Modified Vlasov Model Research Articles

Vibration Analysis of Perovskite Solar Cells Resting on Porous Nanocomposite Substrate in Thermal Environment

The free vibration analysis of a perovskite solar cell (PSC) within thermal environments is studied through a quasi-3D plate model. This model is designed to account for the stretching effects and non-uniform shear strains throughout the thickness. The PSC film is represented in the model as a thin laminated plate, comprising five distinct plies: ITO, PEDOT:PSS, perovskite, PCBM, and Au. A graphene platelets reinforced composite (GPLRC) substrate, made of Poly (methyl methacrylate), is assumed to be located under the noted five layers. The GPLRC substrate is conceptualized in the model as a porous foundation with finite depth. The foundation stiffnesses are determined using a modified Vlasov model, and the equivalent Young modulus of the foundation is evaluated using a modified Halpin–Tsai model, introducing the porosity coefficient. It is also considered that the material properties of GPLRC substrates exhibit temperature dependency. For the PSC with all edges simply supported, Navier solution method is applied to obtain the frequencies and associated mode numbers. Based on the results presented in this study, an increase in the porosity and thickness of the substrate can negatively impact the frequencies of the structure. However, natural frequencies experience almost no change if the temperature rises.

Analysis of Settlement of an Existing Tunnel Subjected to Undercrossing Tunneling Based on the Modified Vlasov Model

Analysis of Settlement of an Existing Tunnel Subjected to Undercrossing Tunneling Based on the Modified Vlasov Model

Reply to the discussion on “The modified Vlasov model on a nonhomogeneous and nonlinear soil layer”

Reply to the discussion on “The modified Vlasov model on a nonhomogeneous and nonlinear soil layer”

Soil–Structure Interaction Effect on the Resistance of a Steel Frame against Progressive Collapse Using Linear Static and Nonlinear Dynamic Procedures

In recent years, increases in terrorist attacks or other unexpected explosions have shown that their effects can cause critical damages to buildings and cause partial or total collapse of buildings. This chain collapse mechanism is named a progressive collapse. Subsoil effects on a building are often ignored in studies on progressive collapse. In this study, the effect of soil–structure interaction on the risk of progressive collapse of a steel frame is investigated by using the modified Vlasov model, which has not been used in the studies on progressive collapse before. For this purpose, a steel building model was investigated. A linear static procedure (LSP) and nonlinear dynamic procedure (NDP) with alternative path method were used for the analysis of the frame. SAP2000 software was used to model subsoil effect on the frame via an interface coded in MATLAB interactively. The results from the analyses showed that the soil–structure interaction effect can significantly affect the progressive collapse resistance of the building.

Dynamic analysis of a laterally loaded rectangular pile in multilayered viscoelastic soil

Rectangular piles are usually used as the foundation for many infrastructures, but there are fewer theoretical solutions for the lateral vibration. This study presents a semi-analytical methodology for the dynamic analysis of laterally loaded rectangular pile in multi-layered viscoelastic soils. The pile-soil system is modeled as a continuum, the horizontal continuous displacement model is proposed as products of the separating variables function. The coupled governing equations for rectangular pile-soil system in the frame of Euler-Bernoulli beam and modified Vlasov model are derived with the aid of Hamilton's Variation principle and calculus of variations. The physical mechanisms of soil reaction and dynamic equilibrium equation are interpreted by employing thin-layer element of soil. The dynamic responses are solved analytically and numerically by an iterative procedure. The verification and accuracy of the research are obtained thorough comparison with the relevant examples from the literatures and finite element analysis. The effects of cross-section shapes and soil stratification on the complex dynamic response are investigated and discussed in detail.

Static Analysis of thin Rectangular Plate Resting on Elastic Foundation Using Modified Vlasov Model

A four-nodded rectangular plate bending element based on Kirchhoff theory resting on elastic foundation using modified Vlasov model. For evaluate the two soil parameter for Vlasov foundation the modulus of elasticity and Poisson ratio of the soil is assumed constant from top surface to the top of bottom rigid base. All the deformation stiffness matrix of plate and subsoil are evaluated using finite element method. A Matlab code is developed and convergence study is carried out and then some realistic cases of plate under static load on elastic foundations are solved to determine the static response. The results, thus obtained, are compared, with the available results obtained by other researchers. It behaves extremely well for thin plates and convergence rate is high.

