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.

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 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.

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