Stability of Beams on Bi-Moduli Elastic Foundation

2000 ◽  
Vol 68 (4) ◽  
pp. 668-670
Author(s):  
Z. H. Liu ◽  
L. Wang ◽  
L. Z. Pan
Keyword(s):  
Exact Solutions ◽  
Elastic Foundation ◽  
Displacement Function ◽  
Buckling Load ◽  
Adjacent Transition ◽  
Transition Points

This paper adopts the newly structured δ function and displacement function. Using two adjacent transition points as two interval terminals while beams buckle makes the interval [xi−1,xi]. According to the Winkler’s beam buckling theory on elastic foundation, we present the energy solutions of beams and then the exact solutions of buckling load of simple supported beams on bi-moduli elastic foundation.

Analytical Solution of Sidewise Buckling of Two-Hinged Circular Arch under Concentrated Force

2013 ◽  
Vol 676 ◽  
pp. 170-174
Author(s):  
Ju Tao Kuang ◽  
Ai Rong Liu ◽  
Qi Ca Yu ◽  
Jiang Dong Deng
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Lateral Displacement ◽  
Displacement Function ◽  
Buckling Load ◽  
The Finite Element Method ◽  
Concentrated Force ◽  
Critical Buckling Load ◽  
Circular Arch ◽  
Good Agreement

By the setting torsional and lateral displacement function of sidewise buckling of two-hinged circular arch under concentrated force, the single-arch structure's bending, torsional deformation and external force potential can be constructed. An analytical solution for the lateral critical buckling load of two-hinged arch is first deduced by using the energy method; the results are also compared and analyzed by the finite element method. The results show that the analytical solution of single arch’s lateral critical buckling load is in good agreement with the finite element numerical solution, and the validity of the formula is proven.

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.

Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part I: Buckling analysis

2009 ◽  
Vol 44 (3) ◽  
pp. 968-978 ◽  
Author(s):  
H. Akhavan ◽  
Sh. Hosseini Hashemi ◽  
H. Rokni Damavandi Taher ◽  
A. Alibeigloo ◽  
Sh. Vahabi
Keyword(s):  
Exact Solutions ◽  
Elastic Foundation ◽  
Buckling Analysis ◽  
Pasternak Elastic Foundation

scholarly journals Dynamic Buckling of a Clamped Finite Column Resting on a Non – linear Elastic Foundation

2019 ◽  
pp. 1-47
Author(s):  
E. Julius, Bassey ◽  
M. Anthony, Ette ◽  
U. Joy, Chukwuchekwa ◽  
C. Atulegwu, Osuji
Keyword(s):  
Elastic Foundation ◽  
Governing Equation ◽  
Asymptotic Expansions ◽  
Perturbation Technique ◽  
Dynamic Buckling ◽  
Buckling Load ◽  
Linear Elastic ◽  
Non Linear ◽  
Relevant Variables ◽  
Independent Parameters

The analysis of the dynamic buckling of a clamped finite imperfect viscously damped column lying on a quadratic-cubic elastic foundation using the methods of asymptotic and perturbation technique is presented. The proposed governing equation contains two small independent parameters (δ and ϵ) which are used in asymptotic expansions of the relevant variables. The results of the analysis show that the dynamic buckling load of column decreases with its imperfections as well as with the increase in damping. The results obtained are strictly asymptotic and therefore valid as the parameters δ and ϵ become increasingly small relative to unity.

scholarly journals Mechanical Buckling Analysis of Saturated Porous Functionally Graded Elliptical Plates Subjected to In-Plane Force Resting on Two Parameters Elastic Foundation Based on HSDT

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Mohammad Hossein Sharifan ◽  
Mohsen Jabbari
Keyword(s):  
Elastic Foundation ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Potential Energy Function ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Mechanical Buckling ◽  
Two Parameters

Abstract In this paper, mechanical buckling analysis of a functionally graded (FG) elliptical plate, which is made up of saturated porous materials and is resting on two parameters elastic foundation, is investigated. The plate is subjected to in-plane force and mechanical properties of the plate assumed to be varied through the thickness of it according to three different functions, which are called porosity distributions. Since it is assumed that the plate to be thick, the higher order shear deformation theory (HSDT) is employed to analyze the plate. Using the total potential energy function and using the Ritz method, the critical buckling load of the plate is obtained and the results are verified with the simpler states in the literature. The effect of different parameters, such as different models of porosity distribution, porosity variations, pores compressibility variations, boundary conditions, and aspect ratio of the plate, is considered and has been discussed in details. It is seen that increasing the porosity coefficient decreases the stiffness of the plate and consequently the critical buckling load will be reduced. Also, by increasing the pores' compressibility, the critical buckling load will be increased. Adding the elastic foundation to the structure will increase the critical buckling load. The results of this study can be used to design more efficient structures in the future.

