• Structural Engineering and Mechanics
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• v.88 no.5
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• pp.439-449
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• 2023

Non-linear vibration characteristics of functionally graded CNT-reinforced composite (FG-CNTRC) cylindrical shell panel on elastic foundation have not been sufficiently examined. In this situation, this study aims at the profound numerical investigation of the non-linear vibration response of FG-CNTRC cylindrical panels on Winkler-Pasternak foundation by introducing an accurate and effective 2-D meshfree-based non-linear numerical method. The large-amplitude free vibration problem is formulated according to the first-order shear deformation theory (FSDT) with the von Karman non-linearity, and it is approximated by Laplace interpolation functions in 2-D natural element method (NEM) and a non-linear partial derivative operator H_NL. The complex and painstaking numerical derivation on the curved surface and the crucial shear locking are overcome by adopting the geometry transformation and the MITC3+ shell elements. The derived nonlinear modal equations are iteratively solved by introducing a three-step iterative solving technique which is combined with Lanczos transformation and Jacobi iteration. The developed non-linear numerical method is estimated through the benchmark test, and the effects of foundation stiffness, CNT volume fraction and functionally graded pattern, panel dimensions and boundary condition on the non-linear vibration of FG-CNTRC cylindrical panels on elastic foundation are parametrically investigated.

• Interaction and multiscale mechanics
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• v.5 no.1
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• pp.13-26
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• 2012

In this paper, the wave propagation in a generalized thermo elastic plate embedded in an elastic medium (Winkler model) is studied based on the Lord-Schulman (LS) and Green-Lindsay (GL) generalized two dimensional theory of thermo elasticity. Two displacement potential functions are introduced to uncouple the equations of motion. The frequency equations that include the interaction between the plate and foundation are obtained by the traction free boundary conditions using the Bessel function solutions. The numerical calculations are carried out for the material Zinc and the computed non-dimensional frequency and attenuation coefficient are plotted as the dispersion curves for the plate with thermally insulated and isothermal boundaries. The wave characteristics are found to be more stable and realistic in the presence of thermal relaxation times and the foundation parameter. A comparison of the results for the case with no thermal effects shows well agreement with those by the membrane theory.

• Steel and Composite Structures
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• v.17 no.1
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• pp.1-19
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• 2014

Buckling and vibration characteristics of circular laminated plates under in-plane edge loads and resting on Winkler-type foundation are solved by the Ritz method. Inclusive numerical data are presented for the first three eigen-frequencies as a function of in-plane load for different classical edge conditions. Moreover, the effects of fiber orientation on the natural frequencies and critical buckling loads of laminated angle-ply plates with stacking sequence of $[({\beta}/-{\beta}/{\beta}/-{\beta})]_s$, are studied. Also, selected deformation mode shapes are illustrated. The correctness of results is established using finite element software as well as by comparison with the existing results in the literature.

• Coupled systems mechanics
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• v.1 no.2
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• pp.115-131
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• 2012

Paper presents an improved solution algorithm based on Finite Element Method to analyse piled raft foundation. Piles are modelled as beam elements with soil springs. Finite element analysis of raft is based on the classical theory of thick plates resting on Winkler foundation that accounts for the transverse shear deformation of the plate. Four node, isoparametric rectangular elements with three degrees of freedom per node are considered in the development of finite element formulation. Independent bilinear shape functions are assumed for displacement and rotational degrees of freedom. Effect of raft thickness, soil modulus and load pattern on the response is considered. Significant improvement in the settlements and moments in the raft is observed.

• Advances in nano research
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• v.4 no.4
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• pp.309-326
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• 2016

The buckling response of a single-layered graphene sheet (SLGS) embedded in visco-Pasternak's medium is presented. The nonlocal first-order shear deformation elasticity theory is used for this purpose. The visco-Pasternak's medium is considered by adding the damping effect to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's (shear) foundation modulus. The SLGS be subjected to distributive compressive in-plane edge forces per unit length. The governing equilibrium equations are obtained and solved for getting the critical buckling loads of simply-supported SLGSs. The effects of many parameters like nonlocal parameter, aspect ratio, Winkler-Pasternak's foundation, damping coefficient, and mode numbers on the buckling analysis of the SLGSs are investigated in detail. The present results are compared with the corresponding available in the literature. Additional results are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak's parameters for future comparisons.

