The Behavior of Column during Constrained Buckling Process

2012 ◽  
Vol 166-169 ◽  
pp. 385-391
Author(s):  
Xiu Gen Wu ◽  
Bai Lin Zheng ◽  
Peng Fei He ◽  
Shu Guang Liu
Keyword(s):  
Load Capacity ◽  
Reaction Force ◽  
Governing Equations ◽  
Buckling Mode ◽  
Euler Buckling ◽  
Post Buckling ◽  
Contact Models ◽  
Side Walls ◽  
Lateral Displacements ◽  
Fixed End

The elastic Euler buckling of an inextensible column is confined in a plane, and subject to fixed end displacement, in the presence of rigid, frictionless side-walls which constrain overall lateral displacements. The whole deflection is divided into some typical columns because of the symmetry. The governing equations of constrained buckling mode and deflection about axial load are deduced, based on linearized differential equation of beam. Point and line contact models are introduced to describe the behavior of the column in constrained buckling process, including load capacity, buckling wave and reaction force. The analysis on the deflection of column is helpful to the research about possible post-buckling paths.

Nonlinear Stability Analysis of Sandwich Wide Panels—Part II: Postbuckling Response

2018 ◽  
Vol 85 (8) ◽  
Author(s):  
Zhangxian Yuan ◽  
George A. Kardomateas
Keyword(s):  
Continuation Method ◽  
Weak Form ◽  
Arc Length ◽  
Nonlinear Stability Analysis ◽  
Governing Equations ◽  
Buckling Mode ◽  
The Core ◽  
Global Buckling ◽  
Post Buckling ◽  
Branch Switching

The nonlinear post-buckling response of sandwich panels based on the extended high-order sandwich panel theory (EHSAPT) is presented. The model includes the transverse compressibility, the axial rigidity, and the shear effect of the core. Both faces and core are considered undergoing large displacements with moderate rotations. Based on the nonlinear weak form governing equations, the post-buckling response is obtained by the arc-length continuation method together with the branch switching technique. Also, the post-buckling response with imperfections is studied. The numerical examples discuss the post-buckling response corresponding to global buckling and wrinkling. It is found that due to the interaction between faces and core, localized effects may be easily initiated by imperfections after the sandwich structure has buckled globally. Furthermore, this could destabilize the post-buckling response. The post-buckling response verifies the critical load and buckling mode given by the buckling analysis in part I. The axial rigidity of the core, although it is very small compared to that of the faces, has a significant effect on the post-buckling response.

scholarly journals Effect of magnetic field on nanofluid free convection in Conical Partially Annular Space

2020 ◽  
Vol 330 ◽  
pp. 01005
Author(s):  
Abderrahmane AISSA ◽  
Mohamed Amine MEDEBBER ◽  
Khaled Al-Farhany ◽  
Mohammed SAHNOUN ◽  
Ali Khaleel Kareem ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Boussinesq Approximation ◽  
Simulation Software ◽  
Comsol Multiphysics ◽  
Governing Equations ◽  
Element Analysis ◽  
Vertical Side ◽  
Side Walls

Natural convection of a magneto hydrodynamic nanofluid in a porous cavity in the presence of a magnetic field is investigated. The two vertical side walls are held isothermally at temperatures Th and Tc, while the horizontal walls of the outer cone are adiabatic. The governing equations obtained with the Boussinesq approximation are solved using Comsol Multiphysics finite element analysis and simulation software. Impact of Rayleigh number (Ra), Hartmann number (Ha) and nanofluid volume fraction (ϕ) are depicted. Results indicated that temperature gradient increases considerably with enhance of Ra and ϕ but it reduces with increases of Ha.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

A numerical approach based on finite element method for the wrinkling analysis of dielectric elastomer membranes

