• Structural Engineering and Mechanics
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• v.21 no.6
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• pp.699-712
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• 2005

The response of a plate-column system having five-degree-of-freedom supported by an elastic foundation and subjected to static lateral load, harmonic ground motion and earthquake motion is studied. Two Winkler foundation models are assumed: a conventional model which supports compression and tension and a tensionless model which supports compression only. The governing equations of the problem are obtained, solved numerically and the results are presented in figures to demonstrate the behavior of the system for various values of the system parameters comparatively for the conventional and the tensionless Winkler foundation models.

• Geomechanics and Engineering
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• v.11 no.1
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• pp.95-116
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• 2016

A novel higher order shear-deformable beam model, which provides linear variation of transversal normal strain and quadratic variation of shearing strain, is proposed to describe the beam resting on foundation. Then, the traditional two-parameter Pasternak foundation model is modified to capture the effects of the axial deformation of beam. The Masing's friction law is incorporated to deal with nonlinear interaction between the foundation and the beam bottom, and the nonlinear properties of the beam material are also considered. To solve the mathematical problem, a displacement-based finite element is formulated, and the reliability of the proposed model is verified. Finally, numerical examples are presented to study the effects of the interfacial friction between the beam and foundation, and the mechanical behavior due to the tensionless characteristics of the foundation is also examined. Numerical results indicate that the effects of tensionless characteristics of foundation and the interfacial friction have significant influences on the mechanical behavior of the beam-foundation system.

• Structural Engineering and Mechanics
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• v.34 no.3
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• pp.319-334
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• 2010

The dynamic response of a finite Bernoulli-Euler beam resting on a tensionless Pasternak foundation and subjected to a concentrated harmonic load is investigated in this study. This load may be applied at the center of the beam, or it may be offset from the center. Since the elastic foundation is assumed to be tensionless, the beam may lift off the foundation, resulting in contact and non-contact regions in the system. An analytical/numerical solution is obtained from the governing equations of the contact and non-contact regions to determine the coordinates of the lift-off points. Although there is no nonlinear term in the equations, the problem appears to be nonlinear since the contact regions are not known in advance. Due to that nonlinearity, the essentials of the problem (the coordinates of the lift-off points) are calculated numerically using the Newton-Raphson technique. The results, which represent the symmetric and asymmetric responses of the beam, are presented graphically in this work. They illustrate the effects of the forcing frequency and the beam length on the extent of the contact regions and displacements.

• Structural Engineering and Mechanics
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• v.30 no.1
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• pp.21-36
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• 2008

The static response of a finite beam resting on a tensionless Pasternak foundation and subjected to a concentrated vertical load is assessed in this study. The concentrated vertical load may be applied at the center of the beam, or it may be offset from the center. The tensionless character of the foundation results in the creation of lift-off regions between the beam and the foundation. An analytical/ numerical solution is obtained from the governing equations of the contact and lift-off regions to determine the extent of the contact region. Although there is no nonlinear term in the equations, the problem shows a nonlinear character since the contact region is not known in advance. Due to that nonlinearity, the essentials of the problem (the coordinates of the lift-off points) are calculated numerically using the Newton-Raphson technique. The numerical results are presented in figures to illustrate the behaviours of the free-free and pinned-pinned beams under symmetric or asymmetric loading. The figures illustrate the effects of the shear foundation parameter and the symmetric and asymmetric loading options on the variation of the contact lengths and the displacement of the beam.

• Structural Engineering and Mechanics
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• v.27 no.5
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• pp.555-574
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• 2007

Static response of an elastic beam on a two-parameter tensionless foundation is investigated by assuming that the beam is symmetrically subjected to a uniformly distributed load and concentrated edge loads. Governing equations of the problem are obtained and solved by pointing out that a concentrated edge foundation reaction in addition to a continuous foundation reaction along the beam axis in the case of complete contact and a discontinuity in the foundation reactions in the case of partial contact come into being as a direct result of the two-parameter foundation model. The numerical solution of the complete contact problem is straightforward. However, it is shown that the problem displays a highly non-linear character when the beam lifts off from the foundation. Numerical treatment of the governing equations is accomplished by adopting an iterative process to establish the contact length. Results are presented in figures to demonstrate the linear and non-linear behavior of the beam-foundation system for various values of the parameters of the problem comparatively.

