• Smart Structures and Systems
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• v.9 no.2
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• pp.127-143
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• 2012

The present paper deals with the nonlinear analysis of the functionally graded piezoelectric (FGP) annular plate with two smart layers as sensor and actuator. The normal pressure is applied on the plate. The geometric nonlinearity is considered in the strain-displacement equations based on Von-Karman assumption. The problem is symmetric due to symmetric loading, boundary conditions and material properties. The radial and transverse displacements are supposed as two dominant components of displacement. The constitutive equations are derived for two sections of the plate, individually. Total energy of the system is evaluated for elastic solid and piezoelectric sections in terms of two components of displacement and electric potential. The response of the system can be obtained using minimization of the energy of system with respect to amplitude of displacements and electric potential. The distribution of all material properties is considered as power function along the thickness direction. Displacement-load and electric potential-load curves verify the nonlinearity nature of the problem. The response of the linear analysis is investigated and compared with those results obtained using the nonlinear analysis. This comparison justifies the necessity of a nonlinear analysis. The distribution of the displacements and electric potential in terms of non homogenous index indicates that these curves converge for small value of piezoelectric thickness with respect to elastic solid thickness.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.295-303
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• 2018

The semi-analytical method to study the nonlinear dynamic behavior of simply supported spiral stiffened functionally graded (FG) cylindrical shells subjected to an axial compression is presented. The FG shell is surrounded by damping and linear/nonlinear elastic foundation. The proposed linear model is based on the two-parameter elastic foundation (Winkler and Pasternak). A three-parameter elastic foundation with hardening/softening cubic nonlinearity is used for nonlinear model. The material properties of the shell and stiffeners are assumed to be FG. Based on the classical plate theory of shells and von $K{\acute{a}}rm{\acute{a}}n$ nonlinear equations, smeared stiffeners technique and Galerkin method, this paper solves the nonlinear vibration problem. The fourth order Runge-Kutta method is used to find the nonlinear dynamic responses. Results are given to consider effects of spiral stiffeners with various angles, elastic foundation and damping coefficients on the nonlinear dynamic response of spiral stiffened simply supported FG cylindrical shells.

• Smart Structures and Systems
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• v.19 no.1
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• pp.33-38
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• 2017

This research tries to present a nonlinear thermo-elastic solution for a functionally graded spherical shell subjected to mechanical and thermal loads. Geometric nonlinearity is considered using the Lagrange or finite strain tensor. Non-homogeneous material properties are considered based on a power function. Adomian's decomposition method is used for calculation of nonlinear results. Nonlinear results such as displacement can be evaluated for sphere in terms of different indexes of non-homogeneity. A comprehensive comparison between linear and nonlinear results and evaluation of the percentage of difference between them can be performed in this paper. The obtained results indicate that the improvement of the results due to usage of nonlinear analysis is depending on the non-homogeneous index.

• Geomechanics and Engineering
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• v.31 no.3
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• pp.329-337
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• 2022

In this paper, the thermal post-buckling characteristics of functionally graded (FG) pipes with initial geometric imperfection are studied. Considering the influence of initial geometric defects, temperature and geometric nonlinearity, Euler-Lagrange principle is used to derive the nonlinear governing equations of the FG pipes. Considering three different boundary conditions, the two-step perturbation method is used to solve the nonlinear governing equations, and the expressions of thermal post-buckling responses are also obtained. Finally, the correctness of this paper is verified by numerical analyses, and the effects of initial geometric defects, functional graded index, elastic foundation, porosity, thickness of pipe and boundary conditions on thermal post-buckling response are analyzed. It is found that, bifurcation buckling exists for the pipes without initial geometric imperfection. In contrast, there is no bifurcation buckling phenomenon for the pipes with initial geometric imperfection. Meanwhile, the elastic stiffness can significantly improve thermal post-buckling load and thermal post-buckling strength. The larger the porosity, the greater the thermal buckling load and the thermal buckling strength.

• Steel and Composite Structures
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• v.22 no.1
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• pp.91-112
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• 2016

In this paper, post-buckling behavior of sandwich plates with functionally graded (FG) face sheets under uniform temperature rise loading is examined based on both sinusoidal shear deformation theory and stress function. It is supposed that the sandwich plate is in contact with an elastic foundation during deformation, which acts in both compression and tension. Thermo-elastic non-homogeneous properties of FG layers change smoothly by the variation of power law within the thickness, and temperature dependency of material constituents is considered in the formulation. In the present development, Von Karman nonlinearity and initial geometrical imperfection of sandwich plate are also taken into account. By employing Galerkin method, analytical solutions of thermal buckling and post-buckling equilibrium paths for simply supported plates are determined. Numerical examples presented in the present study discuss the effects of gradient index, sandwich plate geometry, geometrical imperfection, temperature dependency, and the elastic foundation parameters.