2021 ◽  
pp. 1-37
Author(s):  
Guoyong Mao ◽  
Wei Hong ◽  
Martin Kaltenbrunner ◽  
Shaoxing Qu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thickness Distribution ◽  
Numerical Approach ◽  
Dielectric Elastomer ◽  
Equivalent Model ◽  
Maxwell Stress ◽  
Buckling Mode ◽  
Post Buckling ◽  
Element Method

Abstract Dielectric elastomer (DE) actuators are deformable capacitors capable of a muscle-like actuation when charged. When subjected to voltage, DE membranes coated with compliant electrodes may form wrinkles due to the Maxwell stress. Here, we develop a numerical approach based on the finite element method (FEM) to predict the morphology of wrinkled DE membranes mounted on a rigid frame. The approach includes two steps, I) pre-buckling and II) post-buckling. In step I, the first buckling mode of the DE membrane is investigated by substituting the Maxwell stress with thermal stress in the built-in function of the FEM platform SIMULIA Abaqus. In step II, we use this first buckling mode as an artificial geometric imperfection to conduct the post-buckling analysis. For this purpose, we develop an equivalent model to simulate the mechanical behavior of DEs. Based on our approach, the thickness distribution and the thinnest site of the wrinkled DE membranes subjected to voltage are investigated. The simulations reveal that the crests/troughs of the wrinkles are the thinnest sites around the center of the membrane and corroborate these findings experimentally. Finally, we successfully predict the wrinkles of DE membranes mounted on an isosceles right triangle frame with various sizes of wrinkles generated simultaneously. These results shed light on the fundamental understanding of wrinkled dielectric elastomers but may also trigger new applications such as programmable wrinkles for optical devices or their prevention in DE actuators.

scholarly journals Effects of plies orientations and initial geometric imperfections on buckling strength of a composite stiffened panel

2018 ◽  
Vol 191 ◽  
pp. 00008
Author(s):  
Ikram Feddal ◽  
Abdellatif Khamlichi ◽  
Koutaiba Ameziane
Keyword(s):  
Stiffened Panel ◽  
Buckling Mode ◽  
Element Analysis ◽  
Geometric Imperfections ◽  
Stiffened Panels ◽  
Specific Strength ◽  
Euler Buckling ◽  
Buckling Behavior ◽  
Composite Stiffened Panel ◽  
Strength And Stiffness

The use of composite stiffened panels is common in several activities such as aerospace, marine and civil engineering. The biggest advantage of the composite materials is their high specific strength and stiffness ratios, coupled with weight reduction compared to conventional materials. However, any structural system may reach its limit and buckle under extreme circumstances by a progressive local failure of components. Moreover, stiffened panels are usually assembled from elementary parts. This affects the geometric as well as the material properties resulting in a considerable sensitivity to buckling phenomenon. In this work, the buckling behavior of a composite stiffened panel made from carbon Epoxy Prepregs is studied by using the finite element analysis under Abaqus software package. Different plies orientations sets were considered. The initial distributed geometric imperfections were modeled by means of the first Euler buckling mode. The nonlinear Riks method of analysis provided by Abaqus was applied. This method enables to predict more consistently unstable geometrically nonlinear induced collapse of a structure by detecting potential limit points during the loading history. It was found that plies orientations of the composite and the presence of geometric imperfections have huge influence on the strength resistance.

scholarly journals A reduced order computational model of a semi-active variable-stiffness foot prosthesis

2020 ◽  
Author(s):  
Michael McGeehan ◽  
Peter Adamczyk ◽  
Kieran Nichols ◽  
Michael Hahn
Keyword(s):  
Body Weight ◽  
Center Of Pressure ◽  
Reaction Force ◽  
Variable Stiffness ◽  
Performance Standard ◽  
Design Parameters ◽  
Compression Tests ◽  
Static Compression ◽  
Lumped Parameter ◽  
Contact Models

