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 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.

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.

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.

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 Exact Three-Dimensional Stability Analysis of Plate Using an Direct Variational Energy Method

2022 ◽  
Vol 8 (1) ◽  
pp. 60-80
Author(s):  
F. C. Onyeka ◽  
B. O. Mama ◽  
T. E. Okeke
Keyword(s):  
Stability Analysis ◽  
Potential Energy ◽  
Governing Equation ◽  
Thick Plate ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Energy Functional ◽  
Total Potential Energy ◽  
Average Percentage ◽  
Total Potential

In this paper, direct variational calculus was put into practical use to analyses the three dimensional (3D) stability of rectangular thick plate which was simply supported at all the four edges (SSSS) under uniformly distributed compressive load. In the analysis, both trigonometric and polynomial displacement functions were used. This was done by formulating the equation of total potential energy for a thick plate using the 3D constitutive relations, from then on, the equation of compatibility was obtained to determine the relationship between the rotations and deflection. In the same way, governing equation was obtained through minimization of the total potential energy functional with respect to deflection. The solution of the governing equation is the function for deflection. Functions for rotations were obtained from deflection function using the solution of compatibility equations. These functions, deflection and rotations were substituted back into the energy functional, from where, through minimizations with respect to displacement coefficients, formulas for analysis were obtained. In the result, the critical buckling loads from the present study are higher than those of refined plate theories with 7.70%, signifying the coarseness of the refined plate theories. This amount of difference cannot be overlooked. However, it is shown that, all the recorded average percentage differences between trigonometric and polynomial approaches used in this work and those of 3D exact elasticity theory is lower than 1.0%, confirming the exactness of the present theory. Thus, the exact 3D plate theory obtained, provides a good solution for the stability analysis of plate and, can be recommended for analysis of any type of rectangular plates under the same loading and boundary condition. Doi: 10.28991/CEJ-2022-08-01-05 Full Text: PDF

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.

scholarly journals Stabilization of systems of galaxies by subclustering

1978 ◽  
Vol 79 ◽  
pp. 98-100
Author(s):  
L. M. Ozernoy ◽  
M. Reinhardt
Keyword(s):  
Potential Energy ◽  
Velocity Dispersion ◽  
Total Potential Energy ◽  
Groups Of Galaxies ◽  
Total Potential ◽  
Group Members ◽  
The Mean ◽  
Mass Segregation ◽  
The Stability ◽  
Good Agreement

Subclustering might help to solve the virial theorem paradox for systems of galaxies by hiding a major part of the potential energy in gravitationally bound subsystems. We have shown (Ozernoy and Reinhardt 1976, Astr. Astrophys., 52, 31) that even in groups of galaxies there is mass segregation, in the sense that bright group members tend to be concentrated towards the centre. Recently Wesson and Lermann (1977, Astrophys. Sp. Sci., 46, 327), realizing the importance of subclustering, proposed a quantitative method for estimating its effect on the stability of systems of galaxies. However, their assumption about the frequency of subsystems of multiplicity n is not in accord with Holmberg's (1962) result. the mean frequency of galaxies in pairs is 0.37 for the Turner and Gott groups (1976) and 0.23 for the de Vauceulours groups (1976), in good agreement with the value of 0.25 required by Holmberg's distribution. Assuming Holmberg's frequency of gravitationally bound subsystems and that they are homogeneously distributed throughout the system, we have for the ratio of the total potential energy of a system of N equal masses Ω to the potential energy calculated in the usual way neglecting subclustering Ωs, Ω/Ωs≈ 1+(Rc)/(<r2>N), if the velocity dispersion <σr2(n)> = constant. Here Rc is the effective radius of the system and <r2> the mean distance of binaries. the assumption σr2(n) = const is reasonable for n ≤ 7, when Holmberg's distribution holds, since σr2(2) = 203 km s−1 according to Karachentsev (1974), and increases to only ≃ 1000 km s−1 for rich clusters. Since Karachentsev's data give an <r2> = 33 kpc for HO = 55 km s−1 Mpc−1, we have Ω/Ωs≈ 4 for groups of galaxies with Rc≈ 1 Mpc and N = 10. Thus it seems that subclustering cannot remove the mass discrepancy for rich clusters and for groups only in moderate cases.

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.

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.

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