• Journal of the Korean Geotechnical Society
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• v.29 no.10
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• pp.57-66
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• 2013

Societal interest on a faster transportation demands an increase of the train speed exceeding current operation speed of 350 km/h. To trace the pattern of variations in displacements and subsoil stresses in the concrete slab track system, finite element simulations were conducted. For a simple track-vehicle modeling, a mass-point system representing the moving train load was developed. Dynamic responses with various train speeds from 100 to 700 km/h were investigated. As train speeds increase the displacement at rail and subsoil increases nonlinearly, whereas significant dynamic amplification at the critical velocity has not been found. At low train speed, the velocity of elastic wave carrying elastic energy is faster than the train speed. At high train speed exceeding 400 km/h, however, the train speed is approximately identical to the elastic wave velocity. Nonlinearity in the stress history in subsoil is amplified with increasing train speeds, which may cause significant plastic strains in path-dependent subsoil materials.

• Steel and Composite Structures
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• v.21 no.5
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• pp.1121-1144
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• 2016

This paper presents a displacement-based finite element procedure for second-order distributed plasticity analysis of planar steel frames with semi-rigid beam-to-column connections under static loadings. A partially strain-hardening elastic-plastic beam-column element, which directly takes into account geometric nonlinearity, gradual yielding of material, and flexibility of semi-rigid connections, is proposed. The second-order effects and distributed plasticity are considered by dividing the member into several sub-elements and meshing the cross-section into several fibers. A new nonlinear solution procedure based on the combination of the Newton-Raphson equilibrium iterative algorithm and the constant work method for adjusting the incremental load factor is proposed for solving nonlinear equilibrium equations. The nonlinear inelastic behavior predicted by the proposed program compares well with previous studies. Coupling effects of three primary sources of nonlinearity, geometric imperfections, and residual stress are investigated and discussed in this paper.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.211-223
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• 2012

This paper deals with large deformation post-buckling of a linear-elastic and hygrothermal beam with axially nonmovable pinned-pinned ends and subjected to a significant increase in swelling by an alternative method. Analytical approximate solutions for the geometrically nonlinear problem are presented. The solution for the limiting case of a string is also obtained. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-nonlinear equation, and supplementary condition with cosinoidal nonlinearity can also be simplified to be a polynomial integral equation. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. Two approximate formulae for load along axis, potential strain for free hygrothermal expansion and periodic solution are established for small as well as large angle of rotation at the end of the beam. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.175-182
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• 1998

The object of this study is shape finding and cutting pattern generation of membrane structures under the following assumptions : (1) material is linearly elastic (2) stress state is plane stress. Cable and membrane structures should introduce the nonlinear analysis considering geometric nonlinearity because these structures deform largely under the external loads. The analysis procedure is consisted of three steps considering geometric nonlinearity unlike any other structures. First step is the shape finding analysis to determine the initial equilibrium shape. Second step is the stress-deformation analysis to investigate the behaviors of structures under various external loads. Once a satisfactory shape has been found, a cutting pattern based on the shape finding analysis may be generated from the view point of construction. In this paper, (1) shape finding analysis formulation and an example, (2) cutting pattern determination procedure using weighted least-square minimization flattening method and some results are presented.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.266-273
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• 1998

The object of this study is shape finding and cutting pattern generation of membrane structures under the following assumptions: (1) material is linearly elastic (2) stress state is plane stress. Cable and membrane structures should introduce the nonlinear analysis considering geometric nonlinearity because these structures deform largely under the external loads. The analysis procedure is consisted of three steps considering geometric nonlinearity unlike any other structures. First step is the shape finding analysis to determine the initial equilibrium shape. Second step is the stress-deformation analysis to investigate the behaviors of structures under various external loads. Once a satisfactory shape has been found, a cutting pattern based on the shape finding analysis may be generated from the view point of construction. In this paper, after shape finding analysis, cutting pattern determination procedure using weighted least-square minimization flattening method and some results are presented.