scholarly journals Nonlinear Analysis of Buckling & Postbuckling

2014 ◽  
Vol 14 (1) ◽  
pp. 75-80
Author(s):  
Martin Psotný
Keyword(s):  
Potential Energy ◽  
Iteration Algorithm ◽  
Nonlinear Finite Element Method ◽  
Buckling Mode ◽  
Initial Imperfections ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
Ansys System ◽  
Raphson Iteration

Abstract The stability analysis of slender web loaded in compression was presented. To solve this problem, a specialized computer program based on FEM was created. The nonlinear finite element method equations were derived from the variational principle of minimum of potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm was used. Corresponding levels of the total potential energy were defined. The peculiarities of the effects of the initial imperfections were investigated. Special attention was focused on the influence of imperfections on the post-critical buckling mode. The stable and unstable paths of the nonlinear solution were separated. Obtained results were compared with those gained using ANSYS system.

Stability Analysis of an Imperfect Slender Web Subjected to the Shear Load

2016 ◽  
Vol 837 ◽  
pp. 52-57
Author(s):  
Martin Psotny
Keyword(s):  
Stability Analysis ◽  
Potential Energy ◽  
Total Potential Energy ◽  
Iteration Algorithm ◽  
Buckling Mode ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
Ansys System ◽  
Raphson Iteration

The stability analysis of an imperfect slender web subjected to the shearing load is presented, a specialized code based on FEM has been created. The nonlinear finite element method equations are derived from the variational principle of minimum of total potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. The peculiarities of the effects of the initial imperfections are investigated. Special attention is paid to the influence of imperfections on the post-critical buckling mode. Obtained results are compared with those gained using ANSYS system.

scholarly journals Buckling And Postbuckling Of An Imperfect Plate Subjected To The Shear Load

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Martin Psotný
Keyword(s):  
Potential Energy ◽  
Total Potential Energy ◽  
Iteration Algorithm ◽  
Shear Load ◽  
Buckling Mode ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
Ansys System ◽  
Raphson Iteration

Abstract The stability analysis of an imperfect plate subjected to the shear load is presented. To solve this problem, a specialized computer program based on FEM has been created. The nonlinear finite element method equations are derived from the variational principle of minimum of total potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. Special attention is paid to the influence of imperfections on the post-critical buckling mode. Obtained results are compared with those gained using ANSYS system.

scholarly journals Postbuckling Analysis Of A Rectangular Plate Loaded In Compression

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Jozef Havran ◽  
Martin Psotný
Keyword(s):  
Rectangular Plate ◽  
User Program ◽  
Nonlinear Fem ◽  
Buckling Mode ◽  
Energy Principle ◽  
Initial Imperfections ◽  
Potential Energy Principle ◽  
Total Potential ◽  
The Stability ◽  
Minimum Total Potential Energy

Abstract The stability analysis of a thin rectangular plate loaded in compression is presented. The nonlinear FEM equations are derived from the minimum total potential energy principle. The peculiarities of the effects of the initial imperfections are investigated using the user program. Special attention is paid to the influence of imperfections on the post-critical buckling mode. The FEM computer program using a 48 DOF element has been used for analysis. Full Newton-Raphson procedure has been applied.

scholarly journals Slender metal web stability analysis: Impact of initial imperfection on the mode of buckling

2020 ◽  
Vol 313 ◽  
pp. 00006
Author(s):  
Martin Psotný
Keyword(s):  
Initial Imperfection ◽  
Iteration Algorithm ◽  
Initial Shape ◽  
Aspect Ratios ◽  
Nonlinear Approach ◽  
Linearized Problem ◽  
Nonlinear Equilibrium ◽  
Post Buckling ◽  
Ansys System ◽  
Raphson Iteration

The post buckling of a rectangular slender web in compression has been analyzed. Shapes of a buckling area obtained from the nonlinear analysis have been compared with buckling modes from the linearized problem for various aspect ratios. Effects of initial shape imperfections upon the analysis have been investigated using nonlinear approach. To trace the complete nonlinear equilibrium curves, specialized code based on FEM was created. The Newton-Raphson iteration algorithm was used, load versus displacement control was changed during the process of calculation. Obtained results were verified using Ansys system, in this case arc-length method was activated for overcoming critical points.

Stable Paths in the Postbuckling of an Imperfect Slender Web Loaded in Compression

2016 ◽  
Vol 837 ◽  
pp. 28-33 ◽  
Author(s):  
Jozef Havran ◽  
Martin Psotny
Keyword(s):  
Stability Analysis ◽  
Variational Principle ◽  
Finite Elements ◽  
Potential Energy ◽  
User Program ◽  
Buckling Mode ◽  
Fem Model ◽  
Initial Imperfections ◽  
Newton Raphson ◽  
The Stability

The stability analysis of a slender web loaded in compression is presented. The non-linear FEM equations are derived from the variational principle of minimum of potential energy. The peculiarities of the effects of the initial imperfections are investigated using user program. Special attention is paid to the influence of imperfections on the post-critical buckling mode. Stable load-displacement paths are investigated. The FEM computer program using a 48 DOF element has been used for analysis. FEM model consists of 4x4 finite elements. Full Newton-Raphson procedure has been applied.

scholarly journals Aspect Ratio of Slender Web & Postbuckling Behaviour / Pomer Strán Štíhlej Steny A Pokritické Pôsobenie

2012 ◽  
Vol 12 (2) ◽  
pp. 153-160
Author(s):  
Martin Psotný
Keyword(s):  
Variational Principle ◽  
Aspect Ratio ◽  
Total Potential Energy ◽  
Iteration Algorithm ◽  
Initial Imperfections ◽  
Total Potential ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Iteration ◽  
The Web

Abstract Postbuckling analysis of slender web loaded in compression is presented. The non-linear FEM equations [14] are derived from the variational principle of minimum of total potential energy [13]. To obtain the non-linear equilibrium paths, Newton-Raphson iteration algorithm [11], [12] is used. Peculiarities of the effect of the initial imperfections [7], [8] on load-deflection paths are investigated with respect to aspect ratio of the web. Special attention is focused on the postbuckling mode of the web.

