Foundation Parameters Research Articles

Buckling analysis of FG cylindrical nano shell integrated with CNTRC patches

Buckling analysis of a functionally graded (FG) cylindrical nano shell is studied in this paper based on nonlocal elasticity theory and first-order shear deformation theory. The nano shell is made from a combination of ceramic and metal integrated with carbon-nanotube reinforced composite (CNTRC) sheets on outer radius. The reinforced composite nano shell is resting on Pasternak’s foundation. The governing equations of motion are derived using vitual work principle. The effective material properties of carbon-nanotube reinforced composite (CNTRC) sheets are evaluated using rule of mixture. A comparative study is performed before full presentation of numerical results for verification of the model and solution procedure. A large parametric analysis is performed to investigate effect of dimensions of the core as well as CNTRC sheets, CNT volume fraction, nonlocal parameter, number of CNTRC sheets, FG-index and foundation parameters on the buckling results.

Discussion of Stick-Slip Dynamics of 2DOF Sliding Systems Based on Dynamic Vibration Absorbers Analysis

In this study, we discussed the occurrence condition stick-slip model based on a 2DOF system, in which a 1DOF system model commonly used in stick-slip analysis was attached on an elastic foundation. Specifically, the effects of the mass, stiffness, and damping coefficient of the elastic foundation on the occurrence and non-occurrence of stick-slip were investigated. It was found that when the elastic foundation parameters were determined based on the optimal parameter tuning method of the dynamic vibration absorber (DVA) theory, the range of stick-slip occurrences reduced compared to the sliding system without the elastic foundation.

The thermal vibration of small-sized rotating fractional viscoelastic beams positioned on a flexible foundation in the light of the Moore–Gibson–Thompson model

The current analysis examined the thermoviscoelastic vibration of Pasternak-based viscoelastic microbeams using fractional calculus. The viscoelastic property of the foundation is described using the Kelvin-Voigt constitutive equation. Fractional calculus is widely recognized as one of the most powerful mathematical tools for modelling physical responses to many materials and is particularly suitable for creating time-dependent foundational models. A new Kelvin-Voigt type with fractional derivatives and fractional orders was introduced because it needs fewer parameters to represent the experimental data correctly. It is particularly well suited to the construction of time-dependent constitutive models. In addition, the Moore-Gibson-Thompson (MGT) equation of heat transfer and Euler-Bernoulli beam theories were used to derive the system equations. The microbeam is exposed to mechanical and thermal loads and ultrafast laser heating. The system equations governing the transient response of microbeams were combined into a single differential equation and processed by means of the Laplace transform technique. The influences of various parameters on microbeam behavior have been highlighted and explored in-depth, including viscosity modulus, axial pressure, fractional order, laser pulse length, and foundation parameters. Finally, previous models have been compared to validate the proposed theory and numerical solutions.

Critical electro-magneto-mechanical loads of a higher-order shear deformable cylindrical nano panel

This work studies electro-magneto-mechanical critical loads of a shear deformable cylindrical panel subjected to a combination of electric, magnetic, and mechanical loads. A higher-order shear deformation model is used to derive kinematic relations. The critical load equations are extracted using the virtual work’s principle. The buckling loads are obtained with calculation of external works due to electro-magneto-mechanical loads. Zero out of plane shear strains at the top and the bottom surfaces are satisfied using application of third-order shear deformation theory with some modifications. The analytical solution is presented to investigate impact of influencing parameters such as nano-scale length, length to radius ratio, span angle, and Pasternak’s foundation parameters on the electro-magneto-mechanical buckling loads. A large parametric analysis is presented to discuss the impact of influencing parameters such as nano-scale parameter, span angle, Pasternak’s foundation parameters, and length to radius ratio on the critical loads.

Modified couple stress and thickness-stretching included formulation of a sandwich micro shell subjected to electro-magnetic load resting on elastic foundation

This paper studies electromagnetoelastic static investigation of a sandwich doubly curved microshell subjected to multi-field loading based on a new thickness stretching included refined higher order shear/normal deformable model. Modified-couple-stress-theory (MCST) is used for accounting small-scale-dependency. The numerical results are derived using an analytical method. The effect of small scale parameter in micro scale, initial electric and magnetic potentials and foundation parameters is studied on the electromagnetoelastic bending results. It is confirmed an enhancing in stiffness of small scale shell with an increase in micro length scale parameter.

