio on the buckling loads of the size-dependent FGP nanobeams. The accuracy of the present model is verified by comparing it with nonlocal Timoshenko FG beams. So, this study makes the first attempt for analyzing buckling behavior of higher order shear deformable FGP nanobeams.

• Steel and Composite Structures
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• v.46 no.6
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• pp.759-772
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• 2023

This manuscript presents a comprehensive mathematical model to investigate buckling stability and postbuckling response of bio-inspired composite beams with helicoidal orientations. The higher order shear deformation theory as well as the Timoshenko beam theories are exploited to include the shear influence. The equilibrium nonlinear integro-differential equations of helicoidal composite beams are derived in detail using the energy conservation principle. Differential integral quadrature method (DIQM) is employed to discretize the nonlinear system of differential equations and solve them via the Newton iterative method then obtain the response of helicoidal composite beam. Numerical calculations are carried out to check the validity of the present solution methodology and to quantify the effects of helicoidal rotation angle, elastic foundation constants, beam theories, geometric and material properties on buckling, postbuckling of bio-inspired helicoidal composite beams. The developed model can be employed in design and analysis of curved helicoidal composite beam used in aerospace and naval structures.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.453-464
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• 2018

In this paper, an efficient higher-order shear deformation theory is presented to analyze thermomechanical bending of temperature-dependent functionally graded (FG) plates resting on an elastic foundation. Further simplifying supposition are made to the conventional HSDT so that the number of unknowns is reduced, significantly facilitating engineering analysis. These theory account for hyperbolic distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Nonlinear thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from the principle of virtual displacements. Analytical solutions for the thermomechanical bending analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent FG plates and validated with those of other shear deformation theories. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature field on the thermomechanical bending characteristics. It can be concluded that the present theory is not only accurate but also simple in predicting the thermomechanical bending responses of temperature-dependent FG plates.

• Steel and Composite Structures
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• v.20 no.5
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• pp.1043-1066
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• 2016

A new analytical solution based on a third order shear deformation theory for the problem of static analysis of cross-ply doubly-curved shells is presented. The boundary-discontinuous generalized double Fourier series method is used to solve highly coupled linear partial differential equations with the mixed type simply supported boundary conditions prescribed on the edges. The complementary boundary constraints are introduced through boundary discontinuities generated by the selected boundary conditions for the derivation of the complementary solution. The numerical accuracy of the solution is compared by studying the comparisons of deflections, stresses and moments of symmetric and anti-symmetric laminated shells with finite element results using commercially available software under uniformly distributed load. Results are in good agreement with finite element counterparts. Additional results of the symmetric and anti-symmetric laminated and sandwich shells under single point load at the center and pressure load, are presented to provide data for the unsolved boundary conditions, benchmark comparisons and verifications.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.11
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• pp.98-109
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• 1995

An investigation was performed to study the inner damage of laminated composite plates subjected to out-of-plane load. During the investigation, inpact velocity and equivalent static load relationship was derived. Reddy's higher-order shear deformation theory(HSDT) and Hashin's failure criteria were used to determine inner stresses and damaged area. And impact testing was carried out on laminated composite plates by air gun type impact testing machine. The CFRP specimens were composed of [ .+-. 45 .deg. ]$_{4}$and [ .+-. 45 .deg. /0 .deg. /90 .deg. ]$_{2}$ stacking sequences with 0.75$^{t}$ * 26$^{w}$ * 100$^{l}$ (mm) dimension. After impact testing. As a result, a relationship holds between damaged area and impact energy, and a matrix cracking was caused by the interlaminar shear stress in the middle ply and was caused by the inplane transverse stress in the bottom ply.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.4 s.74
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• pp.407-418
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• 2006

In this paper, an efficient yet accurate stress analysis based on the first-order shear deformation theory (FSDT) is presented. The transverse shear strain energy is modified via the mixed variational theorem, so that the shear correction factors are automatically involved in the formulation. In the mixed variational formulation, the transverse stresses are taken to be functions subject to variations. The transverse shear stresses based on an efficient higher order plate theory (EHOPT, Cho and Parmerter, 1993) are utilized and modified, while the transverse normal stress is assumed to be the third-order polynomial of thickness coordinates, which satisfies both zero transverse shear stresses and prescribed surface fractions in top and bottom surfaces. On the other hand, the displacements are assumed to be those of the FSDT Resulting strain energy expressions are referred to as an EFSDTM3D that stands for an enhanced first-order shear deformation theory based on the mixed formulation for three dimensional elasticity, The developed EFSDTM3D preserves the computational advantage of the classical FSDT while allowing for important local through-the-thickness variations of displacements and stresses through the recovery procedure that is based on the least square minimization of in-plane stresses. Comparisons of displacements and stresses of both laminated and sandwich plates using the present theory are made with the classical FSDT, three-dimensional exact solutions, and available data in the literature.

• Steel and Composite Structures
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• v.33 no.5
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• pp.699-716
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• 2019

In this paper, wave propagations in sigmoid functionally graded (S-FG) plates are studied using new Higher Shear Deformation Theory (HSDT) based on two-dimensional (2D) elasticity theory. The current higher order theory has only four unknowns, which mean that few numbers of unknowns, compared with first shear deformations and others higher shear deformations theories and without needing shear corrector. The material properties of sigmoid functionally graded are assumed to vary through thickness according sigmoid model. The S-FG plates are supposed to be imperfect, which means that they have a porous distribution (even and uneven) through the thickness of these plates. The governing equations of S-FG plates are derived employed Hamilton's principle. Using technique of Navier, differential equations of S-FG in terms displacements are solved. Extensive results are presented to check the efficient of present methods to predict wave dispersion and velocity wave in S-FG plates.