Elastic Buckling and Post-Buckling of Von Mises Planar Trusses

2015 ◽  
Vol 769 ◽  
pp. 49-54
Author(s):  
Martin Kalina ◽  
Zdenek Kala ◽  
Petr Frantik
Keyword(s):  
Vertical Displacement ◽  
Mathematical Concept ◽  
Structural Deformation ◽  
Incremental Method ◽  
Critical Effect ◽  
Post Buckling ◽  
Load Action ◽  
The Stability ◽  
The Moment ◽  
Von Mises

The article deals with the computational model of an elastic von Mises planar truss. The description of a mathematical concept, which is intended for the creation of computational programmes based on a finite number of segments, is presented. The mathematical solution is suitable for the analysis of load-deflection curves. Structural deformation is evaluated by seeking the minimal potential energy. The article examines the effects of change in the vertical displacement of the top joint on strut axes. The step by step incremental method is used in combination with the Newton-Raphson method. The presented study is aimed at the evaluation of the force in the bifurcation point, which determines the moment when loading of the model causes passing from the pre-critical effect (attainment of maximum vertical load action) to the post-critical effect. Symmetric and asymmetric initial axis imperfections are considered and relevant symmetric and asymmetric shapes of buckling are identified. The stability problem of the von Mises truss is discussed in connection with the random effects of imperfections.

Stability of Isolators at Large Horizontal Displacements

1997 ◽  
Vol 13 (3) ◽  
pp. 415-430 ◽  
Author(s):  
Maura Imbimbo ◽  
James M. Kelly
Keyword(s):  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Closed Form Expression ◽  
Elastic Analysis ◽  
Form Expression ◽  
Elastomeric Bearings ◽  
Post Buckling ◽  
Link Model ◽  
The Stability ◽  
Horizontal Displacements

Elastomeric bearings used as seismic isolators are susceptible to a buckling type of instability similar to that of structural columns. The buckling load and buckling behaviour can be determined from an elastic analysis of the isolator modelled as a continuous composite column with bending and shear flexibility; this analysis cannot be used, however, to assess the post-buckling behaviour or the stability of the isolator at large horizontal displacements. By using a two-spring rigid link model that considers large angles without using linear approximations, it is possible to predict the post-buckling behaviour of an isolator. Using the simple closed form expression, this paper will model three aspects of post-buckled isolator behaviour: the dependence of horizontal stiffness on vertical load, the stability at large horizontal displacements, and the increase of horizontal displacement with respect to axial load and vertical displacement.

scholarly journals Experimental Study on the Softening Characteristics of Sandstone and Mudstone in Relation to Moisture Content

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Gui-chen Li ◽  
Chong-chong Qi ◽  
Yuan-tian Sun ◽  
Xiao-lin Tang ◽  
Bao-quan Hou
Keyword(s):  
Moisture Content ◽  
Vertical Displacement ◽  
Surface Porosity ◽  
Shear Tests ◽  
Moisture Contents ◽  
Dynamic Finite Element ◽  
Rock Types ◽  
Underground Roadway ◽  
The Stability ◽  
Kinetics Of

The kinetics of fluid-solid coupling during immersion is an important topic of investigation in rock engineering. Two rock types, sandstone and mudstone, are selected in this work to study the correlation between the softening characteristics of the rocks and moisture content. This is achieved through detailed studies using scanning electron microscopy, shear tests, and evaluation of rock index properties during exposure to different moisture contents. An underground roadway excavation is simulated by dynamic finite element modeling to analyze the effect of moisture content on the stability of the roadway. The results show that moisture content has a significant effect on shear properties reduction of both sandstone and mudstone, which must thus be considered in mining or excavation processes. Specifically, it is found that the number, area, and diameter of micropores, as well as surface porosity, increase with increasing moisture content. Additionally, stress concentration is negatively correlated with moisture content, while the influenced area and vertical displacement are positively correlated with moisture content. These findings may provide useful input for the design of underground roadways.

A characteristic type of instability in the large deflexions of elastic plates III. Curved rectangular plates in axial compression

1954 ◽  
Vol 222 (1148) ◽  
pp. 44-59 ◽  
Keyword(s):  
Axial Compression ◽  
Rectangular Plates ◽  
Bending Moments ◽  
Elastic Plates ◽  
Characteristic Type ◽  
Circular Tubes ◽  
Axis Parallel ◽  
Post Buckling ◽  
Thin Walled ◽  
The Stability

The analysis of part I is extended to deal with the case of free-edged rectangular plates having an initial curvature about an axis parallel to one pair of opposite edges and loaded by distributed bending moments applied to the straight edges and compressive forces applied to the curved edges. In particular, the stability and post-buckling behaviour of such plates subjected to the compressive forces alone is studied. The axially symmetrical buckling of thin-walled circular tubes in axial compression is also considered. Experimental plates are found to buckle at loads rather lower than those predicted.

scholarly journals Efficacy of Selective Grinding Guided by an Occlusal Splint in Management of Myofascial Pain: A Prospective Clinical Trial