Influence of Inertial Vlasov Foundation Parameters on the Dynamic Response of the Bernoulli-Euler Beam Subjected to A Group of Moving Forces-Analytical Approach.

The subject of this study is the vibration of the Bernoulli–Euler beam on a three-parameter inertial foundation caused by a group of moving forces. The solution to the problem is obtained analytically. The influence of deformable foundation properties on the dynamic response of the beam in the case of forced vibration and the case of free vibration after the load has left the beam is analysed. The influence of velocity on the dynamic response of the beam is also investigated in both cases. The results can be used as a benchmark for calculating more complex engineering structures under moving loads caused by road or railroad vehicles. The results of the investigation are presented in the figures. It is evident that the coefficient determining the foundation inertia has a significant influence on the dynamic deflection of the beam. Taking shear into account in the Vlasov foundation model has little effect on the dynamic deflections of the beam. The equivalent damping number introduced into the Kelvin–Voigt model takes into account the structure damping and mass damping of the beam.

A critical review on cytogenetics of Cucurbitaceae with updates on Indian taxa.

The cytogenetic relationships in the species of Cucurbitaceae are becoming immensely important to answer questions pertaining to genome evolution. Here, a simplified and updated data resource on cytogenetics of Cucurbitaceae is presented on the basis of foundational parameters (basic, zygotic and gametic chromosome numbers, ploidy, genome size, karyotype) and molecular cytogenetics. We have revised and collated our own findings on seven agriculturally important Indian cucurbit species in a comparative account with the globally published reports. Chromosome count (of around 19% species) shows nearly three-fold differences while genome size (of nearly 5% species) shows 5.84-fold differences across the species. There is no significant correlation between chromosome numbers and nuclear genome sizes. The possible trend of evolution is discussed here based on molecular cytogenetics data, especially the types and distribution of nucleolus organizer regions (NORs). The review supersedes the scopes of general chromosome databases and invites scopes for continuous updates. The offline resource serves as an exclusive toolkit for research and breeding communities across the globe and also opens scope for future establishment of web-database on Cucurbitaceae cytogenetics.

Effect of in-plane loads on the natural frequencies of transversely isotropic thick annular sector plates resting on elastic foundation

This paper has studied the effects of in-plane load on the vibration of transversely isotropic annular sector plates resting on the Winkler and Pasternak elastic foundations. The governing coupled partial differential equations are obtained based on the third-order shear deformation plate theory. Based on Levy’s solution, the radial edges are assumed to be simply supported, and various boundary conditions are considered for circular edges. Therefore, nine different boundary conditions are considered here. At first, stability equations are analytically solved, and the critical buckling loads are obtained. Then, the natural frequency is extracted from the governing equations of motion subjected to in-plane loads. The effects of different in-plane loads on first natural frequencies of laminated thick annular sector plates with different aspect ratios, various thickness-length ratios, and some Winkler and Pasternak elastic foundation parameters are investigated. In addition, the effects of in-plane load on mode shape contour plots are presented for various boundary conditions. The obtained results show that the in-plane loads have a significant effect on the natural frequency of transversely isotropic annular sector plates. Also, increasing the in-plane force can affect the natural frequencies of the sector plate. For unique industrial designs, the natural frequency of the plate from the work area can be changed or prevent vibrations. Therefore, the resonance phenomenon can be easily changed and modified.

Nonlinear frequency behavior of cracked functionally graded porous beams resting on elastic foundation using Reddy shear deformation theory

