• Journal of Mechanical Science and Technology
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• v.14 no.1
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• pp.19-29
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• 2000

A viscoelastic finite element analysis is presented to investigate residual stresses occurred in a laminated cylindrical shell during cure. An incremental viscoelastic constitutive equation that can describe stress relaxation during the cure is derived as a recursive formula which can be used conveniently for a numerical analysis. The finite element analysis program is developed on the basis of a 3-D degenerated shell element and the first order shear deformation theory, and is verified by comparing with an one dimensional exact solution. Viscoelastic effect on the residual stresses in the laminated shell during the cure is investigated by performing both the viscoelastic and linear elastic analyses considering thermal deformation and chemical shrinkage simultaneously. The results show that there is big difference between viscoelastic stresses and linear elastic stresses. The effect of cooling rates and cooling paths on the residual stresses is also examined.

• Steel and Composite Structures
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• v.24 no.4
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• pp.499-512
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• 2017

This paper deals with nonlinear dynamic stability of embedded piezoelectric nano-composite separators conveying pulsating fluid. For presenting a realistic model, the material properties of structure are assumed viscoelastic based on Kelvin-Voigt model. The separator is reinforced with single-walled carbon nanotubes (SWCNTs) which the equivalent material properties are obtained by mixture rule. The separator is surrounded by elastic medium modeled by nonlinear orthotropic visco Pasternak foundation. The separator is subjected to 3D electric and 2D magnetic fields. For mathematical modeling of structure, three theories of classical shell theory (CST), first order shear deformation theory (FSDT) and sinusoidal shear deformation theory (SSDT) are applied. The differential quadrature method (DQM) in conjunction with Bolotin method is employed for calculating the dynamic instability region (DIR). The detailed parametric study is conducted, focusing on the combined effects of the external voltage, magnetic field, visco-Pasternak foundation, structural damping and volume percent of SWCNTs on the dynamic instability of structure. The numerical results are validated with other published works as well as comparing results obtained by three theories. Numerical results indicate that the magnetic and electric fields as well as SWCNTs as reinforcer are very important in dynamic instability analysis of structure.

• Steel and Composite Structures
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• v.49 no.3
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• pp.307-323
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• 2023

In this research, the study of the thermoelastic flexural analysis of silicon carbide/Aluminum graded (FG) sandwich 2D uniform structure (plate) under harmonic sinusoidal temperature load over time is presented. The plate is modeled using a simple two dimensional integral shear deformation plate theory. The current formulation contains an integral terms whose aim is to reduce a number of variables compared to others similar solutions and therefore minimize the computation time. The transverse shear stresses vary according to parabolic distribution and vanish at the free surfaces of the structure without any use of correction factors. The external load is applied on the upper face and varying in the thickness of the plates. The structure is supposed to be composed of "three layers" and resting on nonlinear visco-Pasternak's-foundations. The governing equations of the system are deduced and solved via Hamilton's principle and general solution. The computed results are compared with those existing in the literature to validate the current formulation. The impacts of the parameters (material index, temperature exponent, geometry ratio, time, top/bottom temperature ratio, elastic foundation type, and damping coefficient) on the dynamic flexural response are studied.

• Steel and Composite Structures
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• v.28 no.1
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• pp.13-24
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• 2018

A size-dependent novel hyperbolic shear deformation theory of simply supported functionally graded beams is presented in the frame work of the non-local strain gradient theory, in which the stress accounts for only the nonlocal strain gradients stress field. The thickness stretching effect (${\varepsilon}_z{\neq}0$) is also considered here. Elastic coefficients and length scale parameter are assumed to vary in the thickness direction of functionally graded beams according to power-law form. The governing equations are derived using the Hamilton principle. The closed-form solutions for exact critical buckling loads of nonlocal strain gradient functionally graded beams are obtained using Navier's method. The derived results are compared with those of strain gradient theory.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.3
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• pp.313-318
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• 1983

It is required in designing a spot welding to get in advance an estimated figure of nugget diameter. A method of estimating nugget diameter of low carbon steel sheets is suggested in tesms of utilizing elastic calculation in theory and of making a sectional observation of specimen of spot welding in experiment. The resultant findings are summarized as follows: 1) A contact diameter of sheet, 2.gamma.$_{o}$=d sub e/+(1.1)t, wheer de is the electrode tip diameter and t is the thickness of sheets. 2) The practical measurement of the nugget diameter reveals that $d_{n}$=(1.05) $d_{e}$+(0.9)t, and $d_{b}$ is less by 0.8-4.3% than 2.gamma.$_{o}$. 3) The more $d_{n}$ is as compared with t, the less the difference between a theoretical value and an experimental value is. 4) In the spot welding of thin steel sheets less than 3mm in thickness that are commonly used in sheet metal works, the contact diameter equals the nugget diameter. In this case, either the theoretical or experimental approach can be used for estimating the nugget diameter.meter.ter.r.

