• Structural Engineering and Mechanics
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• v.28 no.6
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• pp.635-658
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• 2008

An application is presented of a modified Vlasov model to the free vibration analysis of plates resting on elastic foundations. The effects of the subsoil depth, the ratio of the plate dimensions, the ratio of the subsoil depth to the plate dimension in the longer direction, and the value of the vertical deformation parameter within the subsoil on the frequency parameters of plates on an elastic foundation are investigated. This analysis has been caried out by the aid of a computer program. The first ten frequency parameters are presented in tabular and the graphical forms to evaluate the effects of the parameters considered in this study. Then mode shapes corresponding to the first six of the frequency parameters are given in graphs. It is concluded that the effect of the subsoil depth on the frequency parameters of the plates on an elastic foundation is generally larger than those of the other parameters considered in this study.

• Structural Engineering and Mechanics
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• v.57 no.6
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• pp.969-988
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• 2016

Vibration analysis of the beams on elastic foundation has gained the great interest of many researchers. In the literature, there are many studies that focus on the free vibration analysis of the beams on one or two parameter elastic foundations. On the other hand, there are no sufficient studies especially focus on the comparison of dynamic response including the bending moment and shear force of the beams resting on Winkler and two parameter foundations. In this study, dynamic response of the axially loaded Timoshenko beams resting on modified Vlasov type elastic soil was investigated by using the separation of variables method. Governing equations were obtained by assuming that the material had linear elastic behaviour and mass of the beam was distributed along its length. Numerical analysis were provided and presented in figures to find out the differences between the modified Vlasov model and conventional Winkler type foundation. Furthermore, the effect of shear deformation of elastic soil on the dynamic response of the beam was investigated.

• Structural Engineering and Mechanics
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• v.88 no.3
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• pp.273-285
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• 2023

This study examines how the interaction between soil and a wind turbine's supporting system affects the optimal design. The supporting system resting on an elastic soil foundation consists of a steel conical tower and a concrete circular raft foundation, and it is subjected to wind loads. The material cost of the supporting system is aimed to be minimized employing various metaheuristic optimization algorithms including teaching-learning based optimization (TLBO). To include the influence of the soil in the optimization process, modified Vlasov and Gazetas elastic soil models are integrated into the optimization algorithms using the application programing interface (API) feature of the structural analysis program providing two-way data flow. As far as the optimal designs are considered, the best minimum cost design is achieved for the TLBO algorithm, and the modified Vlasov model makes the design economical compared with the simple Gazetas and infinitely rigid soil models. Especially, the optimum design dimensions of the raft foundation extremely reduce when the Vlasov realistic soil reactions are included in the optimum analysis. Additionally, as the designated design wind speed is decreased, the beneficial impact of soil interaction on the optimum material cost diminishes.

• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.23-31
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• 2017

In the study, dynamic behavior of laminated orthotropic beams on elastic foundation is investigated. Consistent model presented here combines the finite element solution of the system with SAP2000 software and the calculation of soil parameters with MATLAB software using Modified Vlasov Model type elastic foundation. For this purpose, a computing tool is coded in MATLAB which employs Open Application Programming Interface (OAPI) feature of SAP2000 to provide two-way data flow during execution. Firstly, an example is taken from the literature to demonstrate the accuracy of the consistent FEM-Vlasov Model. Subsequently, the effects of boundary conditions, subsoil depth, elasticity modulus of subsoil, slenderness ratio, velocity of moving load and lamination scheme on the behavior of laminated orthotropic beams on elastic foundation are investigated on a new numerical example. It can be concluded that it is really convenient to use OAPI feature of SAP2000 to model this complex behavior of laminated orthotropic beams on elastic foundation under moving load.

• Wind and Structures
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• v.22 no.6
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• pp.617-633
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• 2016

In this paper, the analysis of hyperbolic cooling tower on elastic subsoil exposed to unsymmetrical wind loading is presented. Modified Vlasov foundation model is used to determine the soil parameters as a function of vertical deformation profile within subsoil. The iterative parameter updating procedure involves the use of Open Application Programming Interface (OAPI) feature of SAP2000 to provide two way data flow during execution. A computing tool coded in MATLAB employing OAPI is used to perform the analysis of hyperbolic cooling tower with supporting columns over a hollow annular raft founded on elastic subsoil. The analysis of such complex soil-structure system is investigated under self-weight and unsymmetrical wind load. The response of the cooling tower on elastic subsoil is compared with that of a tower that its supporting raft foundation is treated as fixed at the base. The results show that the effect of subsoil on the behavior of cooling tower is considerable at the top and bottom of the wall as well as supporting columns and raft foundation. The application of a full-size cooling tower has demonstrated that the procedure is simple, fast and can easily be implemented in practice.

• Geotechnical Engineering
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• v.14 no.3
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• pp.25-46
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• 1998

This paper shows that there are the results of a series of model tests on the behavior of single pipe pile which is subjected to lateral load in, Nak-dong River sand. The purpose of the present paper is to estimate the effect of Non-homogeneity. constraint condition of pile head, lateral load velocity, relative density, and embedded length of pile on the behavior of single pile. These effects can be quantified only by the results of model tests. Also, these are compared with the results of the numerical methods (p-y method, modified Vlasov method; new ${\gamma}$ parameter, Characteristic Load Method'CLM). In this study, a new ${\gamma}$ parameter equation based on the Vlasov method was developed to calculate the modulus of subgrade reaction (E. : nhz.) proportional to the depth. The p-y method of analysis is characterized by nonlinear behavior. and is an effective method of designing deep foundations subjected to lateral loads. The new method, which is called the characteristic load method (CLM). is simpler than p-y analysis. but its results closely approximates p-y analysis results. The method uses dimensional analysis to characterize the nonlinear behavior of laterally loaded piles with respect to be relationships among dimensionless variables. The modulus of subgrade reaction used in p-y analysis and modified Vlasov method obtained from back analysis using direct shear test (DST) results. The coefficients obtained from DST and the modified ones used for the prediction of lateral behavior of ultimate soil reaction range from 0.014 to 0.05. and from 0.2 to 0.4 respectively. It is shown that the predicted numerical results by the new method (CLM), p-y analysis, and modified Vlasov method (new parameter) agree well with measured results as the relative density increases. Also, the characteristic load method established applicability on the Q-Mnu. relationship below y/D=0.2.

• 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.

• Geomechanics and Engineering
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• v.23 no.3
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• pp.275-287
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• 2020

Rectangular barrettes have been increasingly used as foundations for many infrastructure projects, but the vertical vibration of a barrette has been rarely addressed theoretically. This paper presents an analysis method of dynamic response for a rectangular barrette subjected to a time-harmonic vertical force with the aid of a modified Vlasov foundation model in multilayered viscoelastic soil. The barrette-soil system is modeled as a continuum, the vertical continuous displacement model for the barrette and soil is proposed. The governing equations of the barrette-soil system and the boundary conditions are obtained and the vertical shaft resistance of barrette is established by employing Hamilton's principle for the system and thin layer element, respectively. The physical meaning of the governing equations and shaft resistance is interpreted. The iterative solution algorithm flow is proposed to obtain the dynamic response of barrette. Good agreement of the analysis and comparison confirms the correctness of the present solution. A parametric study is further used to demonstrate the effects of cross section aspect ratio of barrettes, depth of soil column, and module ratio of substratum to the upper soil layers on the complex barrette-head stiffness and the resistance stiffness.