Analytical method for the kinematic response and signal error of a downhole seismometer subjected to P-waves

This paper presents an analytical method for the steady-state kinematic response of downhole seismometers to vertically incident P-waves, based on a modified Vlasov model. The governing equations and boundary conditions of a soil–well system were obtained using Hamilton's principle. The three unknown functions were then decoupled using an iterative algorithm. The accuracy of the proposed method was validated by placing a downhole seismometer in the well and comparing the responses with previously reported results. A parametric study was performed to investigate the effects of the soil–well system properties on the kinematic response and monitoring errors of the downhole seismometer. Results indicated that the incident frequency, thickness of the foundation of the downhole seismometer, soil–well modulus ratio Ew/Es, and slenderness ratio of the downhole seismometer considerably influence the monitoring error, whereas soil damping has little effect on it.

Modeling and evaluation for large amplitude vibration and nonlinear bending of perovskite solar cell

The large amplitude vibration and nonlinear bending analyses for a perovskite solar cell (PSC) in thermal environments are presented through the plate-substrate model. The PSC film is modeled as a thin laminated plate which consists of five plies including ITO, PEDOT:PSS, perovskite, PCBM, and Au. Two kinds of graphene platelets reinforced composite (GPLRC) substrates are considered. The GPLRC substrate is modeled as a porous foundation with finite depth. The foundation stiffnesses are predicted by modified Vlasov model and the equivalent Young’s modulus of the foundation is estimated through a modified Halpin–Tsai model where the porosity coefficient is introduced. The material properties of GPLRC substrates are assumed to be temperature dependent. The thermal effect and plate-foundation interaction are involved in the governing equations which are solved by means of a two-step perturbation approach. The numerical investigations are carried out for the PSC plate rested on GPL/PMMA and GPL/Al substrates. It is shown that the substrate depth and porosity coefficient have substantial influences on the vibration response and nonlinear bending behavior of PSC plates.

Modeling and low-velocity impact analysis of perovskite solar cells resting on porous substrates reinforced by graphene platelets

A nanoplate-foundation model is proposed for the perovskite solar cells (PSCs) on porous substrates reinforced by graphene platelets (GPLs). The coating film of PSCs is modeled as a laminate plate with nano-scale thickness and consists of five plies including ITO, PEDOT: PSS, perovskite, PCBM, and Au. The GPL reinforced substrate is modeled as an elastic foundation with finite depth, and the spring stiffness is predicted by the modified Vlasov model. The equivalent Young's modulus of the GPL/Al composites is estimated through a modified Mori-Tanaka model, where the GPLs are regarded as particle reinforcements. The effect of the porosity coefficient is taken into account by a quartic polynomial. FE Modeling and low-velocity impact analysis are then carried out. It is shown that the depth and porosity coefficient of the substrate have substantial influences on the dynamic response of PSCs.

Two Novel Vlasov Models for Bending Analysis of Finite-Length Beams Embedded in Elastic Foundations

