• Steel and Composite Structures
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• v.17 no.5
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• pp.753-776
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• 2014

In this paper, nonlinear vibration and post-buckling analysis of beams made of functionally graded materials (FGMs) resting on nonlinear elastic foundation subjected to thermo-mechanical loading are studied. The thermo-mechanical material properties of the beams are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and to be temperature-dependent. The assumption of a small strain, moderate deformation is used. Based on Euler-Bernoulli beam theory and von-Karman geometric nonlinearity, the integral partial differential equation of motion is derived. Then this PDE problem which has quadratic and cubic nonlinearities is simplified into an ODE problem by using the Galerkin method. Finally, the governing equation is solved analytically using the variational iteration method (VIM). Some new results for the nonlinear natural frequencies and buckling load of the FG beams such as the influences of thermal effect, the effect of vibration amplitude, elastic coefficients of foundation, axial force, end supports and material inhomogenity are presented for future references. Results show that the thermal loading has a significant effect on the vibration and post-buckling response of FG beams.

• Nuclear Engineering and Technology
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• v.55 no.11
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• pp.4295-4306
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• 2023

The vibration of fuel rods in axial flow is a universally recognized issue within both engineering and academic communities due to its significant importance in ensuring structural safety. This paper aims to thoroughly investigate the stability and nonlinear vibration of a fuel rod subjected to axial flow in a newly designed high temperature gas cooled reactor. Considering the possible presence of thermal expansion and large deformation in practical scenarios, the thermal effect and geometric nonlinearity are modeled using the von Karman equation. By applying Hamilton's principle, we derive the comprehensive governing equation for this fluid-structure interaction system, which incorporates the quadratic nonlinear stiffness. To establish a connection between the fluid and structure aspects, we utilize the Galerkin method to solve the perturbation potential function, while employing mode expansion techniques associated with the structural analysis. Following convergence and validation analyses, we examine the stability of the structure under various conditions in detail, and also investigate the bifurcation behavior concerning the buckling amplitude and flow velocity. The findings from this research enhance the understanding of the underlying physics governing fuel rod behavior in axial flow under severe yet practical conditions, while providing valuable guidance for reactor design.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.1
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• pp.85-92
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• 2015

This article presents the dynamic instability response of sigmoid functionally graded material plates on elastic foundation using the higher-order shear deformation theory. The higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The governing equations are then written in the form of Mathieu-Hill equations and then Bolotin's method is employed to determine the instability regions. The boundaries of the instability regions are represented in the dynamic load and excitation frequency plane. The results of dynamic instability analysis of sigmoid functionally graded material plate are presented using the Navier's procedure to illustrate the effect of elastic foundation parameter on dynamic response. The relations between Winkler and Pasternak elastic foundation parameter are discussed by numerical results. Also, the effects of static load factor, power-law index and side-to-thickness ratio on dynamic instability analysis are investigated and discussed. In order to validate the present solutions, the reference solutions are used and discussed. The theoretical development as well as numerical solutions presented herein should serve as reference for the dynamic instability study of S-FGM plates.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.1
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• pp.436-444
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• 2013

This article presents the dynamic response of nano-scale plates using the nonlocal continuum theory and higher-order shear deformation theory. The nonlocal elasticity of Eringen has ability to capture the small scale effects and the higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The solutions of transient dynamic analysis of nano-scale plate are presented using these theories to illustrate the effect of nonlocal theory on dynamic response of the nano-scale plates. The relations between nonlocal and local theories are discussed by numerical results. Also, the effects of nonlocal parameters, aspect ratio, side-to-thickness ratio, size of nano-scale plate and time step on dynamic response are investigated and discussed. The amplitude and cycle increase when nonlocal parameter increase. In order to validate the present solutions, the reference solutions are used and discussed. The theoretical development as well as numerical solutions presented herein should serve as reference for nonlocal theories as applied to the transient dynamic analysis of nano-scale structures.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.11
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• pp.5542-5550
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• 2012

Third-order shear deformation theory is reformulated using the nonlocal elasticity of Eringen. The equation of equilibrium of the nonlocal elasticity are derived. This theory has ability to capture the both small scale effects and quadratic variation of shear strain through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported boundary conditions. Analytical solutions of buckling of nano-scale plates are presented using this theory to illustrate the effect of nonlocal theory on buckling load of the nano-scale plates. The relations between nonlocal third-order and local theories are discussed by numerical results. Further, effects of (i) length (ii) nonlocal parameter, (iii) aspect ratio and (iv) mode number on nondimensional buckling load are studied. In order to validate the present solutions, the reference solutions are used and discussed. The present results of nano-scale plates using the nonlocal theory can provide a useful benchmark to check the accuracy of related numerical solutions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.8
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• pp.1195-1208
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• 1997