• Steel and Composite Structures
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• v.24 no.6
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• pp.697-709
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• 2017

The current study addresses the local buckling analysis of an infinite thin rectangular symmetrically laminated composite plate restrained by a tensionless Winkler foundation and subjected to uniform in-plane shear loading. An analytic method (i.e., one-dimensional mathematical method) is used to achieve the analytical solution estimate of the contact buckling coefficient. In addition, to study the effect of ply angle and foundation stiffness on the critical buckling coefficients for the laminated composite plates, the parametric studies are implemented. Moreover, the convergence for finite element (FE) mesh is analysed, and then the examples in the parametric study are validated by the FE analysis. The results show that the FE analysis has a good agreement with the analytical solutions. Finally, an example with the analytical solution and FE analysis is presented to demonstrate the availability and feasibility of the presented analytical method.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.4
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• pp.251-258
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• 1993

The main purpose of this paper is to present both the natural frequencies and the buckling loads of beam-columns on Winkler-type foundations. The ordinary differential equations governing the free vibrations and the buckling loads of beam-columns on Winkler-type foundation are derived as nondimensional forms. The Runge-Kutta method and Determinant Search method are used to perform the integration of the differential equations and to determine the eigenvalues(natural frequencies and buckling loads), respectively. Hinged-hinged and damped-clamped end constraints are applied in numerical examples. The relation between frequency parameter and elastic foundation parameter is presented in figure. The effects of axial loads on the natural frequencies of beam-columns on elastic foundations are investigated and the relation between buckling load parameter and elastic foundation parameter is also analyzed. The relation between foundation rested ratio and frequency parameter, buckling load parameter are investigated. The beam-columns on non-homogeneous elastic foundation are analyzed and typical mode shapes are also presented.

• Geomechanics and Engineering
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• v.18 no.1
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• pp.41-48
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• 2019

Bending moments in the raft of a pile raft system is affected by pile-pile interaction and pile-raft interaction, amongst other factors. Three-Dimensional finite element program has to be used to evaluate these bending moments. Winkler type analysis is easy to use but it however ignores these interactions. This paper proposes a very simplified and novel method for finding bending moments in raft of a piled raft based on Winkler type where raft is supported on bed of springs considering pile-pile and pile-raft interaction entitled as "Winkler model for piled raft (WMPR)" The pile and raft spring stiffness are based on load share between pile and raft and average pile raft settlement proposed by Randolph (1994). To verify the results of WMPR, raft bending moments are compared with those obtained from PLAXIS 3D software. A total of sixty analysis have Performed varying different parameters. It is found that raft bending moments obtained from WMPR closely match with bending moments obtained from PLAXIS 3D. A comparison of bending moments ignoring any interaction in Winkler model is also made with PLAXIS-3D, which results in large difference of bending moments. Finally, bending moment results from eight different methods are compared with WMPR for a case study. The WMPR, though, a simple method yielded comparable raft bending moments with the most accurate analysis.

• Steel and Composite Structures
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• v.46 no.1
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• pp.1-13
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• 2023

Elastic bending of imperfect functionally graded sandwich plates (FGSPs) laying on the Winkler-Pasternak foundation and subjected to sinusoidal loads is analyzed. The analyses have been established using the quasi-3D sinusoidal shear deformation model. In this theory, the number of unknowns is condensed to only five unknowns using integral-undefined terms without requiring any correction shear factor. Moreover, the current constituent material properties of the middle layer is considered homogeneous and isotropic. But those of the top and bottom face sheets of the graded porous sandwich plate (FGSP) are supposed to vary regularly and continuously in the direction of thickness according to the trigonometric volume fraction's model. The corresponding equilibrium equations of FGSPs with simply supported edges are derived via the static version of the Hamilton's principle. The differential equations of the system are resolved via Navier's method for various schemes of FGSPs. The current study examine the impact of the material index, porosity, side-to-thickness ratio, aspect ratio, and the Winkler-Pasternak foundation on the displacements, axial and shear stresses of the sandwich structure.

• Advances in nano research
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• v.10 no.1
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• pp.25-42
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• 2021

In this article, the vibration behavior of embedded Functionally Graded Nanoplate (FGNP) employing nonlocal Kirchhoff's plate theory has been investigated under hygrothermal environment. The FGNP is considered to be supported by Winkler-Pasternak foundation. The Eringen's differential theory is used for size effect on the vibration of the FGNP. Rayleigh-Ritz method with orthogonal polynomials are employed for the governing equations and edge constraints. The advantage of this method is that it overcomes all the drawbacks of edge constraints and can easily handle any combinations of mixed edge constraints. The coefficients viz. moisture expansion, thermal expansion and elastic coefficients are considered to be transversely graded across the FGNP. The similarity of the calculated natural frequencies is examined with the previous research, and a good concurrency is seen. The objective of this article is to analyze the parameters' effect on the nondimensionalized frequency of embedded FGNP under hygrothermal environment subjected to all possible edge constraints. For this, uniform and linear rise of temperature and moisture concentration are considered. The study highlights that the nonlocal effect is pronounced for higher modes. Moreover, the effect of the Pasternak modulus is seen to be prominent compared to the Winkler modulus on non dimensionalized frequencies of FGNP.