Effect of a Bending Stiffness on the Load-Displacement Path of Von Mises Truss

2015 ◽  
Vol 769 ◽  
pp. 43-48
Author(s):  
Martin Psotny ◽  
Jozef Havran
Keyword(s):  
Theoretical Models ◽  
Load Level ◽  
Buckling Analysis ◽  
Iteration Algorithm ◽  
Linear Solution ◽  
Nonlinear Equilibrium ◽  
Von Mises ◽  
Ansys System ◽  
Raphson Iteration ◽  
Linear Buckling Analysis

Von Misses truss is one of the best examples to explain nature of non-linear solution and define the snap-through. Linear buckling analysis and nonlinear finite element approaches are compared in presented paper. At the present time theoretical models for the evaluation of the ultimate load assume a structure with imperfections. The peculiarities of the effect of the magnitude and mode of initial imperfections are investigated. Effect of member stiffness on the load level in critical point of nonlinear solution, as well as the relative position with respect to the critical load from buckling analysis are analyzed. To obtain the nonlinear equilibrium paths, Newton-Raphson iteration algorithm has been used. Obtained results are compared with those gained using ANSYS system.

Stability of the neutral equilibrium of columns with a rotational end restraint by the generalized Fourier series

2019 ◽  
Vol 25 (4) ◽  
pp. 961-967
Author(s):  
Yan-Ping Zhao ◽  
Lin Li ◽  
Ming Jin
Keyword(s):  
Fourier Series ◽  
Potential Energy ◽  
Energy Functional ◽  
Buckling Mode ◽  
Generalized Fourier Series ◽  
Order Variation ◽  
Neutral Equilibrium ◽  
Post Buckling ◽  
The Stability ◽  
End Restraint

In this paper, stability of the neutral equilibrium and initial post-buckling of a column with a rotational end restraint is analyzed based on Koiter initial post-buckling theory. The potential energy functional is written in terms of the angle. By the generalized Fourier series of the disturbance angle, it is proved that the second-order variation of the potential energy is semi-positive definite at the neutral equilibrium. The stability of the neutral equilibrium is determined by the sign of the fourth-order variation for the buckling mode. For all values of the stiffness of the rotational end restraint, the neutral equilibrium is stable and the bifurcation equilibrium is upward in the initial post-buckling.

On Post-Critical Behavior of a Beam on an Elastic Foundation

2018 ◽  
Vol 18 (06) ◽  
pp. 1850082 ◽  
Author(s):  
Lidija Z. Rehlicki ◽  
Marko B. Janev ◽  
Branislava N. Novaković ◽  
Teodor M. Atanacković
Keyword(s):  
Total Energy ◽  
Elastic Foundation ◽  
Nonlinear Problem ◽  
Bifurcation Analysis ◽  
Nontrivial Solutions ◽  
Buckling Mode ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
The One ◽  
Two Parameter

In this paper, we analyze the nonlinear equilibrium equation corresponding to the two-parameter bifurcation problem arising in the stability analysis of an elastic simply supported beam on the Winkler type elastic foundation for the case when bimodal buckling occurs. We perform the bifurcation analysis of the nonlinear problem, by using Lyapunov–Schmidt reduction, thus obtaining the number of the nontrivial solutions to the nonlinear problem and qualitatively characterizing the solution patterns. We also give the formulation of the problem and bifurcation analysis from the total energy viewpoint and determine the energy of each bifurcating solution. We assert that the solution with the smallest energy is the one that will be observed in the post-critical state. For specific choice of parameters, the bifurcating solution in the form of the second buckling mode has the smallest total energy. The numerical results illustrating the theory are also provided.

Dilute Aqueous Dispersions of Zro2 And Al2O3

1985 ◽  
Vol 60 ◽  
Author(s):  
Evelyn M. De Liso ◽  
W. Roger Cannon ◽  
A. Srinivasa Rao
Keyword(s):  
Potential Energy ◽  
Total Potential Energy ◽  
Alumina Powder ◽  
Maximum Height ◽  
Colloidal Interactions ◽  
Total Potential ◽  
Particle Size Data ◽  
Theoretical Predictions ◽  
Alumina Composite ◽  
The Stability

AbstractColloidal interactions in a heteroparticulate mixture of zirconia and alumina in water were studied for use in a transformation toughened alumina composite. The microelectrophoresis technique was used to measure the mobility of three zirconia powders and an alumina powder. The electro-phoretic mobility and particle size data were used to calculate total potential energy curves. The maximum height of the total potential energy barrier was used to predict the stability of a zirconia/alumina mixture. Theoretical predictions were compared to experimental results obtained from sedimentation and rheology measurements carried out as a function of pH of the dispersion. For a 5 v/o aqueous zirconia/alumina system stable dispersions were made at pH 3 and pH 5.

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