scholarly journals Nonlinear Stability Analysis of Eccentrically Stiffened Functionally Graded Truncated Conical Sandwich Shells with Porosity

Materials ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2200 ◽  
Author(s):  
Duc-Kien Thai ◽  
Tran Minh Tu ◽  
Le Kha Hoa ◽  
Dang Xuan Hung ◽  
Nguyen Ngọc Linh
Keyword(s):  
Physical Properties ◽  
Elastic Foundation ◽  
Core Layer ◽  
Functionally Graded ◽  
Buckling Load ◽  
Vertex Angle ◽  
Thickness Direction ◽  
Conical Shells ◽  
Pasternak Elastic Foundation ◽  
Post Buckling

: This paper analyzes the nonlinear buckling and post-buckling characteristics of the porous eccentrically stiffened functionally graded sandwich truncated conical shells resting on the Pasternak elastic foundation subjected to axial compressive loads. The core layer is made of a porous material (metal foam) characterized by a porosity coefficient which influences the physical properties of the shells in the form of a harmonic function in the shell’s thickness direction. The physical properties of the functionally graded (FG) coatings and stiffeners depend on the volume fractions of the constituents which play the role of the exponent in the exponential function of the thickness direction coordinate axis. The classical shell theory and the smeared stiffeners technique are applied to derive the governing equations taking the von Kármán geometrical nonlinearity into account. Based on the displacement approach, the explicit expressions of the critical buckling load and the post-buckling load-deflection curves for the sandwich truncated conical shells with simply supported edge conditions are obtained by applying the Galerkin method. The effects of material properties, core layer thickness, number of stiffeners, dimensional parameters, semi vertex angle and elastic foundation on buckling and post-buckling behaviors of the shell are investigated. The obtained results are validated by comparing with those in the literature.

Snapping of Low Pinned Arches on an Elastic Foundation

1973 ◽  
Vol 40 (3) ◽  
pp. 741-744 ◽  
Author(s):  
G. J. Simitses
Keyword(s):  
Critical Load ◽  
Elastic Foundation ◽  
Critical Loads ◽  
Entire Range ◽  
Buckling Load ◽  
Stability Studies ◽  
Deflection Curve ◽  
The Stability ◽  
Load Deflection Curve ◽  
Range Of Values

The problem of a low half-sine pinned arch under a quasi-statically applied half-sine load is considered. The low arch is resting on an elastic foundation. Critical loads are obtained by investigating the stability of the equilibrium positions by considering all possible modes of deformation. It is assumed that the behavior of the arch is linearly elastic up to the critical load. The entire range of values for the modulus of the foundation is considered. The results are presented graphically as either critical load (snap-through) or classical buckling load (stable bifurcation) versus the rise parameters for a large number of values of the modulus of foundations. This investigation presents an interesting model for stability studies, because, depending on the value of the rise parameter and the modulus of the foundation, the load-deflection curve exhibits the possibilities of the top-of-the-knee buckling, snap-through buckling through unstable bifurcation, and classical buckling (stable bifurcation).

Comparisons of Probabilistic and Two Nonprobabilistic Methods for Uncertain Imperfection Sensitivity of a Column on a Nonlinear Mixed Quadratic-Cubic Foundation

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
Xiaojun Wang ◽  
Isaac Elishakoff ◽  
Zhiping Qiu ◽  
Lihong Ma
Keyword(s):  
Elastic Foundation ◽  
Probabilistic Method ◽  
Initial Imperfection ◽  
Theoretical Models ◽  
Buckling Load ◽  
Dimensional Euclidean Space ◽  
Limited Information ◽  
Imperfection Sensitivity ◽  
Sensitive Structure ◽  
Range Of Variation

Two nonprobabilistic set-theoretical treatments of the initial imperfection sensitive structure—a finite column on a nonlinear mixed quadratic-cubic elastic foundation—are presented. The minimum buckling load is determined as a function of the parameters, which describe the range of possible initial imperfection profiles of the column. The two set-theoretical models are “interval analysis” and “convex modeling.” The first model represents the range of variation of the most significant N Fourier coefficients by a hypercuboid set. In the second model, the uncertainty in the initial imperfection profile is expressed by an ellipsoidal set in N-dimensional Euclidean space. The minimum buckling load is then evaluated in both the hypercuboid and the ellipsoid. A comparison between these methods and the probabilistic method are performed, where the probabilistic results at different reliability levels are taken as the benchmarks of accuracy for judgment. It is demonstrated that a nonprobabilistic model of uncertainty may be an alternative method for buckling analysis of a column on a nonlinear mixed quadratic-cubic elastic foundation under limited information on initial imperfection.

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