INTRODUCTION: Passive energy storage and return (ESR) feet are the current performance standard in lower limb prostheses. A recently developed semi-active variable-stiffness foot (VSF) prosthesis balances the simplicity of a passive ESR device with the adaptability of a powered design. The purpose of this study was to model and simulate the ESR properties of the VSF prosthesis. METHODS: The ESR properties of the VSF were modeled as a lumped parameter overhung beam. The overhung length is variable, allowing the model to exhibit variable ESR stiffness. Foot-ground contact was modeled using sphere-to-plane contact models. Contact parameters were optimized to represent the geometry and dynamics of the VSF and its foam base. Static compression tests and gait were simulated. Simulation outcomes were compared to corresponding experimental data. RESULTS: Stiffness of the model matched that of the physical VSF (R2: 0.98, RMSE: 1.37 N/mm). Model-predicted resultant ground reaction force (GRFR) matched well under optimized parameter conditions (R2: 0.98, RMSE: 5.3% body weight,) and unoptimized parameter conditions (R2: 0.90, mean RMSE: 13% body weight). Anterior-posterior center of pressure matched well with R2 > 0.94 and RMSE < 9.5% foot length in all conditions. CONCLUSIONS: The ESR properties of the VSF were accurately simulated under benchtop testing and dynamic gait conditions. These methods may be useful for predicting GRFR arising from gait with novel prostheses. Such data are useful to optimize prosthesis design parameters on a user-specific basis.

Post-Buckling of Piezoelectric Thin Plates

2015 ◽  
Vol 15 (07) ◽  
pp. 1540020 ◽  
Author(s):  
Michael Krommer ◽  
Hans Irschik
Keyword(s):  
Nonlinear Partial Differential Equation ◽  
Nonlinear Behavior ◽  
Dirichlet Boundary Conditions ◽  
Thin Plates ◽  
Governing Equations ◽  
Simply Supported ◽  
Buckling Behavior ◽  
Single Term ◽  
Post Buckling ◽  
Special Case

In the present paper, the geometrically nonlinear behavior of piezoelastic thin plates is studied. First, the governing equations for the electromechanically coupled problem are derived based on the von Karman–Tsien kinematic assumption. Here, the Berger approximation is extended to the coupled piezoelastic problem. The general equations are then reduced to a single nonlinear partial differential equation for the special case of simply supported polygonal edges. The nonlinear equations are approximated by using a problem-oriented Ritz Ansatz in combination with a Galerkin procedure. Based on the resulting equations the buckling and post-buckling behavior of a polygonal simply supported plate is studied in a nondimensional form, where the special geometry of the polygonal plate enters via the eigenvalues of a Helmholtz problem with Dirichlet boundary conditions. Single term as well as multi-term solutions are discussed including the effects of piezoelectric actuation and transverse force loadings upon the solution. Novel results concerning the buckling, snap through and snap buckling behavior are presented.

The Role of Adhesive in the Load Response of Adhesively Bonded Aluminum Hat Sections Under Axial Compression

2001 ◽  
Author(s):  
Jianping Lu ◽  
Golam M. Newaz ◽  
Ronald F. Gibson
Keyword(s):  
Compressive Strength ◽  
Plastic Collapse ◽  
Adhesively Bonded ◽  
Buckling Mode ◽  
Buckling Loads ◽  
Buckling Modes ◽  
Load Response ◽  
Peak Loads ◽  
Post Buckling

Abstract Aluminum hat section, either adhesively bonded or unbonded, experiences buckling, post buckling and plastic collapse when axially compressed. However, there exist obvious differences in the load response between the bonded and unbonded hat sections. Finite element eigenvalue buckling analysis is carried out to predict the buckling load and mode. Experiments show that when adhesively bonded hat sections begin to buckle there is a transformation from the first buckling mode to the higher ones, while the unbonded hat sections develop the post buckling based on the lowest buckling mode. The different buckling modes result in not only different buckling loads but different peak loads of the hat sections as well. Finally, the ultimate compressive strength formulae are proposed for the hat sections.

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.

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