On the Influence of the Elastic Medium Stiffness in the Buckling Behavior of Compressed Beams on Elastic Foundation

2012 ◽  
Vol 166-169 ◽  
pp. 776-783 ◽  
Author(s):  
Fabio de Angelis ◽  
Donato Cancellara
Keyword(s):  
Elastic Medium ◽  
Elastic Foundation ◽  
Elastic Stiffness ◽  
Structural System ◽  
Buckling Loads ◽  
Buckling Behavior ◽  
Half Wave ◽  
Overall Stability ◽  
Beams On Elastic Foundation ◽  
The Stability

In the present work the stability and buckling behavior of compressed beams on elastic foundation are analyzed. The influence of the elastic stiffness of the medium on the overall stability of the structural system is investigated. The analysis is performed via energetic methods. The buckling loads are evaluated as a function of the stiffness of the beam and the stiffness of the elastic medium. Considerations are illustrated on the influence of the elastic medium stiffness and on the effects of the ratio of the length of the beam and the characteristic half-wave on the stability of the structural system.

On the Stability of Discrete Models of Compressed Beams in Elastic Media

2012 ◽  
Vol 152-154 ◽  
pp. 982-989 ◽  
Author(s):  
Fabio de Angelis
Keyword(s):  
Elastic Medium ◽  
Great Influence ◽  
Elastic Stiffness ◽  
Discrete Models ◽  
Elastic Media ◽  
Structural System ◽  
Equilibrium Configurations ◽  
Overall Stability ◽  
Post Buckling ◽  
The Stability

The equilibrium configurations of compressed elastic beams in an elastic medium are investigated. The analysis is performed on discrete models by means of a geometric non linear treatment. The effect of the elastic stiffness of the medium on the overall stability of the structural system is taken into account through a parameter which represents the ratio between the elastic medium stiffness and the beam stiffness. This parameter shows to have a great influence on the buckling and post-buckling behaviour of the structure.

scholarly journals Joint Effect of the Nonlinearity of Elastic Foundations and the Variation of the Inertia Ratio on Buckling Behavior of Prismatic and Nonprismatic Columns Using a GDQ Method

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Ramzy M. Abumandour ◽  
Fathi A. Abdelmgeed ◽  
Adel M. Elrefaey
Keyword(s):  
Elastic Foundation ◽  
Nonlinear Problems ◽  
Joint Effect ◽  
Buckling Loads ◽  
Elastic Foundations ◽  
Winkler Elastic Foundation ◽  
Cross Section Area ◽  
Buckling Behavior ◽  
Section Area ◽  
Engineering Problems

In this paper, we present a simple, powerful, yet efficient and easily applicable technique based on the GDQ method for solving nonlinear problems. The proposed technique is implemented to some nonlinear engineering problems in structure analysis. The results reveal that the proposed technique is effective. Then, the proposed technique is used to explain the effects of the variation of cross section area on the nondimensional critical buckling loads for columns with and without elastic foundation for three sets of boundary conditions. Finally, the proposed technique is used to investigate the effect of the nonlinearity term of Winkler elastic foundation on the nondimensional critical buckling loads of nonuniform columns resting on elastic foundations. The effectiveness of the proposed technique is validated through comparing the present results with exact solutions and other numerical results available in references. The proposed method benefits the optimum design of columns against buckling in engineering applications. The most important conclusions from this paper can be summarized as follows. When the inertia ratio varies parabolically, the nondimensional critical buckling loads increase in comparison with varying linearly. Moreover, the nondimensional critical buckling loads increase in the presence of the elastic foundation.

Buckling of Fully Embedded Single Piles by Using the Modified Vlasov Foundation Model

2017 ◽  
Vol 17 (01) ◽  
pp. 1750007 ◽  
Author(s):  
Tao Deng ◽  
Qijian Liu ◽  
Ming Huang
Keyword(s):  
Elastic Medium ◽  
Material Properties ◽  
Iterative Procedure ◽  
Mode Shapes ◽  
Modulus Ratio ◽  
Buckling Mode ◽  
Buckling Loads ◽  
Buckling Behavior ◽  
Foundation Model ◽  
Single Piles

An analytical method for analyzing the buckling of fully embedded single piles in an elastic medium is developed. The medium is simulated by the modified Vlasov foundation model. The governing differential equations of the pile and the surrounding elastic medium in the soil–pile system are derived by the variational principle, which are coupled when the pile buckles. A numerical iterative procedure is introduced to obtain the buckling loads and the corresponding mode shapes of the pile. Parametric study is performed to investigate the effects of the material properties of the soil–pile system on the buckling capacity of the pile. Numerical results show that the medium stiffness has significant influence on the buckling mode when the modulus ratio of the soil to the pile is large. Moreover, the effect of Poisson’s ratio of the soil on the buckling behavior of pile is negligible.

