Mechanical behaviour of bistable struts

2011 ◽  
Vol 226 (5) ◽  
pp. 1321-1325 ◽  
Author(s):  
J G Cai ◽  
Y X Xu ◽  
J Feng ◽  
J Zhang
Keyword(s):  
Mechanical Behaviour ◽  
Displacement Curve ◽  
Equilibrium Path ◽  
Equilibrium Equations ◽  
Structural Element ◽  
Total Potential ◽  
Bifurcation Buckling ◽  
The Stability ◽  
Von Mises ◽  
Joint Behaviour

The mechanical behaviour of a bistable structural element, which is based on the snap-through and bifurcation properties of the von Mises truss, has been investigated in this article. By assuming the joint behaviour as ideal hinges and using the large deformation theory based on a linear elastic material, a simple analytical model for the stability of the von Mises truss was formulated. The governing set of non-linear equilibrium equations was obtained by applying the principle of stationary total potential energy. Then, the formulae of the snap-through and bifurcation buckling loads and the equilibrium path were given. In addition to the well-known cases of primary and secondary branches, a third type that the bifurcation buckling point lying on the descending branch of the load versus displacement curve was discussed. In this case, although its upper bifurcation load is lower than its upper snap-through buckling load, the truss experiences a symmetric snap-through mode first, and hence the bifurcation point is not physically relevant. Finally, the assumptions of the classical von Mises truss analysis are discussed.

Instability of Discrete Pseudo-Conservative Structural Systems

1991 ◽  
Vol 44 (11S) ◽  
pp. S194-S198 ◽  
Author(s):  
Anibal E. Mirasso ◽  
Luis A. Godoy
Keyword(s):  
Classical System ◽  
Potential Energy Function ◽  
Structural Systems ◽  
Equilibrium Path ◽  
Equilibrium Equations ◽  
Total Potential ◽  
Approximate Form ◽  
Nonlinear Equilibrium ◽  
Mechanical Models ◽  
New Formulation

Critical and postcritical states of pseudo-conservative discrete structural systems are studied by means of a new formulation leading to a classification of critical states and to an approximate form of the postcritical equilibrium path. The nonlinear equilibrium equations are derived from the total potential energy function of a classical system, but with the addition of at least one control parameter. The follower force effect is thus included by nonlinear constraints to the equilibrium equation. The nonlinear equations are solved by perturbation techniques. Finally the theory is applied to investigate the instability of some simple mechanical models.

The Effect of Porosity on Elastic Stability of Toroidal Shell Segments Made of Saturated Porous Functionally Graded Materials

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Hadi Babaei ◽  
Mohsen Jabbari ◽  
M. Reza Eslami
Keyword(s):  
Elastic Stability ◽  
Functionally Graded ◽  
Toroidal Shell ◽  
Geometrical Parameters ◽  
Equilibrium Equations ◽  
Closed Form Solutions ◽  
Porous Shell ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability

Abstract This research deals with the stability analysis of shallow segments of the toroidal shell made of saturated porous functionally graded (FG) material. The nonhomogeneous material properties of porous shell are assumed to be functionally graded as a function of the thickness and porosity parameters. The porous toroidal shell segments with positive and negative Gaussian curvatures and nonuniform distributed porosity are considered. The nonlinear equilibrium equations of the porous shell are derived via the total potential energy of the system. The governing equations are obtained on the basis of classical thin shell theory and the assumptions of Biot's poroelasticity theory. The equations are a set of the coupled partial differential equations. The analytical method including the Airy stress function is used to solve the stability equations of porous shell under mechanical loads in three cases. Porous toroidal shell segments subjected to lateral pressure, axial compression, and hydrostatic pressure loads are analytically analyzed. Closed-form solutions are expressed for the elastic buckling behavior of the convex and concave porous toroidal shell segments. The effects of porosity distribution and geometrical parameters of the shell on the critical buckling loads of porous toroidal shell segments are studied.