This paper presents the nonlinear frequency behavior of cracked functionally graded porous beams subjected to various boundary conditions using Reddy shear deformation theory and Green’s tensor together with the Von Karman geometric nonlinearity. The material properties of the beam vary exponentially in thickness direction. A generalized differential quadrature method (GDQM) in conjunction with a direct numerical iteration method is developed to solve the system of equations derived by means of Hamilton’s principle. Demonstrating the convergence of this method, the verification is performed by using extracted results from a previous study based on the Euler and Timoshenko beam theory. The results for extensive studies are provided to understand the influences of the different gradient indexes, vibration amplitude ratios, porosity indexes, shear and elastic foundation parameters, and boundary conditions on the nonlinear frequency behavior. The location of crack plays the significant role on the nonlinear frequency ratios. The frequency ratios hit the minimum when the crack is located in mid-span of the beam. In this regard, the effect of shear stiffness of foundation is much more than that of Winkler one in the increasing mid-span value of nonlinear frequency ratio. It is also shown that the crack location results in decline of frequency ratios in the mid-span of beam specially for the cracks located closer to surface, the deeper ones lead to get nonlinear frequency ratios rise much more due to the fact that the deeper the crack is, the weaker the crack section becomes. The results of this paper and the effects of these parameters can be used in the optimal design of functionally graded beams and in crack prediction, detection, and monitoring techniques.

Wave propagation in carbon nanotube-reinforced nanocomposite doubly-curved shells resting on a viscoelastic foundation

This research aims at studying the propagation of waves in doubly-curved nanoshells made of carbon nanotube-reinforced composite (CNTRC) nanoshell panels while resting on a viscoelastic foundation. For the first time, a nonlocal strain gradient model of first-order shear deformation theory (FSDT) is developed in curvilinear coordinate for the wave propagation analysis of such properties, geometry, and foundation. The effective material properties of four types of CNTs’ distribution are estimated using a modified rule of mixture. The size-dependent governing equations are found using the Hamiltonian principle and after derivation, the equations are solved to find the damped flexural wave responses using a harmonic solving procedure. The results show the influence of viscoelastic foundation parameters, small-scale parameters, CNTs’ distribution schemes, and weight fraction of CNTs on the wave behavior of CNTRC doubly-curved shells with spherical, hyperbolic, cylindrical, and elliptical panels.

Stability of three-layered beam on elastic foundation

Stability analysis of an axially compressed three-layered beam on an elastic foundation is the main objective of presented work. The analytical model of the beam on the elastic foundation has been proposed. New approach to the structures on the elastic foundation has been presented by the authors which referred to the generalization of common models of the foundation by adopting its variable properties. The assumption proposed by the authors allows for a continuous description of the interaction of the beam with the foundation and a modification of the parameters of this substrate, unlike the discrete Winkler model. The shape function for symmetrical properties of the foundation has been assumed. The critical loads as a function of geometric and mechanical properties of the three-layered beam and the parameters of the elastic foundation were calculated. The original shape function and the function of the deflection have been proposed. In addition, the numerical analysis has been prepared and performed. Sample analytical and numerical calculations have been carried out, sharing a good agreement between the results obtained with both models.

Assessing effects of parameters of viscoelastic foundation on the dynamic response of functionally graded plates using a novel HSDT theory

In this study, vibration response of functionally graded plate resting on a viscoelastic foundation is studied. An analytical solution is proposed using a high-order shear deformation theory with only four unknowns, which means that the current theory has few unknowns compared to the first and other high shear deformation theories. The present theory uses a displacement field with integer terms instead of derivative terms by also including the shear deformation effect without introducing the shear correction factors. The mathematical model of the foundation used followed the Winkler–Pasternak two-coefficient model, with an additional term added to represent the damping effect. The governing equations were generated using the principle of virtual works. Subsequently, the analytical solution is based on Navier's principle to solve the vibration problem of a simply supported FG plate resting on a viscoelastic foundation. Some numerical results are presented to demonstrate the impact of the material index, the type of elastic foundation and the damping coefficient of the foundation on the dynamic response of FG plates resting on viscoelastic foundations. In the end, it is concluded that the current results with the proposed theory are found to be in good agreement with the other available results and this theory can easily be used to solve the free vibration problems of FGM plates resting on visco-Pasternak medium.

New finite modelling of the nonlinear static bending analysis of piezoelectric FG sandwich plates resting on nonlinear elastic foundations

This paper presents a new finite modelling of the nonlinear static bending analysis of piezoelectric functionally graded (FG) sandwich plates resting on nonlinear elastic foundations. Finite element formulations are derived by using the first-order shear deformation theory (FSDT) of Mindlin and the finite element method. The proposed theory and mathematical model of this work are verified by comparing the results with those of other methods, and they are in good agreement. A parameter study is conducted to investigate the effects of geometrical and physical properties such as nonlinear factors, volume fraction index, nonlinear foundation parameters, applied voltages, boundary conditions, etc., on the nonlinear mechanical behaviors of piezoelectric FG sandwich plates. The novel numerical results of this work are very important, and can be used as a good reference to examine related structures as well as of use in engineering practice.

