Effect of a Nonlinear Term in a Strain-Displacement Relationship on the Load-Displacement Path of Von Mises Truss

2015 ◽  
Vol 769 ◽  
pp. 85-90
Author(s):  
Jozef Havran ◽  
Martin Psotny
Keyword(s):  
Load Level ◽  
Iteration Algorithm ◽  
Arc Length ◽  
Linear Solution ◽  
Nonlinear Solution ◽  
Total Potential ◽  
Theoretical Approaches ◽  
Newton Raphson ◽  
Von Mises ◽  
Ansys System

Von Misses truss is one of the best examples to explain different theoretical approaches, nature of non-linear solution, define the snap-through, illustrate interactive buckling, etc. The presented paper compares two nonlinear approaches to the problem. Effect of nonlinear terms in strain-displacement relationship on the load level in critical point of nonlinear solution is analyzed. 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. Custom FEM computer program has been used for analysis. Full Newton-Raphson procedure, in which the stiffness matrix is updated at every equilibrium iteration, has been applied. Obtained results are compared with results of the nonlinear analysis using ANSYS system, element type BEAM3 is used. The arc-length method is chosen for analysis, the reference arc-length radius is calculated from the load increment. Only fundamental path of nonlinear solution has been presented.

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 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 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 Effects of intracorneal ring segments implementation technique and design on corneal biomechanics and keratometry in a personalized computational analysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Niksa Mohammadi Bagheri ◽  
Mahmoud Kadkhodaei ◽  
Shiva Pirhadi ◽  
Peiman Mosaddegh
Keyword(s):  
Clinical Data ◽  
Three Dimensional ◽  
Element Model ◽  
Von Mises Stress ◽  
Patient Specific ◽  
Average Error ◽  
Constant Thickness ◽  
Arc Length ◽  
Implementation Techniques ◽  
Von Mises

AbstractThe implementation of intracorneal ring segments (ICRS) is one of the successfully applied refractive operations for the treatment of keratoconus (kc) progression. The different selection of ICRS types along with the surgical implementation techniques can significantly affect surgical outcomes. Thus, this study aimed to investigate the influence of ICRS implementation techniques and design on the postoperative biomechanical state and keratometry results. The clinical data of three patients with different stages and patterns of keratoconus were assessed to develop a three-dimensional (3D) patient-specific finite-element model (FEM) of the keratoconic cornea. For each patient, the exact surgery procedure definitions were interpreted in the step-by-step FEM. Then, seven surgical scenarios, including different ICRS designs (complete and incomplete segment), with two surgical implementation methods (tunnel incision and lamellar pocket cut), were simulated. The pre- and postoperative predicted results of FEM were validated with the corresponding clinical data. For the pre- and postoperative results, the average error of 0.4% and 3.7% for the mean keratometry value ($$\text {K}_{\text{mean}}$$ K mean ) were predicted. Furthermore, the difference in induced flattening effects was negligible for three ICRS types (KeraRing segment with arc-length of 355, 320, and two separate 160) of equal thickness. In contrast, the single and double progressive thickness of KeraRing 160 caused a significantly lower flattening effect compared to the same type with constant thickness. The observations indicated that the greater the segment thickness and arc-length, the lower the induced mean keratometry values. While the application of the tunnel incision method resulted in a lower $$\text {K}_{\text{mean}}$$ K mean value for moderate and advanced KC, the induced maximum Von Mises stress on the postoperative cornea exceeded the induced maximum stress on the cornea more than two to five times compared to the pocket incision and the preoperative state of the cornea. In particular, an asymmetric regional Von Mises stress on the corneal surface was generated with a progressive ICRS thickness. These findings could be an early biomechanical sign for a later corneal instability and ICRS migration. The developed methodology provided a platform to personalize ICRS refractive surgery with regard to the patient’s keratoconus stage in order to facilitate the efficiency and biomechanical stability of the surgery.

scholarly journals Two theoretical approaches to human behavior and social institutions

2021 ◽  
pp. 13-50
Author(s):  
Javier Aranzadi del Cerro
Keyword(s):  
Market Economy ◽  
Social Institutions ◽  
Dynamic Structure ◽  
Chicago School ◽  
Human Action ◽  
Jel Classification ◽  
Market Process ◽  
Ludwig Von Mises ◽  
Theoretical Approaches ◽  
Von Mises