2017 ◽  
Vol 11 (1) ◽  
pp. 301-311
Author(s):  
Felipe J. Fernández-González ◽  
Jorge Cabero-López ◽  
Aritza Brizuela ◽  
Ivan Suazo ◽  
Esteban Pérez-Pevida ◽  
...  
Keyword(s):  
Temporomandibular Joint ◽  
Myofascial Pain ◽  
Vertical Displacement ◽  
Occlusal Splint ◽  
Significant Difference ◽  
Before And After ◽  
Skeletal Pattern ◽  
Condylar Position ◽  
The Stability ◽  
Facial Types

Background:For patients whose centric relation (CR) has not been considered at the start and during treatment, the task of achieving an occlusal scheme that works together with the temporomandibular joint, the muscles, and the structures of the stomatognathic apparatus becomes a major concern.Objective:This study aims to describe a reproducible, predictable and to date unreported procedure of selective grinding guided by an occlusal splint and to analyze condylar position (CP) based on the skeletal pattern.Methods:A total of 72 symptomatic patients (38 females and 34 males) were classified into three groups: hyperdivergent, intermediate and hypodivergent. CP was quantified by mounted casts on a measures condyle displacement (MCD) device. Helkimo index was also performed in order to assess the severity of the temporomandibular joint (TMJ) disorders attending to clinical dysfunction, occlusal state and anamnestic dysfunction. Once the stability had been obtained, the splint was progressively reduced until the maximum intercuspation (MIC) was achieved.Results:The vertical displacement was found to be significantly different between the hyperdivergent and other two groups (p<0.01). Comparisons of MCD analysis before and after the selective grinding procedure identified a statistically significant difference in the horizontal and vertical CP (p<0.01) between the different groups whereas the Helkimo Index showed a clear improvement of TMJ disorders.Conclusion:All facial types, specially the hyperdivergent face type, showed a reduction in condylar displacement (CD) and less craniomandibular symptoms using this procedure, making it an excellent technique for clinicians.

Solving Vlasov-Poisson-Fokker-Planck Equations using NRxx method

2017 ◽  
Vol 21 (3) ◽  
pp. 782-807 ◽  
Author(s):  
Yanli Wang ◽  
Shudao Zhang
Keyword(s):  
Splitting Method ◽  
Linear Convergence ◽  
Mass Conservation ◽  
System A ◽  
Spectral Convergence ◽  
The Stability ◽  
The Moment ◽  
Stability And Accuracy ◽  
Fokker Planck Equations ◽  
Fokker Planck

AbstractWe present a numerical method to solve the Vlasov-Poisson-Fokker-Planck (VPFP) system using the NRxx method proposed in [4, 7, 9]. A globally hyperbolic moment system similar to that in [23] is derived. In this system, the Fokker-Planck (FP) operator term is reduced into the linear combination of the moment coefficients, which can be solved analytically under proper truncation. The non-splitting method, which can keep mass conservation and the balance law of the total momentum, is used to solve the whole system. A numerical problem for the VPFP system with an analytic solution is presented to indicate the spectral convergence with the moment number and the linear convergence with the grid size. Two more numerical experiments are tested to demonstrate the stability and accuracy of the NRxx method when applied to the VPFP system.

scholarly journals Fully localized post-buckling states of cylindrical shells under axial compression

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170177 ◽  
Author(s):  
Tobias Kreilos ◽  
Tobias M. Schneider
Keyword(s):  
Axial Compression ◽  
Stability Boundary ◽  
Axial Direction ◽  
Edge State ◽  
Equilibrium Solutions ◽  
Thin Cylindrical Shell ◽  
Nonlinear Force ◽  
Post Buckling ◽  
The Stability ◽  
Nonlinear Solutions

We compute nonlinear force equilibrium solutions for a clamped thin cylindrical shell under axial compression. The equilibrium solutions are dynamically unstable and located on the stability boundary of the unbuckled state. A fully localized single dimple deformation is identified as the edge state —the attractor for the dynamics restricted to the stability boundary. Under variation of the axial load, the single dimple undergoes homoclinic snaking in the azimuthal direction, creating states with multiple dimples arranged around the central circumference. Once the circumference is completely filled with a ring of dimples, snaking in the axial direction leads to further growth of the dimple pattern. These fully nonlinear solutions embedded in the stability boundary of the unbuckled state constitute critical shape deformations. The solutions may thus be a step towards explaining when the buckling and subsequent collapse of an axially loaded cylinder shell is triggered.

scholarly journals Effect of Ring Material and Diameter on Orthopedic Implant Stability: External Fixation in Femur Bone

2018 ◽  
Vol 7 (4.26) ◽  
pp. 190 ◽  
Author(s):  
Nur Fatin Izzati Ibrahim ◽  
Ruslizam Daud ◽  
Muhammad Khairul Ali Hassan ◽  
Noor Ali Hassan ◽  
Noor Alia Md Zain ◽  
...  
Keyword(s):  
External Fixation ◽  
Von Mises Stress ◽  
Axial Stiffness ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Ring Diameter ◽  
The Stability ◽  
Von Mises ◽  
Fixation Frame ◽  
Ring Material