Behavior of Different Configuration of Piled Raft Foundation for a High-Rise Building by using FEM

Abstract In this paper, the numerical simulation is performed on two piled raft configurations having uniform loading on a piled raft foundation. To investigate the interaction between various parameters of pile soil foundation with varying components of its length of pile, diameter and raft thickness. These components are critical for increasing the foundation’s bearing capacity. It’s important aspect to achieve a reliable design to optimize piled raft foundations subjected to uniformed load- settlement behaviors of the curves. These load – settlements are basically depending on the changing of their components piled raft foundation. These component of piled raft foundations to choose an optimal selection of embedded length of pile (L/dP), normalized diameter of pile (L/dP) and normalized raft thickness (tR/dP). The effect of load-settlement on distributions of shear force and bending moments is also investigated. In this study, a finite elements methods based on numerical tools ELPLA software is used for numerical simulation. The study’s findings validate the numerical analysis for the calculation of proper pile configuration arrangement, as a result of settlements. It will be generated as formation of contours patterns as shear stress and bending moments on the rafts, may be minimized with the total pile length. The conclusion drawn from the study validates the numerical analysis for the computation of proper pile arrangement can results in total and differential settlements, as well as generated shear stress and bending moments on the rafts, are all being reduced, with identical total pile length. Moreover, it captures the contours patterns of different behaviors of piled raft settlements, maximum shear force and maximum moments.

Static and free vibration analysis of stiffened FGM plate on elastic foundation based on physical neutral surface and MK method

This paper analyzes the static and free vibration problems of the stiffened functionally graded material (FGM) plate resting on Pasternak foundation by using the moving Kriging (MK) approximation and the physical neutral surface. The stiffened FGM plates are regarded as composite structures of FGM plates and stiffeners (beams). The displacement transformation relationship between stiffeners and FGM plates is obtained through the displacement compatible conditions and moving kriging interpolation. The total potential energy and kinetic energy of FGM plate resting on Pasternak foundation are derived based on the first-order shear deformation theory (FSDT) and physical neutral surface and by superimposing those energies of the stiffeners and the FGM plate. According to the principle of Minimum Potential Energy and Hamilton's Principle, the meshless governing equations on the static and free vibration of the stiffened FGM plate are obtained, respectively. The convergence and accuracy of the proposed method are demonstrated by calculating several numerical examples. Moreover, the effect of the power-law exponent, boundary conditions and foundation parameter on the static and free vibration behavior of the stiffened FGM plates resting on Pasternak foundation are discussed.

Symmetric and asymmetric thermo-induced buckling and postbuckling of rotating GPLRC annular plates rested on elastic foundation

Investigating the instability of annular plate which revolves on its axis in thermal environment is a valuable subject in vehicle engineering and aerospace industry, for instance, extending the service life of engine bearing. The symmetric and asymmetric buckling and postbuckling induced by the temperature rise of a rotating graphene-platelets-reinforced composite annular plate rested on Pasternak foundation are studied in present paper. Asymmetric deformation forms are captured by adopting the first-order shear deformation theory. Introducing von Kármán’s nonlinearity ensures the accuracy of postbuckling equilibrium paths. Highly coupled governing equations are solved by using the differential quadrature method and postbuckling paths are traced by utilizing the pseudo-arclength continuation algorithm. Parametric studies are conducted to discuss the influences of the dispersion patterns, weight fraction, and dimensions of GPLs, annular plate sizes, elastic foundation, and rotation motion on buckling and postbuckling. Results indicate that the sequence in which symmetric and asymmetric buckling modes appear is inextricably linked to the radial wave number of buckling configuration. Both adding GPLs and adjusting the foundation parameters appropriately can improve the ability to resist symmetric and asymmetric deformation of annular plate. The effect of rotation motion shows a transitional change along with the temperature rise.