This paper deals with theoretical approaches to the real economic crisis we are suffering. I set out the poverty of the theoretical solutions offered by mainstream neoclassical economics and the necessity of a new theoretical approach, which is not obsessed by the positivist method. My argument is based on the work of Ludwig von Mises who was considered to give the best theoretical arguments in the debate on the impossibility of efficient economic calculation under centrally planned socialism. Although nowadays the Austrian School is considered old-fashion and lacking in scientific rigour, I agree with the late Professor Sumantra Ghoshal that it is necessary to escape from strait-jacketed methods and try to understand real economics problems. Our market economy is suffering from what he described as the consequences of bad theories destroying good entrepreneurial practices. For I do think that the triumph over communism is in danger of becoming a Pyrrhic victory if we lose our understanding of the market economy and its dynamic structure based on entrepreneurs and firms. Key words: Human action, Ludwig von Mises, Chicago School, entrepre - neurship, market process, social institutions. JEL Classification: A10; B41; B53; D00. Resumen: Este artículo compara los modelos teóricos con los que se analiza la crisis económica que estamos sufriendo. Planteo la pobreza teórica ofrecida por el paradigma neoclásico dominante y defiendo la necesidad de nuevas aproximaciones teóricas que no estén obsesionadas por el método positivista. Mi argumento se basa en la obra de Ludwig von Mises quien fue considerado el economista que esgrimió los mejores argumentos tóricos en el debate sobre la imposibilidad de una cálculo económico eficiente en una económica de planificación central. Aunque hoy en día se considera que la Escuela Austriaca está pasada de moda y falta de rigor científico, estoy de acuerdo con el difunto profesor Sumantra Ghoshal sobre la necesidad de abandonar los métodos encorsetados e intentar comprender los problemas económicos reales. Nuestra economía de mercado está sufriendo las consecuencias de lo que él describe como malas teorías que destruyen buenas prácticas empresariales. Son estas las razones por las que pienso que el triunfo sobre el comunismo está en riego de convertirse en una victoria pírrica si perdemos nuestra comprensión de la economía de mercado y su estructura dinámica basadas en la empresarialidad y la empresa privada. Palabras clave: Acción humana, Ludwig von Mises, Escuela de Chicago, empresarialidad, proceso de mercado, instituciones sociales. Clasificación JEL: A10; B41; B53; D00.

scholarly journals Nonlinear higher-order spectral solution for a two-dimensional moving load on ice

2009 ◽  
Vol 621 ◽  
pp. 215-242 ◽  
Author(s):  
FÉLICIEN BONNEFOY ◽  
MICHAEL H. MEYLAN ◽  
PIERRE FERRANT
Keyword(s):  
Critical Speed ◽  
Moving Boundary ◽  
Moving Load ◽  
Phase Speed ◽  
Nonlinear Effects ◽  
Higher Order ◽  
Two Dimensions ◽  
Linear Solution ◽  
Nonlinear Solution ◽  
Bernoulli’S Equation

We calculate the nonlinear response of an infinite ice sheet to a moving load in the time domain in two dimensions, using a higher-order spectral method. The nonlinearity is due to the moving boundary, as well as the nonlinear term in Bernoulli's equation and the elastic plate equation. We compare the nonlinear solution with the linear solution and with the nonlinear solution found by Parau & Dias (J. Fluid Mech., vol. 460, 2002, pp. 281–305). We find good agreement with both solutions (with the correction of an error in the Parau & Dias 2002 results) in the appropriate regimes. We also derive a solitary wavelike expression for the linear solution – close to but below the critical speed at which the phase speed has a minimum. Our model is carefully validated and used to investigate nonlinear effects. We focus in detail on the solution at a critical speed at which the linear response is infinite, and we show that the nonlinear solution remains bounded. We also establish that the inclusion of nonlinearities leads to significant new behaviour, which is not observed in the linear solution.

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.

scholarly journals Base functions effect in stability finite element analysis of compressed plate

2020 ◽  
Vol 310 ◽  
pp. 00018 ◽  
Author(s):  
Ivana Veghova ◽  
Martin Psotny
Keyword(s):  
Finite Element Analysis ◽  
Stiffness Matrix ◽  
Nonlinear Problems ◽  
Total Potential Energy ◽  
Element Analysis ◽  
Basic Assumptions ◽  
Total Potential ◽  
Geometric Nonlinear ◽  
Base Functions ◽  
Newton Raphson

Geometric nonlinear solution of a compressed plate is presented in this paper. Basic assumptions are specified and incremental conditional equations are derived from the variational principle of minimum of total potential energy. Full Newton-Raphson procedure, in which the stiffness matrix is updated at every equilibrium iteration, has been applied for solution. The importance of modifications of base functions for solving geometric nonlinear problems is analysed. The solved example is presented, the differences are compared and explained.

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