On the Comparison Between Microscopic and Macroscopic Instability Mechanisms in a Class of Fiber-Reinforced Composites

1985 ◽  
Vol 52 (4) ◽  
pp. 794-800 ◽  
Author(s):  
N. Triantafyllidis ◽  
B. N. Maker
Keyword(s):  
Stable Region ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Equilibrium Equations ◽  
Loss Of Ellipticity ◽  
Reinforced Composite ◽  
Bifurcation Buckling ◽  
Microstructural Instability ◽  
Macroscopic Approach ◽  
The Stability

To investigate the relation between the macroscopic and microscopic instability predictions for certain microstructured media, we study the stability of an axially stretched fiber-reinforced composite under plane strain conditions. The microstructural instability is attributed to a bifurcation buckling of the fibers while the corresponding macroscopic one occurs at the loss of ellipticity in the homogenized incremental equilibrium equations of the material. The effects of geometry and material properties on those phenomena are analyzed. The macroscopic approach consistently and sometimes considerably overestimates the stable region of the composite. The attractive feature in this work is that all the investigations can be done by using analytical solutions instead of the numerical ones employed in similar investigations so far.

scholarly journals Geometrically nonlinear behavior of lattice domes coupled with local Eulerian instability

2020 ◽  
Vol 7 (1) ◽  
pp. 247-260
Author(s):  
Alberto Carpinteri ◽  
Giuseppe Lacidogna ◽  
Domenico Scaramozzino
Keyword(s):  
Lattice Structure ◽  
Local Buckling ◽  
Numerical Procedure ◽  
Nonlinear Behavior ◽  
Geometrical Parameters ◽  
Displacement Curve ◽  
Equilibrium Path ◽  
Geometrically Nonlinear ◽  
Equilibrium Equations ◽  
Load Displacement

AbstractStructural analysis is an intricate subject when nonlinearities occur. They make the structural behavior complex and may have important consequences in the design choice as well. Especially for lattice domes, as snap-through phenomena and local Eulerian instabilities generally affect the structural response, linear analysis is not enough. In this paper, a semi-analytical formulation is used in order to study the geometrically nonlinear behavior of lattice domes subject to vertical loads. The formulation is derived from the equilibrium equations written in the deformed configuration, considering large displacements and taking also into account local buckling conditions. The resulted system of equations, being strongly nonlinear, has been solved by means of a numerical procedure, based on a mixed load-displacement control scheme, leading to the evaluation of the complete equilibrium path. The influence of geometrical parameters on the critical load multiplier and shape of the load-displacement curve is also discussed. In particular, a complex equilibrium path for a sixteen-member five-node lattice structure is analyzed, which is characterized by several branches which can generate ‘snapping’ conditions.

scholarly journals Modelling and Stability Analysis of Articulated Vehicles

2021 ◽  
Vol 11 (8) ◽  
pp. 3663
Author(s):  
Tianlong Lei ◽  
Jixin Wang ◽  
Zongwei Yao
Keyword(s):  
Stability Analysis ◽  
Critical Velocity ◽  
Equations Of State ◽  
Steering System ◽  
Analysis Model ◽  
Nonlinear Dynamic Model ◽  
Equilibrium Equations ◽  
Eigenvalue Method ◽  
Articulated Vehicles ◽  
The Stability

This study constructs a nonlinear dynamic model of articulated vehicles and a model of hydraulic steering system. The equations of state required for nonlinear vehicle dynamics models, stability analysis models, and corresponding eigenvalue analysis are obtained by constructing Newtonian mechanical equilibrium equations. The objective and subjective causes of the snake oscillation and relevant indicators for evaluating snake instability are analysed using several vehicle state parameters. The influencing factors of vehicle stability and specific action mechanism of the corresponding factors are analysed by combining the eigenvalue method with multiple vehicle state parameters. The centre of mass position and hydraulic system have a more substantial influence on the stability of vehicles than the other parameters. Vehicles can be in a complex state of snaking and deviating. Different eigenvalues have varying effects on different forms of instability. The critical velocity of the linear stability analysis model obtained through the eigenvalue method is relatively lower than the critical velocity of the nonlinear model.

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.