• Structural Engineering and Mechanics
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• v.37 no.1
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• pp.61-77
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• 2011

Static and dynamic responses of a completely free elastic beam resting on a two-parameter tensionless Pasternak foundation are investigated by assuming that the beam is symmetrically subjected to a uniformly distributed load and concentrated load at its middle. Governing equations of the problem are obtained and solved by paying attention on the boundary conditions of the problem including the concentrated edge foundation reaction in the case of complete contact and lift-off condition of the beam ina two-parameter foundation. The nonlinear governing equation of the problem is evaluated numerically by adopting an iterative procedure. Numerical results are presented in figures to demonstrate the non-linear behavior of the beam-foundation system for various values of the parameters of the problem comparatively by considering the static and dynamic loading cases.

• 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.

• Structural Engineering and Mechanics
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• v.37 no.5
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• pp.489-507
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• 2011

The dynamic response of a Timoshenko beam on a tensionless Pasternak foundation is investigated by assuming that the beam is subjected to a concentrated harmonic load at its middle. This action results in the creation of lift-off regions between the beam and the foundation that effect the character of the response. Although small displacements for the beam and the foundation are assumed, the problem becomes nonlinear since the contact/lift-off regions are not known at the outset. The governing equations of the beam, which are coupled in deflection and rotation, are obtained in both the contact and lift-off regions. After removing the coupling, the essentials of the problem (the contact regions) are determined by using an analytical-numerical method. The results are presented in figures to demonstrate the effects of some parameters on the extent of the contact lengths and displacements. The results are also compared with those of Bernoulli-Euler, shear, and Rayleigh beams. It is observed that the solution is not unique; for a fixed value of the frequency parameter, more than one solution (contact length) exists. The contact length of the beam increases with the increase of the frequency and rotary-inertia parameters, whereas it decreases with increasing shear foundation parameter.

• Structural Engineering and Mechanics
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• v.81 no.3
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• pp.379-394
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• 2022

Shallow footings usually belonged to the category of thick plate structures. For accurate analysis of thick plates, the contribution of out-of-plane components of the stress tensor should be considered in the formulation. Most of the available shallow footing models are based on the classical plate theories, which usually neglect the effects of the out-of-plane stresses. In this study, a mixed-field plate finite element model (FEM) is developed for the analysis of shallow footings rested on soil foundations. In addition to displacement field variables, the out-of-plane components of the stress tensor are also assumed as a priori unknown variables. For modeling the interaction effect of the soil under and outside of the shallow footings, the modified Vlasov theory is used. The tensionless nature of the supporting soil foundation is taken into account by adopting an incremental, iterative procedure. The equality requirement of displacements at the interface between the shallow footing and soil is fulfilled using the penalty approach. For validation of the present mixed FEM, the obtained results are compared with the results of 3D FEM and previous results published in the literature. The comparisons show the present mixed FEM is an efficient and accurate tool for solving the problems of shallow footings rested on subsoil.

• Steel and Composite Structures
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• v.29 no.3
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• pp.333-348
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• 2018

An analytical method is developed for analysing the contact buckling response of infinitely long, thin corrugated plates and flat plates restrained by a Winkler tensionless foundation and subjected to linearly varying in-plane loadings, where the corrugated plates are modelled as orthotropic plates and the flat plates are modelled as isotropic plates. The critical step in the presented method is the explicit expression for the lateral buckling mode function, which is derived through using the energy method. Simply supported and clamped edges conditions on the unloaded edges are considered in this study. The acquired lateral deflection function is applied to the governing buckling equations to eliminate the lateral variable. Considering the boundary conditions and continuity conditions at the border line between the contact and non-contact zones, the buckling coefficients and the corresponding buckling modes are found. The analytical solution to the buckling coefficients is also expressed through a fitted approximate formula in terms of foundation stiffness, which is verified through previous studies and finite element (FE) method.