Behavior of Thin Elastic Circular Rings With Large Deformations Under Nonuniform Loads

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
E. Azzuni ◽  
S. Guzey
Keyword(s):  
Large Deformations ◽  
Normal Pressure ◽  
Numerical Approach ◽  
Circular Ring ◽  
Order Ordinary Differential Equation ◽  
Pressure Profiles ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Circular Rings ◽  
Small Deformations

Thin elastic circular rings under uniform pressure have been extensively studied by many researchers. Both the deflection and buckling behavior of rings were considered in these studies, but most have focused on the small deformations analysis approach. Even though the use of the small deformations assumption helps find the deflections of the ring prior to reaching the buckling load, it does not accurately capture the behavior of the ring after buckling. The in-plane large deformations analysis of thin elastic circular rings under nonuniform pressure explored in this paper expands on previous work and investigates varying pressure profiles. The pressure profiles studied here can be described by p=p01+qcosnθ. The large deformations assumption allows for the investigating of buckling loads as well as post-buckling behavior. Nonuniform normal pressure acting on a thin elastic circular ring results in a behavior that is described by a second-order ordinary differential equation (ODE) of the Duffing type, which is solved here through a numerical approach.

Buckling and Post-buckling Behavior of Elliptical Plates: Part II—Results

1990 ◽  
Vol 57 (4) ◽  
pp. 989-994 ◽  
Author(s):  
Herzl Chai
Keyword(s):  
Plate Boundary ◽  
Normal Pressure ◽  
Load Level ◽  
Material Body ◽  
Buckling Behavior ◽  
Plate Size ◽  
Bending Stresses ◽  
Post Buckling ◽  
Large Material ◽  
Plate Solution

The large-deflection plate solution developed in Part I is used here to study the buckling and post-buckling deformation and stress characteristics of an elliptically-shaped surface layer that has been delaminated from a large material body. The economical, yet accurate nature of this solution, together with available graphic routines, has made it possible to present, figuratively, a comprehensive description of the plate behavior. The conditions for a layer-substrate overlap and the variations of membrane and bending stresses along the plate boundary are emphasized. Deformations were induced either by a normal pressure or a biaxial displacement field applied to the plate boundary. The problem variables are plate size and shape, details of load biaxiality, and load level.

Buckling and Post-Buckling Behavior of Elliptical Plates: Part I—Analysis

1990 ◽  
Vol 57 (4) ◽  
pp. 981-988 ◽  
Author(s):  
Herzl Chai
Keyword(s):  
Series Expansion ◽  
Degrees Of Freedom ◽  
Plate Boundary ◽  
Normal Pressure ◽  
Solution Procedure ◽  
Buckling Behavior ◽  
Bending Stresses ◽  
Post Buckling ◽  
Polynomial Series ◽  
Plane Displacement

A polynomial series expansion for displacements is used in conjunction with the Rayleigh-Ritz energy method to produce buckling and post-buckling stress solutions for an elliptically-shaped surface layer that has been delaminated from the main load-bearing body. Plate deformations are induced by a combined in-plane displacement field applied to the plate boundary and normal pressure. Convergence of the plate solution is assessed by systematically increasing the number of displacement terms in the series expansion. The convergence of membrane and bending stresses at the plate boundary was generally slow and nonuniform. The degrees-of-freedom necessary for a satisfactory solution typically increase with increasing complexity or magnitude of the plate deformations. By employing as many as 77 displacement terms, practically exact stress solutions are obtained for a wide variety of basic delamination plate problems. The proposed solution procedure is highly efficient and economical, and it may be easily extended to other plate geometries or loading conditions.