The issue of soil–structure interaction (SSI) is essentially to analyze the influence of complex media on the mechanical behavior of supported structures. With the development of underground space, geological structures and space constraints put forward higher requirements for foundations and buildings. In this paper, the effects of soil heterogeneity and embedment depth on the bending of finite-length beams embedded in two novel Vlasov elastic foundations are investigated. Firstly, the constitutive relations of subsoil are simulated by Gibson and transversely isotropic soils, and the type of elastic foundation is described by the modified Vlasov model. Then, based on variational principles, the governing differential equations for the deformation and attenuation parameters of beams embedded in elastic foundations are derived by taking the variation of the minimum potential energy of the system, and the characteristic coefficient related to the embedment depth is introduced. Finally, the mechanical performance of the beam and foundation is obtained by an iterative technique and the Fourier series method, and an extensive parametric study is performed to examine influence of some basic parameters on the deformation and internal forces of the system. The results show that the mathematical expressions of two refined elastic models are in good agreement with those of the traditional Vlasov foundation after degradation. The iterative technique based on the principles of solid mechanics can be employed to obtain more reliable model parameters. More importantly, with the increase in the embedment depth, the mechanical responses of the beam and subgrade forces decrease. The main reason is that the restraint effect of the soil media around structures, which leads to the reduction of the characteristic coefficient affecting the displacement of beams. Moreover, the heterogeneity of soil, including Gibson characteristics and transverse isotropy, should be considered according to specific working conditions in civil engineering.

Discussion on “The modified Vlasov model on a nonhomogeneous and nonlinear soil layer” by Volkan Isbuga, Mehmet Cerezci and M. Zulfu Asik

Discussion on “The modified Vlasov model on a nonhomogeneous and nonlinear soil layer” by Volkan Isbuga, Mehmet Cerezci and M. Zulfu Asik

The modified Vlasov model on a nonhomogeneous and nonlinear soil layer

This study presents a novel approach to account for the soil nonlinearity of nonhomogeneous soil deposits in foundation deflection analyses in the context of a modified Vlasov foundation model. We present an extension of the previously proposed formulation by developing a new formulation employing an improved algorithm that takes the modulus degradation curves at varying strain levels into account in an iterative manner. This new model, which takes the nonlinear soil behavior into account, was first verified against a linear elastic soil model given in the literature to ensure that the new model algorithm can capture the original solution when the soil behavior is assumed to be linear elastic. Later, the experimental data reported in the literature for a specific type of dense and loose sands were used in the example analyses. Example problems were considered for different cases, which presented (i) how the model captures nonlinear behavior and (ii) the significant effect of the nonlinear soil behavior. The result of the new model was also compared with the finite element model results, assuming elastoplastic soil. The results obtained from both models match well, especially for the maximum deflection value, provided that laterally constrained sections underneath the foundation are used.

Dynamic response analysis of Euler–Bernoulli beam on spatially random transversely isotropic viscoelastic soil

A novel dynamic soil-structure interaction model is developed for analysis for Euler–Bernoulli beam rests on a spatially random transversely isotropic viscoelastic foundation subjected to moving and oscillating loads. The dynamic equilibrium equation of beam-soil system is established using the extended Hamilton's principle, and the corresponding partial differential equations describing the displacement of beam and soil and boundary conditions are further obtained by the variational principles. These partial differential equations are discretized in spatial and time domains and solved by the finite difference (FD) method. After the differential equations of beam and soil are discretized in the spatial domain, the implicit iterative scheme is used to solve the equations in the time domain. The solving result shows the FD method is effective and convenient for solving the differential equations of beam-soil system. The spring foundation model adopted the modified Vlasov model, which is a two-parameter model considering the compression and shear of soil. The advantage of the present foundation model is avoided estimating input parameters of the modified Vlasov model using prior knowledge. The present solution is verified by publishing solution and equivalent three-dimensional FE analysis. The present model produced an accurate, faster, and effective displacement response. A few examples are carried out to analyze the parameter variation influence for beam on spatially random transversely isotropic viscoelastic soil under moving loads.

Response Analysis of Second-Order Continuity Rectangular Plate Bending Element Resting on Elastic Foundation Using Modified Vlasov Model

Response Analysis of Second-Order Continuity Rectangular Plate Bending Element Resting on Elastic Foundation Using Modified Vlasov Model

Iterative technique for circular thin plates on Gibson elastic foundation using modified Vlasov model