A field theory approach to stability of radial equilibria in nonlinear elasticity

1986 ◽  
Vol 99 (3) ◽  
pp. 589-604 ◽  
Author(s):  
J. Sivaloganathan
Keyword(s):  
Field Theory ◽  
Calculus Of Variations ◽  
Nonlinear Elasticity ◽  
Isotropic Material ◽  
Theory Approach ◽  
Radial Solutions ◽  
Equilibrium Equations ◽  
The Stability ◽  
State Of Tension

In this paper we study the stability of a class of singular radial solutions to the equilibrium equations of nonlinear elasticity, in which a hole forms at the centre of a ball of isotropic material held in a state of tension under prescribed boundary displacements. The existence of such cavitating solutions has been shown by Ball[1], Stuart [11] and Sivaloganathan[10]. Our methods involve elements of the field theory of the calculus of variations and provide a new unified interpretation of the phenomenon of cavitation.

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 On the Stability of Collinear Points of the RTBP with Triaxial and Oblate Primaries and Relativistic Effects

2021 ◽  
pp. 56-73
Author(s):  
S. E. Abd El-Bar
Keyword(s):  
Characteristic Equation ◽  
Body Problem ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Relativistic Effects ◽  
Three Body Problem ◽  
Total Potential ◽  
The Mean ◽  
The Stability ◽  
Three Body

Under the influence of some different perturbations, we study the stability of collinear equilibrium points of the Restricted Three Body Problem. More precisely, the perturbations due to the triaxiality of the bigger primary and the oblateness of the smaller primary, in addition to the relativistic effects, are considered. Moreover, the total potential and the mean motion of the problem are obtained. The equations of motion are derived and linearized around the collinear points. For studying the stability of these points, the characteristic equation and its partial derivatives are derived. Two real and two imaginary roots of the characteristic equation are deduced from the plotted figures throughout the manuscript. In addition, the instability of the collinear points is stressed. Finally, we compute some selected roots corresponding to the eigenvalues which are based on some selected values of the perturbing parameters in the Tables 1, 2.

scholarly journals Effects of placement angle and direction of orthopedic force application on the stability of orthodontic miniscrews

2012 ◽  
Vol 83 (4) ◽  
pp. 667-673 ◽  
Author(s):  
Jihye Lee ◽  
Ji Young Kim ◽  
Yoon Jeong Choi ◽  
Kyung-Ho Kim ◽  
Chooryung J. Chung
Keyword(s):  
Cortical Bone ◽  
Lateral Force ◽  
Von Mises Stress ◽  
Biomechanical Stability ◽  
Element Analysis ◽  
Force Application ◽  
Pull Out ◽  
The Stability ◽  
Von Mises ◽  
Pull Out Strength

ABSTRACT Objectives: To evaluate the influence of placement angle and direction of orthopedic force application on the stability of miniscrews. Materials and Methods: Finite element analysis was performed using miniscrews inserted into supporting bone at angles of 90°, 60°, and 30° (P90°, P60°, and P30°). An orthopedic heavy force of 800 gf was applied to the heads of the miniscrews in four upward (U0°, U30°, U60°, U90°) or lateral (L0°, L30°, L60°, L90°) directions. In addition, pull-out strength of the miniscrews was measured with various force directions and cortical bone thicknesses. Results: Miniscrews with a placement angle of 30° (P30°) and 60° (P60°) showed a significant increase in maximum von Mises stress following the increase in lateral force vectors (U30°, U60°, U90°) compared to those with a placement angle of 90° (P90°). In accordance, the pull-out strength was higher with the axial upward force when compared to the upward force with lateral vectors. Maximum von Mises stress and displacement of the miniscrew increased as the angle of lateral force increased (L30°, L60°, L90°). However, a more dramatic increase in maximum von Mises stress was noted in P30° than in P60° and P90°. Conclusion: Placement of the miniscrew perpendicular to the cortical bone is advantageous in terms of biomechanical stability. Placement angles of less than 60° can reduce the stability of miniscrews when orthopedic forces are applied in various directions.

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