Stability for Leipholz’s Type of Laminated Box Columns with Nonsymmetric Lay-Ups on Elastic Foundation

2015 ◽  
Vol 7 (2) ◽  
pp. 158-179 ◽  
Author(s):  
Nam-Il Kim ◽  
Jaehong Lee
Keyword(s):  
Elastic Foundation ◽  
Stiffness Matrix ◽  
Beam Theory ◽  
Present Theory ◽  
Elastic Stiffness ◽  
Evaluation Procedures ◽  
Geometric Stiffness ◽  
Mass Matrices ◽  
The Stability ◽  
Box Columns

AbstractThe stability behavior of the Leipholz’s type of laminated box columns with nonsymmetric lay-ups resting on elastic foundation is investigated using the finite element method. Based on the kinematic assumptions consistent with the Vlasov beam theory, a formal engineering approach of the mechanics of the laminated box columns with symmetric and nonsymmetric lay-ups is presented. The extended Hamilton’s principle is employed to obtain the elastic stiffness and mass matrices, the Rayleigh damping and elastic foundation matrices, the geometric stiffness matrix due to distributed axial force, and the load correction stiffness matrix accounting for the uniformly distributed nonconservative forces. The evaluation procedures for the critical values of divergence and flutter loads with/without internal and external damping effects are briefly presented. Numerical examples are carried out to validate the present theory with respect to the previously published results. Especially, the influences of the fiber angle change and damping on the divergence and flutter loads of the laminated box columns are parametrically investigated.

Buckling Behavior of Tire Breaker Structure

1983 ◽  
Vol 11 (1) ◽  
pp. 3-19
Author(s):  
T. Akasaka ◽  
S. Yamazaki ◽  
K. Asano
Keyword(s):  
Elastic Foundation ◽  
Elastic Moduli ◽  
Wave Length ◽  
Bending Moment ◽  
Experimental Results ◽  
Automobile Tire ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Steel Cord ◽  
Interlaminar Shear

Abstract The buckled wave length and the critical in-plane bending moment of laminated long composite strips of cord-reinforced rubber sheets on an elastic foundation is analyzed by Galerkin's method, with consideration of interlaminar shear deformation. An approximate formula for the wave length is given in terms of cord angle, elastic moduli of the constituent rubber and steel cord, and several structural dimensions. The calculated wave length for a 165SR13 automobile tire with steel breakers (belts) was very close to experimental results. An additional study was then conducted on the post-buckling behavior of a laminated biased composite beam on an elastic foundation. This beam is subjected to axial compression. The calculated relationship between the buckled wave rise and the compressive membrane force also agreed well with experimental results.

scholarly journals Stability charts based on the finite element method for underground cavities in soft carbonate rocks: validation through case-study applications

2019 ◽  
Vol 19 (10) ◽  
pp. 2079-2095 ◽  
Author(s):  
Michele Perrotti ◽  
Piernicola Lollino ◽  
Nunzio Luciano Fazio ◽  
Mario Parise
Keyword(s):  
Finite Element ◽  
Safety Margin ◽  
Structural Elements ◽  
The Finite Element Method ◽  
Geometrical Features ◽  
Overall Stability ◽  
Underground Cavities ◽  
The Stability ◽  
Rock Mechanical Properties

Abstract. The stability of man-made underground cavities in soft rocks interacting with overlying structures and infrastructures represents a challenging problem to be faced. Based upon the results of a large number of parametric two-dimensional (2-D) finite-element analyses of ideal cases of underground cavities, accounting for the variability both cave geometrical features and rock mechanical properties, specific charts have been recently proposed in the literature to assess at a preliminary stage the stability of the cavities. The purpose of the present paper is to validate the efficacy of the stability charts through the application to several case studies of underground cavities, considering both quarries collapsed in the past and quarries still stable. The stability graphs proposed by Perrotti et al. (2018) can be useful to evaluate, in a preliminary way, a safety margin for cavities that have not reached failure and to detect indications of predisposition to local or general instability phenomena. Alternatively, for sinkholes that already occurred, the graphs may be useful in identifying the conditions that led to the collapse, highlighting the importance of some structural elements (as pillars and internal walls) on the overall stability of the quarry system.

Low Buckling Loads of Axially Compressed Conical Shells

1970 ◽  
Vol 37 (2) ◽  
pp. 384-392 ◽  
Author(s):  
M. Baruch ◽  
O. Harari ◽  
J. Singer
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Plane Boundary ◽  
Essential Difference ◽  
Physical Reason ◽  
Buckling Loads ◽  
Conical Shells ◽  
Simple Supports ◽  
Interaction Curves ◽  
The Stability

The stability of simply supported conical shells under axial compression is investigated for 4 different sets of in-plane boundary conditions with a linear Donnell-type theory. The first two stability equations are solved by the assumed displacement, while the third is solved by a Galerkin procedure. The boundary conditions are satisfied with 4 unknown coefficients in the expression for u and v. Both circumferential and axial restraints are found to be of primary importance. Buckling loads about half the “classical” ones are obtained for all but the stiffest simple supports SS4 (v = u = 0). Except for short shells, the effects do not depend on the length of the shell. The physical reason for the low buckling loads in the SS3 case is explained and the essential difference between cylinder and cone in this case is discussed. Buckling under combined axial compression and external or internal pressure is studied and interaction curves have been calculated for the 4 sets of in-plane boundary conditions.

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