In this paper, to investigate the influence of soil inhomogeneity on the bending of circular thin plates on elastic foundations, the static problem of circular thin plates on Gibson elastic foundation is solved using an iterative method based on the modified Vlasov model. On the basis of the principle of minimum potential energy, the governing differential equations and boundary conditions for circular thin plates on modified Vlasov foundation considering the characteristics of Gibson soil are derived. The equations for the attenuation parameter in bending problem are also obtained, and the issue of unknown parameters being difficult to determine is solved using the iterative method. Numerical examples are analyzed and the results are in good agreement with those form other literatures. It proves that the method is practical and accurate. The inhomogeneity of modified Vlasov foundations has some influence on the deformation and internal force behavior of circular thin plates. The effects of various parameters on the bending of circular plates and characteristic parameters of the foundation are discussed. The modified model further enriches and develops the elastic foundations. Relevant conclusions that are meaningful to engineering practice are drawn.

Kinematic response of rectangular piles under S waves

An analytical solution was proposed for the kinematic response of rectangular piles under S waves with the aid of a modified Vlasov model. A continuous displacement model was proposed to simulate the motion of soil-pile system. Using Hamilton’s principle, the proposed solution well captures the kinematic response of piles compared with the finite element solution. A parametric study was conducted to investigate the influence of cross-section shapes on the kinematic response of piles and underlying pile bending, Winkler modulus, shear stresses in soil, and inertia of soil and pile. The results reveal that pile bending dominates kinematic responses of piles.

Modelling Laminated Orthotropic Plate-Foundation Interaction Subjected to Moving Load Using Vlasov Model

In this study, dynamic behavior of laminated orthotropic plates on elastic foundation is investigated adapting the three parameter subsoil model. Analysis of the system is performed by using SAP2000 combining with MATLAB code for calculation of soil parameters of modified Vlasov model. A computing tool is coded in MATLAB for the purpose allowing data exchange simultaneously between SAP2000 and MATLAB via Open Application Programming Interface (OAPI) feature. The consistency of the proposed model is shown comparatively with a numerical example taken from the literature. Later, the effects of lamination scheme, various lamination angles, lamination number, subsoil depth, elasticity modulus of subsoil, plate thickness and velocity of moving load on the behavior of laminated orthotropic plates on elastic foundation are investigated. It can be concluded that it is really convenient to use OAPI feature of SAP2000 to model this complex behavior of laminated orthotropic plates on elastic soil under moving load.

Bending analysis of agglomerated carbon nanotube-reinforced beam resting on two parameters modified Vlasov model foundation

The present work deals with bending behavior of nanocomposite beam resting on two parameters modified Vlasov model foundation (MVMF), with consideration of agglomeration and distribution of carbon nanotubes (CNTs) in beam matrix. Equivalent fiber based on Eshelby–Mori–Tanaka approach is employed to determine influence of CNTs aggregation on elastic properties of CNT-reinforced beam. The governing equations are deduced using the principle of minimum potential energy under assumption of the Euler–Bernoulli beam theory. The MVMF required the estimation of γ parameter; to this purpose, unique iterative technique based on variational principles is utilized to compute value of the γ and subsequently fourth-order differential equation is solved analytically. Eventually, the transverse displacements and bending stresses are obtained and compared for different agglomeration parameters, various boundary conditions simultaneously and variant elastic foundation without requirement to instate values for foundation parameters.

Comparative dynamic analysis of axially loaded beams on modified Vlasov foundation

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.

Kinematic Response of Single Piles to Vertical P-Waves in Multilayered Soil

A rigorous mathematical formulation for the kinematic response of single piles embedded in multilayered soil subjected to vertically incident P-waves is proposed based on the modified Vlasov model. The governing equations and boundary conditions of the soil–pile system are obtained by using Hamilton's principle. The soil–pile interaction and the physical properties of the layered soils are taken into consideration in the proposed model. The accuracy of the proposed method is validated by the comparison of the proposed solution results with some existing solutions. A parametric study is conducted to investigate the effects of the soil inhomogeneity on the kinematic response of single piles. The results reveal that: as for the two-layered case, the thickness of the upper soft layer has a significant influence on the kinematic response of single piles; as for the three-layered case, the soil–pile interaction is very sensitive to the thickness and Young's modulus of the middle layer.