Bellows is a component in piping systems which absorbs mechanical deformation with flexibility. Its geometry is an axial symmetric shell which consists of two toroidal shells and one annular plate or conical shell. In order to analyze bellows, this study presents the finite element analysis using a conical frustum shell element. A finite element analysis is developed to analyze various bellows. The validity of the developed program is verified by the experimental results for axial and lateral stiffness. The formula for calculating the natural frequency of bellows is made by the simple beam theory. The formula for fatigue life is also derived by experiments. The shape optimal design problem is formulated using multiple objective optimization. The multiple objective functions are transformed to a scalar function by weighting factors. The stiffness, strength and specified stiffness are considered as the multiple objective function. The formulation has inequality constraints imposed on the fatigue limit, the natural frequencies, and the manufacturing conditions. Geometric parameters of bellows are the design variables. The recursive quadratic programming algorithm is selected to solve the problem. The results are compared to existing bellows, and the characteristics of bellows is investigated through optimal design process. The optimized shape of bellows is expected to give quite a good guideline to practical design.

• Geomechanics and Engineering
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• v.10 no.3
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• pp.357-386
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• 2016

In this research work, an exact analytical solution for thermal stability of solar functionally graded rectangular plates subjected to uniform, linear and non-linear temperature rises across the thickness direction is developed. It is assumed that the plate rests on two-parameter elastic foundation and its material properties vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the efficient hyperbolic plate theory based on exact neutral surface position is employed to derive the governing stability equations. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the quadratic distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Just four unknown displacement functions are used in the present theory against five unknown displacement functions used in the corresponding ones. The non-linear strain-displacement relations are also taken into consideration. The influences of many plate parameters on buckling temperature difference will be investigated. Numerical results are presented for the present theory, demonstrating its importance and accuracy in comparison to other theories.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.501-520
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• 2015

Presence of torsional loadings can significantly affect the flow of internal forces and deformation capacity of reinforced concrete (RC) columns. It increases the possibility of brittle shear failure leading to catastrophic collapse of structural members. This necessitates accurate prediction of the torsional behaviour of RC members for their safe design. However, a review of previously published studies indicates that the torsional behaviour of RC members has not been studied in as much depth as the behaviour under flexure and shear in spite of its frequent occurrence in bridge columns. Very few analytical models are available to predict the response of RC members under torsional loads. Softened truss model (STM) developed in the University of Houston is one of them, which is widely used for this purpose. The present study shows that STM prediction is not sufficiently accurate particularly in the post cracking region when compared to test results. An improved analytical model for RC square columns subjected to torsion with and without axial compression is developed. Since concrete is weak in tension, its contribution to torsional capacity of RC members was neglected in the original STM. The present investigation revealed that, disregard to tensile strength of concrete is the main reason behind the discrepancies in the STM predictions. The existing STM is extended in this paper to include the effect of tension stiffening for better prediction of behaviour of square RC columns under torsion. Three different tension stiffening models comprising a linear, a quadratic and an exponential relationship have been considered in this study. The predictions of these models are validated through comparison with test data on local and global behaviour. It was observed that tension stiffening has significant influence on torsional behaviour of square RC members. The exponential and parabolic tension stiffening models were found to yield the most accurate predictions.

• Structural Engineering and Mechanics
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• v.40 no.1
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• pp.65-84
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• 2011

In this paper a simple mathematical model for approximate static analysis of combined system of framed tube, shear core and two outrigger-belt truss structures subjected to lateral loads is presented. In the proposed methodology, framed tube is modeled as a cantilevered beam with a box section and interaction between shear core and outrigger-belt truss system with framed tube is modeled using torsional springs placed at location of outrigger-belt truss; these torsional springs act in a direction opposite to rotation generated by lateral loads. The effect of shear lag on axial deformation in flange is quadratic and in web it is a cubic function of geometry. Here the total energy of the combined system is minimized with respect to lateral deflection and rotation in plane section. Solution of the resulting equilibrium equations yields the unknown coefficients of shear lag along with the stress and displacement distributions. The results of a numerical example, 50 storey building subjected to three different types of lateral loading obtained from SAP2000 are compared to those of the proposed method and the differences are found to be reasonable. The proposed method can be used during the preliminary design stages of a tall building and can provide a better understanding of the effects of various parameters on the overall structural behavior.

• Coupled systems mechanics
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• v.8 no.5
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• pp.439-457
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• 2019

In this paper, a new application of a four variable refined plate theory to analyze the nonlinear bending of functionally graded plates exposed to thermo-mechanical loadings, is presented. This recent theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces, and similarly, the shear components do not contribute toward bending moments. The derived transverse shear strains has a quadratic variation across the thickness that satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. The solutions are achieved by minimizing the total potential energy. The non-linear strain-displacement relations in the von Karman sense are used to derive the effect of geometric non-linearity. It is concluded that the proposed theory is accurate and simple in solving the nonlinear bending behavior of functionally graded plates.