• Smart Structures and Systems
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• v.19 no.2
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• pp.115-126
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• 2017

In this paper, size dependent bending and free flexural vibration behaviors of functionally graded (FG) nanobeams are investigated using a nonlocal quasi-3D theory in which both shear deformation and thickness stretching effects are introduced. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanostructures. The present theory incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and furthermore accounts for both shear deformation and thickness stretching effects by virtue of a hyperbolic variation of all displacements through the thickness without using shear correction factor. The material properties of FG nanobeams are assumed to vary through the thickness according to a power law. The neutral surface position for such FG nanobeams is determined and the present theory based on exact neutral surface position is employed here. The governing equations are derived using the principal of minimum total potential energy. The effects of nonlocal parameter, aspect ratio and various material compositions on the static and dynamic responses of the FG nanobeam are discussed in detail. A detailed numerical study is carried out to examine the effect of material gradient index, the nonlocal parameter, the beam aspect ratio on the global response of the FG nanobeam. These findings are important in mechanical design considerations of devices that use carbon nanotubes.

• Steel and Composite Structures
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• v.53 no.1
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• pp.1-27
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• 2024

This work presents the effectiveness of differential quadrature shape functions (i.e., Lagrange interpolation polynomial, Cardinal sine function, Delta Lagrange kernel and Regularized Shannon kernel) in the solution of nonlinear vibration of multilayers piezoelectric plates with nonlinear elastic support. A piezoelectric composite laminated plate is rested on nonlinear Winkler and Visco-Pasternak elastic foundations problems. Based on 3D elasticity theory and piezoelectricity, the governing equations of motion are derived. Differential quadrature methods based on four shape functions are presented as numerical techniques for solving this problem. The perturbation method is implemented to solve the obtained nonlinear eigenvalue problem. A MATLAB code is written for each technique for solving this problem and extract the numerical results. To validate these methods, the computed results are we compare with the previous exact results. In addition, parametric analyses are offered to investigate the influence of length to thickness ratio, elastic foundation parameters, various boundary conditions, and piezoelectric layers thickness on the natural frequencies and mode shapes. Consequently, it is discovered that the obtained results via the proposed schemes can be applied in structural health monitoring.

• Geomechanics and Engineering
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• v.18 no.2
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• pp.161-178
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• 2019

In this research, a simple quasi 3D hyperbolic shear deformation model is employed for bending and dynamic behavior of functionally graded (FG) plates resting on visco-Pasternak foundations. The important feature of this theory is that, it includes the thickness stretching effect with considering only 4 unknowns, which less than what is used in the First Order Shear Deformation (FSDT) theory. The visco­Pasternak's foundation is taken into account by adding the influence of damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's foundation modulus. The equations of motion for thick FG plates are obtained in the Hamilton principle. Analytical solutions for the bending and dynamic analysis are determined for simply supported plates resting on visco-Pasternak foundations. Some numerical results are presented to indicate the effects of material index, elastic foundation type, and damping coefficient of the foundation, on the bending and dynamic behavior of rectangular FG plates.

• International Journal of Highway Engineering
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• v.10 no.4
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• pp.213-224
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• 2008

Flexible pavement responses to vehicular loading, such as critical stresses and strains, in each pavement layer, could be predicted by the multilayered elastic analysis. However, multilayered elastic theory suffers from major drawbacks including spatial dimension of a numerical model, material properties considered in the analysis, boundary conditions, and ill-presentation of tire-pavement contact shape and stresses. To overcome these shortcomings, three-dimensional finite element (3D FE) models are developed and numerical analyses are conducted to calculate pavement responses to moving load in this study. This paper introduces a methodology for an effective 3D FE to simulate flexible pavement structure. It also discusses the mesh development and boundary condition analysis. Sensitivity analyses of flexible pavement response to loading are conducted. The infinite boundary conditions and time-dependent history of calculated pavement responses are considered in the analysis. This study found that the outcome of 3D FE implicit dynamic analysis of flexible pavement that utilizes appropriate boundary conditions, continuous moving load, viscoelastic hot-mix asphalt model is comparable to field measurements.

• Smart Structures and Systems
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• v.22 no.3
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• pp.259-276
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• 2018

This paper studies the energies and energy release rate (ERR) for the initially rotationally symmetric compressed (or stretched) in the inward (outward) radial direction of the PZT/Elastic/PZT sandwich circular plate with interface penny-shaped cracks. The investigations are made by utilizing the so-called three-dimensional linearized field equations and relations of electro-elasticity for piezoelectric materials. The quantities related to the initial stress state are determined within the scope of the classical linear theory of piezoelectricity. Mathematical formulation of the corresponding problem and determination of the quantities related to the stress-strain state which appear as a result of the action of the uniformly normal additional opening forces acting on the penny-shaped crack's edges are made within the scope of the aforementioned three-dimensional linearized field equations solution which is obtained with the use of the FEM modelling. Numerical results of the energies and ERR and the influence of the problem parameters on these quantities are presented and discussed for the PZT- 5H/Al/PZT-5H, PZT-4/Al/PZT-4, $BaTiO_3/Al/BaTiO_3$ and PZT-5H/StPZT-5H sandwich plates. In particular, it is established that the magnitude of the influence of the piezoelectricity and initial loading on the ERR increases with crack radius length.