Dynamic and static nonlinear analysis of generally laminated imperfect plates having nonuniform boundary conditions and resting on elastic foundation

1989 ◽  
Vol 40 (5) ◽  
pp. 628-644 ◽  
Author(s):  
Chuen -Yuan Chia
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Analysis ◽  
Elastic Foundation

scholarly journals Analysis of beam-column elements on non-homogeneous soil using the differential transformation method

2021 ◽  
Author(s):  
Juan Sebastián Carvajal-Muñoz ◽  
Carlos Alberto Vega-Posada ◽  
Julio César Saldarriaga-Molina
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Mathematical Formulation ◽  
Transformation Method ◽  
Transverse Load ◽  
Differential Transformation Method ◽  
Differential Transformation ◽  
Pasternak Elastic Foundation ◽  
Wide Range ◽  
Homogeneous Soil

This paper describes an analytical approach to conduct an analysis of beam-column elements with generalized end-boundary conditions on a homogeneous or non-homogeneous Pasternak elastic foundation. The mathematical formulation utilized herein is that presented by the senior author in a recent work. The differential equation (DE) governing the behavior of the beam-column element is solved using the differential transformation method (DTM). The DTM offers practical advantages over other conventional approaches when solving the proposed structural model. The proposed formulation provides the flexibility to account for i) combined lateral and axial load at the ends of the element, ii) homogeneous or non-homogeneous soil, iii) Pasternak elastic foundation, and iv) an external arbitrary transverse load acting on the element. The effects of various slenderness ratios, pile-soil stiffness ratios, and classical and semirigid boundary conditions can be easily studied with the proposed formulation. Examples are presented to validate the accuracy of the model and its applicability over a wide range of analyses.

A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations

2017 ◽  
Vol 21 (6) ◽  
pp. 1906-1929 ◽  
Author(s):  
Abdelkader Mahmoudi ◽  
Samir Benyoucef ◽  
Abdelouahed Tounsi ◽  
Abdelkader Benachour ◽  
El Abbas Adda Bedia ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Refined Theory ◽  
Governing Equations

In this paper, a refined quasi-three-dimensional shear deformation theory for thermo-mechanical analysis of functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation is developed. Unlike the other higher-order theories the number of unknowns and governing equations of the present theory is only four against six or more unknown displacement functions used in the corresponding ones. Furthermore, this theory takes into account the stretching effect due to its quasi-three-dimensional nature. The boundary conditions in the top and bottoms surfaces of the sandwich functionally graded plate are satisfied and no correction factor is required. Various types of functionally graded material sandwich plates are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of the refined theory and the reference solutions. A parametric study is presented to examine the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate resting on elastic foundation subjected to thermo-mechanical loading.

Buckling analysis of functionally graded annular sector plates resting on elastic foundations

2010 ◽  
Vol 225 (2) ◽  
pp. 312-325 ◽  
Author(s):  
A Naderi ◽  
A R Saidi
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Elastic Foundations ◽  
Annular Sector ◽  
Sector Plate ◽  
Annular Sector Plate

In this study, an analytical solution for the buckling of a functionally graded annular sector plate resting on an elastic foundation is presented. The buckling analysis of the functionally graded annular sector plate is investigated for two typical, Winkler and Pasternak, elastic foundations. The equilibrium and stability equations are derived according to the Kirchhoff's plate theory using the energy method. In order to decouple the highly coupled stability equations, two new functions are introduced. The decoupled equations are solved analytically for a plate having simply supported boundary conditions on two radial edges. Satisfying the boundary conditions on the circular edges of the plate yields an eigenvalue problem for finding the critical buckling load. Extensive results pertaining to critical buckling load are presented and the effects of boundary conditions, volume fraction, annularity, plate thickness, and elastic foundation are studied.

On the Solution of Beam-on-elastic-foundation Problems by Means of a Mechanical Analogue

1950 ◽  
Vol 163 (1) ◽  
pp. 307-310 ◽  
Author(s):  
A. A. Wells
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Pressure Vessel ◽  
Finite Differences ◽  
Specific Problem ◽  
Elastic Shells ◽  
Elastic Foundations ◽  
Mechanical Analogue ◽  
Method Of Solution ◽  
Direct Use

The equation d4 y/ dx4- f(x)y + g(x) = 0 may be solved by means of the differential analyser, but only straightforwardly when the four boundary conditions are specified at one point. When the equation is associated with beams on elastic foundations, or elastic shells, the boundary conditions are more often specified at two points, and a quicker method of solution is desirable. In the analogue, direct use is made of the beam in the form of an elastic wire, supported at intervals in cradles on which weights may be made to simulate the terms f(x)y and g(x); the wire takes up a transversely deflected form which may be measured, and boundary conditions are imposed where they are required. A specific problem is examined and the results are shown to agree reasonably with the solution by calculation. A disadvantage when d2 y/dx2 is required is the inaccuracy inherent in differentiating by finite differences, but for engineering calculations the simplicity of the method may have its advantages. The solution of a typical pressure-vessel problem, by means of the analogue, is described.

