• Structural Engineering and Mechanics
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• v.19 no.1
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• pp.43-53
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• 2005

The linearized buckling problem is considered for an isotropic clamped-clamped cylindrical shell with an oblique end. A theoretical solution based on the Budiansky shell theory is developed, and numerical results are determined using the differential quadrature method. In formulating the solutions, the surface of the shell is developed onto a plane, and the resulting irregular domain is then mapped, using blending functions, onto a square parent domain. The analysis is carried out in the parent domain. Convergence, validation, and parametric studies are conducted for a uniform external pressure loading. Results determined are compared with finite element results. The paper ends with an appropriate set of conclusions.

• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.131-157
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• 2018

In this study, Eringen nonlocal elasticity theory in conjunction with surface elasticity theory is employed to study nonlinear free vibration behavior of FG nano-plate lying on elastic foundation, on the base of Reddy's plate theory. The material distribution is assumed as a power-law function and effective material properties are modeled using Mori-Tanaka homogenization scheme. Hamilton's principle is implemented to derive the governing equations which solved using DQ method. Finally, the effects of different factors on natural frequencies of the nano-plate under hygrothermal situation and various boundary conditions are studied.

• Journal of the Korean Society of Safety
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• v.16 no.4
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• pp.208-212
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• 2001

DQM(differential quadrature method) is applied to computation of two dimensional elasticity problems in helical spring. Elastic shear stresses in an axially loaded helical spring having rectangular and square cross sections are calculated. The results are compared with those obtained using the method of successive approximations. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.459-475
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• 2005

This paper deals with a novel application of the Generalized Differential Quadrature (G.D.Q.) method to the linear elastic static analysis of isotropic rotational shells. The governing equations of equilibrium, in terms of stress resultants and couples, are those from Reissner-Mindlin shear deformation shell theory. These equations, written in terms of internal-resultants circular harmonic amplitudes, are first put into generalized displacements form, by use of the strain-displacements relationships and the constitutive equations. The resulting systems are solved by means of the G.D.Q. technique with favourable precision, leading to accurate stress patterns.

• Structural Engineering and Mechanics
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• v.20 no.4
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• pp.465-476
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• 2005

Free vibration of orthotropic functionally graded beams, whose material properties can vary arbitrarily along the thickness direction, is investigated based on the two-dimensional theory of elasticity. A hybrid state-space/differential quadrature method is employed along with an approximate laminate model, which allows us to obtain the semi-analytical solution easily. With the introduction of continuity conditions at each fictitious interface and boundary conditions at the top and bottom surfaces, the frequency equation for an inhomogeneous beam is derived. A completely exact solution of an FGM beam with material constants varying in exponential way through the thickness is also presented, which serves a benchmark to verify the present method. Numerical results are performed and discussed.

• Geomechanics and Engineering
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• v.29 no.6
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• pp.667-681
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• 2022

This paper presents a thermoelastic analysis of variable thickness plates made of functionally graded materials (FGM) subjected to mechanical and thermal loads. The thermal load is applied to the plate as a temperature difference between the top and bottom surfaces. Temperature distribution in the plate is obtained using the steady-state heat equation. Except for Poisson's ratio, all mechanical properties of the plate are assumed to vary linearly along the thickness direction based on the volume fractions of ceramic and metal. The plate is resting on an elastic foundation modeled based on the Winkler foundation model. The governing equations are derived based on the third-order shear deformation theory (TSDT) and are solved numerically for various boundary conditions using the differential quadrature method (DQM). The effects of various parameters on the stress distribution and deflection of the plate are investigated such as the value of thermal and mechanical loads, volume fractions of ceramic and metal, and the stiffness coefficients of the foundation.

• Advances in materials Research
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• v.12 no.2
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• pp.133-159
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• 2023

In this paper, a size-dependent dynamic investigation of a porous metal foams microbeamsis presented. The novelty of this study is to use a metal foam microbeam that contain porosities based on the refined high order shear deformation beam model, with sinusoidal shear strain function, and the modified strain gradient theory (MSGT) for the first time. The Lagrange's principle combined with differential quadrature hierarchicalfinite element method (DQHFEM) are used to obtain the porous microbeam governing equations. The solutions are presented for the natural frequencies of the porous and homogeneoustype microbeam. The obtained results are validated with the analytical methods found in the literature, in order to confirm the accuracy of the presented resolution method. The influences of the shape of porosity distribution, slenderness ratio, microbeam thickness, and porosity coefficient on the free vibration of the porous microbeams are explored in detail. The results of this paper can be used in various design formetallic foammicro-structuresin engineering.

• Advances in nano research
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• v.15 no.1
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• pp.75-89
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• 2023

In this paper, Bishop theory performs longitudinal vibration analysis of Nano-beams. Its governing equation, due to integrated displacement field and more considered primarily effects compared with other theories, enjoys fully completed status, and more reliable results as well. This article aims to find how Bishop theory and Two-phase elasticity work together. In other words, whether Bishop theory will be compatible with Two-phase local/nonlocal elasticity. Hamilton's principle is employed to derive governing equation of motion, and then the 6th order of Generalized Differential Quadrature Method (GDQM) as a constructive numerical method is utilized to attain the discretized two-phase formulation. To acquire a proper verification procedure, exact solution is prepared to be compared with current results. Furthermore, the effects of key parameters on the objective are investigated.

• Structural Engineering and Mechanics
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• v.17 no.6
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• pp.789-817
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• 2004

This paper deals with the modal analysis of rotational shell structures by means of the numerical solution technique known as the Generalized Differential Quadrature (G. D. Q.) method. The treatment is conducted within the Reissner first order shear deformation theory (F. S. D. T.) for linearly elastic isotropic shells. Starting from a non-linear formulation, the compatibility equations via Principle of Virtual Works are obtained, for the general shell structure, given the internal equilibrium equations in terms of stress resultants and couples. These equations are subsequently linearized and specialized for the rotational geometry, expanding all problem variables in a partial Fourier series, with respect to the longitudinal coordinate. The procedure leads to the fundamental system of dynamic equilibrium equations in terms of the reference surface kinematic harmonic components. Finally, a one-dimensional problem, by means of a set of five ordinary differential equations, in which the only spatial coordinate appearing is the one along meridians, is obtained. This can be conveniently solved using an appropriate G. D. Q. method in meridional direction, yielding accurate results with an extremely low computational cost and not using the so-called "delta-point" technique.

• Smart Structures and Systems
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• v.15 no.5
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• pp.1233-1252
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• 2015

This study investigates the problem of crack detection in post-buckled beam-type structures. The beam under the axial compressive force has a crack, assumed to be open and through the width. The crack, which is modeled by a massless rotational spring, divides the beam into two segments. The crack detection is considered as an optimization problem, and the weighted sum of the squared errors between the measured and computed natural frequencies is minimized by the bees algorithm. To find the natural frequencies, the governing nonlinear equations of motion for the post-buckled state are first derived. The solution of the nonlinear differential equations of the two segments consists of static and dynamic parts. The differential quadrature method along with an arc length strategy is used to solve the static part, while the same method is utilized for the solution of the linearized dynamic part and the extraction of the natural frequencies of the cracked beam. The investigation includes several numerical as well as experimental case studies on the post-buckled simply supported and clamped-clamped beams having open cracks. The results show that several parameters such as the amount of applied compressive force and boundary conditions influences the outcome of the crack detection scheme. The identification results also show that the crack position and depth can be predicted well by the presented method.