Axial stiffness is the most important factor in stability. It is known that any changes in the diameter of any components of the frame will either increase or decrease the axial stiffness of the fixation. The model of implant and bone will be variety as the variables changes. Current studies states that ring stability are one of the most important factors in ensuring fractured bones to have a successful re-union. In circular external fixation, the stability of the pin-bone interaction is influenced by the stability of the fixation frame where the major component is the rings. The objective is to study the finite element analysis (FEA) of the external fixator assembled in human diaphysis under compression force with different materials of the exoskeleton which are stainless steel, titanium alloy, magnesium alloy and carbon fiber. The results obtained show the mechanical strength of each material where it will be used to compare the value of von-Mises stress, stiffness and total deformation to acquire the best suitable ring diameter and material. Based on the result, as the diameter of the ring increases, the stiffness of the ring will be decreased. 

scholarly journals INCREMENTAL METHOD FOR UNLOADING PHENOMENON FIXATION AT SHAKEDOWN

2003 ◽  
Vol 9 (3) ◽  
pp. 178-191
Author(s):  
Dovilė Merkevičiūtė ◽  
Juozas Atkočiūnas
Keyword(s):  
Deformation Energy ◽  
Programming Approach ◽  
Problem Solution ◽  
Energy Principle ◽  
Incremental Method ◽  
Perfectly Plastic ◽  
Residual Strains ◽  
Residual Force ◽  
Elastic Perfectly Plastic ◽  
Von Mises

Incremental method for shakedown analysis of the elastic perfectly plastic structures is based on the extremum energy principles and non-linear mathematical programming approach. Residual force increment calculation problem is developed applying minimum complementary deformation energy principle. The Rozen project gradient and equilibrium finite element methods were applied for solution. The Rozen optimality criterion (Kuhn-Tucker conditions) ensures compatibility of residual strains and allows plastic strain and residual displacement increment calculation without dual problem solution. The possibility to fix the structure cross-section unloading phenomenon during shakedown process was developed. The proposed technique is illustrated by annular bending plate residual force and deflection calculation examples, when the von Mises criterion is taken into account.

scholarly journals Modeling of the emulsion stability using fractal dimensions

2008 ◽  
Vol 14 (3) ◽  
pp. 153-158 ◽  
Author(s):  
Snezana Pasalic ◽  
Predrag Jovanic
Keyword(s):  
Emulsion Stability ◽  
Fractal Dimensions ◽  
Ccd Camera ◽  
Stability Evaluation ◽  
Stable States ◽  
Water Emulsion ◽  
Box Counting Method ◽  
The Stability ◽  
The Moment ◽  
Life Circle

There are many developed strategies in the emulsion stability evaluation, for purpose of determining the life circle of emulsions. Most of them are based on the reological properties of the emulsions. There are very few which relay on the direct emulsion observations. In this paper we present the developed method for the emulsion stability evaluation by the direct observation of optical properties. As the stability quantification measure we propose the fractal dimension approach. The method is based on the measure of the emulsion transmittance properties, which are directly dependent on the emulsion stability at the moment of measurement. As the test emulsion the oil in the water emulsion was used. The system is classified as the stable emulsion and our intention was to find the moment when the emulsion starts to break. The emulsion transmittance properties were measured using an acquisition system, consisting of a CCD camera and a fast PC configuration equipped with the capturing software. The fractal dimensions were determined by the so called box counting method. The experimental emulsions were measured continuously within the period of 1200 h, from the moment of the emulsion creation. The changes of fractal dimensions were observed which indicates that the emulsion changed its state and therefore the stability during the time. Three regions of the emulsion life circle were divided according to the fractal dimensions measurement, which can be connected with the stable, unstable, and meta-stable states of the emulsion life circle. In the end, the model of the emulsion behavior was developed for the purpose of quantifying the changes in the experimental emulsion.

scholarly journals EXPERIMENTAL AND NUMERICAL INVESTIGATIONS ON THE STABILITY OF CYLINDRICAL SHELLS

2021 ◽  
Vol 26 (4) ◽  
pp. 34-39
Author(s):  
ATTILA BAKSA ◽  
DAVID GONCZI ◽  
LASZLA PETER KISS ◽  
PETER ZOLTAN KOVACS ◽  
ZSOLT LUKACS
Keyword(s):  
Cylindrical Shells ◽  
Element Model ◽  
Tolerance Range ◽  
Axial Pressure ◽  
Geometric Imperfections ◽  
Numerical Investigations ◽  
Negative Effect ◽  
Geometrical Imperfections ◽  
Post Buckling ◽  
The Stability

The stability of thin-walled cylindrical shells under axial pressure is investigated. The results of both experiments and numerical simulations are presented. An appropriate finite element model is introduced that accounts not only for geometric imperfections but also for non-linearities. It is found that small geometrical imperfections within a given tolerance range have considerable negative effect on the buckling load compared to perfect geometry. Various post buckling shell shapes are possible, which depend on these imperfections. The experiments and simulations show a very good correlation.

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