Sound Radiation Analysis of Functionally Graded Porous Plates with Arbitrary Boundary Conditions and Resting on Elastic Foundation

2020 ◽  
Vol 20 (05) ◽  
pp. 2050068 ◽  
Author(s):  
Zhengmin Hu ◽  
Kai Zhou ◽  
Yong Chen
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Sound Radiation ◽  
Functionally Graded ◽  
Harmonic Load ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Arbitrary Boundary Conditions ◽  
Porosity Coefficient

In this paper, the sound radiation behaviors of the functionally graded porous (FGP) plate with arbitrary boundary conditions and resting on elastic foundation are studied by means of the modified Fourier series method. It is assumed that a total of three types of porosity distributions are considered in the present study. The material parameters are determined according to the porosity coefficient used to denote the size of pores in the plate. The governing equations of the FGP plate are derived by utilizing the Hamilton’s principle on the basis of the first-order deformation theory (FSDT). Each displacement component of the FGP plate is expanded as the Fourier cosine series combined with auxiliary polynomial functions introduced to enhance the convergence rate of the series expansions. The acoustic response of the FGP plate due to a concentrated harmonic load is calculated by evaluating the Rayleigh integral. Good agreements are attained by comparing the present results with those in available literatures, which show the accuracy and versatility of the developed method in this paper. Finally, the influences of the porosity distribution type, porosity coefficient, boundary condition and elastic foundation on the sound radiation of the FGP plate are analyzed in detail.

scholarly journals Snap-Through of the Very Shallow Shell with Initial Imperfection

2016 ◽  
Vol 16 (2) ◽  
pp. 43-48
Author(s):  
Jozef Havran ◽  
Martin Psotný
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Analysis ◽  
Shallow Shell ◽  
Initial Imperfection ◽  
Limit Load ◽  
External Pressure ◽  
Load Level ◽  
Nonlinear Equilibrium ◽  
Load Displacement ◽  
Ansys System

Abstract Elastic shallow shell of translation subjected to the external pressure is analysed in the paper numerically by FEM. Nonlinear equilibrium paths are calculated for the different boundary conditions. Special attention is paid to the influence of initial imperfection on the limit load level of fundamental load-displacement path of nonlinear analysis. ANSYS system was used for analysis, arclength method was chosen for obtain fundamental load-displacement path of solution.

scholarly journals Modeling of smart magnetically affected flexoelectric/piezoelectric nanostructures incorporating surface effects

2017 ◽  
Vol 7 ◽  
pp. 184798041771310 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Surface Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Surface Effects ◽  
Geometrical Parameters ◽  
Various Boundary Conditions ◽  
Buckling Behavior

In this article, electromechanical buckling behavior of size-dependent flexoelectric/piezoelectric nanobeams is investigated based on nonlocal and surface elasticity theories. Flexoelectricity represents the coupling between the strain gradients and electrical polarizations. Flexoelectric/piezoelectric nanostructures can tolerate higher buckling loads compared with conventional piezoelectric ones, especially at lower thicknesses. Nonlocal elasticity theory of Eringen is applied for analyzing flexoelectric/piezoelectric nanobeams for the first time. The flexoelectric/piezoelectric nanobeams are assumed to be in contact with a two-parameter elastic foundation which consists of infinite linear springs and a shear layer. The residual surface stresses which are usually neglected in modeling of flexoelectric nanobeams are incorporated into nonlocal elasticity to provide better understanding of the physics of the problem. Applying an analytical method which satisfies various boundary conditions, the governing equations obtained from Hamilton’s principle are solved. The reliability of the present approach is verified by comparing the obtained results with those provided in literature. Finally, the influences of nonlocal parameter, surface effects plate geometrical parameters, elastic foundation, and boundary conditions on the buckling characteristics of the flexoelectric/piezoelectric nanobeams are explored in detail.

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