Vibration analysis of cracked plates resting on elastic foundation via moving least squares differential quadrature method

In this work, moving least squares differential quadrature scheme is employed to formulate and solve the free vibration analysis of cracked plates resting on the Winkler–Pasternak elastic foundation. Two types of cracks as a part-through surface and internal crack are studied in a rectangular plate. Formulation of the problem is dependent on transverse shear deformation theory and line spring model. Also, continuous weight functions around the crack are produced by diffraction method. Boundary conditions are augmented in the equation of motion and the problem is converted to a discrete eigenvalue problem. The accuracy and efficiency of the present results is validated by comparing with exact, experimental and numerical results. Moreover, the effects of different boundary conditions, crack length, crack depth and foundation parameters on the vibration frequencies and mode shapes are examined in detail. The obtained results may be used for structural health monitoring.

Exact Solution of Nonlinear Behaviors of Imperfect Bioinspired Helicoidal Composite Beams Resting on Elastic Foundations

This paper presents exact solutions for the nonlinear bending problem, the buckling loads, and postbuckling configurations of a perfect and an imperfect bioinspired helicoidal composite beam with a linear rotation angle. The beam is embedded on an elastic medium, which is modeled by two elastic foundation parameters. The nonlinear integro-differential governing equation of the system is derived based on the Euler–Bernoulli beam hypothesis, von Kármán nonlinear strain, and initial curvature. The Laplace transform and its inversion are directly applied to solve the nonlinear integro-differential governing equations. The nonlinear bending deflections under point and uniform loads are derived. Closed-form formulas of critical buckling loads, as well as nonlinear postbuckling responses of perfect and imperfect beams are deduced in detail. The proposed model is validated with previous works. In the numerical results section, the effects of the rotation angle, amplitude of initial imperfection, elastic foundation constants, and boundary conditions on the nonlinear bending, critical buckling loads, and postbuckling configurations are discussed. The proposed model can be utilized in the analysis of bio-inspired beam structures that are used in many energy-absorption applications.

Natural Frequencies of Beams with Axial Material Gradation Resting on Two Parameter Elastic Foundation

Free vibration analysis is carried out on axially inhomogeneous beams resting on Winkler-Pasternak elastic foundation. The material properties of the beam like Young’s modulus, modulus of rigidity and material density are considered to be varying along the length direction following constant, linear and exponential material models. The beam is subjected to different combinations of clamped and simply supported boundary conditions. The formulation is based on Timoshenko beam theory and energy method along with Hamilton’s principle is used to derive the governing equations. The effect of material gradation and the 2 parameters of elastic foundation on the natural frequencies are studied in detail. The present results are validated by comparing them with established ones and satisfactory matching is observed.
 HIGHLIGHTS
 
 Free vibration behavior of axially functionally graded beams in investigated
 Three different material models and three boundary conditions are considered
 Effect of two parameter elastic foundation is considered
 Timoshenko beam theory and Rayleigh Ritz method are employed
 It is found that the stiffness of elastic foundation significantly affects the natural frequency of the beam
 
 GRAPHICAL ABSTRACT

Sigmoid functionally graded plates embedded on Winkler-Pasternak foundation: Free vibration analysis by dynamic stiffness method

In this present paper, the dynamic stiffness method has been formulated to calculate the natural frequency of sigmoid functionally graded material (S-FGM) plate embedded on the Winkler-Pasternak elastic foundation. The material properties of S-FGM continuously vary along the transverse direction of the plate by using two power-law variations in terms of volume fraction of the constituent's material. Hamilton's principle is implemented to derive the governing partial differential equation of motion based on the classical plate theory considering the physical neutral surf ace of the FGM rectangular plate. The Wittrick -Williams algorithm is applied as a solution technique to solve the transcendental nature of the dynamic stiffness matrix and extract the natural frequencies of the FGM plate with the desired accuracy. The S-FGM plate parameters’ variation of natural frequencies with the change of parametric numerical values (aspect ratio, sigmoid volume fraction index, boundary conditions and elastic foundation parameters, density ratio, and modulus ratio) are also highlighted. The DSM results are compared and validated with the available published literature. A new set of natural frequency results for the S-FGM plate embedded on the Winkler-Pasternak elastic foundation are generated.