Fiber Orientation Effect in the Dynamic Buckling of Debonded Regions in Laterally Loaded FRP Strengthened Walls

2014 ◽  
Vol 624 ◽  
pp. 470-477 ◽  
Author(s):  
Dvir Elmalich ◽  
Oded Rabinovitch
Keyword(s):  
Fiber Orientation ◽  
Numerical Approach ◽  
Shear Loading ◽  
Element Formulation ◽  
Geometrically Nonlinear ◽  
Nonlinear Dynamic Response ◽  
Critical Displacement ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Laterally Loaded

This paper studies the effect of lamination and fiber orientation on the geometrically nonlinear dynamic response of debonded regions in walls strengthened with FRP. The paper adopts an analytical/numerical approach and uses a specially tailored finite element formulation for the layered structure. By means of this analytical/numerical tool, two strengthening layouts for a wall segment subjected to a dynamic shear loading are compared. In the first layout, the fibers are oriented along the width and height of the segment and in the second one, they are oriented along its diagonals. The analysis reveals that the two layouts are involved with significantly different critical points and significantly different dynamic post-buckling behaviors. Specifically, it shows that the diagonal layout, which better serves the shear loading scenario, is involved with a much smaller critical displacement and a dynamic post-buckling behavior that is governed by the stiffer compressed and tensed diagonals.

Large Deformations of Circular Rings Under Nonuniform Normal Pressure

1974 ◽  
Vol 41 (1) ◽  
pp. 192-196 ◽  
Author(s):  
P. Seide ◽  
T. M. M. Jamjoom
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Large Deformations ◽  
Normal Pressure ◽  
Static Stability ◽  
Deformation Pattern ◽  
Center Line ◽  
Asymmetric Deformation ◽  
Circular Rings

The deformations and static stability of thin elastic circular rings under nonuniform pressures are studied. The investigation takes into account large bending deformations of the ring which is treated as an elastica. The loads considered remain normal to the center line during deformations. Numerical methods are used to solve the ordinary differential equations of equilibrium and of perturbed equilibrium for a particular case of loads which vary as p = p0(1 + q cos 2θ). The ring is found to deform only in a doubly symmetric fashion. Static buckling into an asymmetric deformation pattern does not occur.

Buckling Behavior of Tire Breaker Structure

1983 ◽  
Vol 11 (1) ◽  
pp. 3-19
Author(s):  
T. Akasaka ◽  
S. Yamazaki ◽  
K. Asano
Keyword(s):  
Elastic Foundation ◽  
Elastic Moduli ◽  
Wave Length ◽  
Bending Moment ◽  
Experimental Results ◽  
Automobile Tire ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Steel Cord ◽  
Interlaminar Shear

Abstract The buckled wave length and the critical in-plane bending moment of laminated long composite strips of cord-reinforced rubber sheets on an elastic foundation is analyzed by Galerkin's method, with consideration of interlaminar shear deformation. An approximate formula for the wave length is given in terms of cord angle, elastic moduli of the constituent rubber and steel cord, and several structural dimensions. The calculated wave length for a 165SR13 automobile tire with steel breakers (belts) was very close to experimental results. An additional study was then conducted on the post-buckling behavior of a laminated biased composite beam on an elastic foundation. This beam is subjected to axial compression. The calculated relationship between the buckled wave rise and the compressive membrane force also agreed well with experimental results.

Appraisal of Allowable Loads by Simplified Rules

1986 ◽  
Vol 108 (2) ◽  
pp. 131-137
Author(s):  
D. Moulin
Keyword(s):  
Experimental Investigation ◽  
Plastic Region ◽  
Thin Structures ◽  
Geometric Imperfections ◽  
Buckling Behavior ◽  
Simplified Method ◽  
Post Buckling ◽  
Initial Geometric Imperfections ◽  
Fast Breeder Reactors ◽  
Breeder Reactors

This paper presents a simplified method to analyze the buckling of thin structures like those of Liquid Metal Fast Breeder Reactors (LMFBR). The method is very similar to those used for the buckling of beams and columns with initial geometric imperfections, buckling in the plastic region. Special attention is paid to the strain hardening of material involved and to possible unstable post-buckling behavior. The analytical method uses elastic calculations and diagrams that account for various initial geometric defects. An application of the method is given. A comparison is made with an experimental investigation concerning a representative LMFBR component.

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

2012 ◽  
Vol 28 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. D. Yau ◽  
S.-R. Kuo
Keyword(s):  
Stiffness Matrix ◽  
Virtual Work ◽  
Bending Moment ◽  
Beam Element ◽  
Narrow Beam ◽  
Cross Sectional ◽  
Geometric Stiffness ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

ABSTRACTUsing conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yanget al.'s simplified geometric stiffness matrix [kg]12×12of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.

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.

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