The Effect of Shear Deformation on Post-Buckling Behavior of Laminated Beams

1987 ◽  
Vol 54 (3) ◽  
pp. 558-562 ◽  
Author(s):  
I. Sheinman ◽  
M. Adan
Keyword(s):  
Finite Difference ◽  
Shear Deformation ◽  
Nonlinear Differential Equations ◽  
Kinematic Model ◽  
Transverse Shear Deformation ◽  
Shear Effect ◽  
Laminated Beams ◽  
Buckling Behavior ◽  
Geometrical Nonlinear ◽  
Post Buckling

A geometrical nonlinear theory of composite laminated beams is derived with the effect of transverse shear deformation taken into account. The theory is based on a high-order kinematic model, with the nonlinear differential equations solved by Newton’s method and a special finite-difference scheme. A parametric study of the shear effect involving several kinematic approaches was carried out for isotropic and anisotropic beams.

The Effect of Transverse Shear on the Postbuckling and Growth Characteristics of Delaminations in Composites

1999 ◽  
Vol 121 (4) ◽  
pp. 406-412 ◽  
Author(s):  
Catherine H. Ferrie ◽  
Izhak Sheinman ◽  
George A. Kardomateas
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Shear Deformation ◽  
Release Rate ◽  
Transverse Shear ◽  
Coupling Effect ◽  
Nonlinear Differential Equations ◽  
Kinematic Model ◽  
Initial Imperfection ◽  
Plate Length

A geometrically nonlinear formulation for the behavior of composite delaminated beams of arbitrary stacking sequence, and with the effects of transverse shear deformation included, is presented. The formulation is based on a first-order shear deformation kinematic model, which incorporates the bending-stretching coupling effect and also assumes an arbitrary initial imperfection. The nonlinear differential equations are solved by Newton’s method using a finite-difference scheme. The growth of the delamination is also studied by applying the J-integral in order to derive a formula for the energy release rate, which includes transverse shear. Results are presented which illustrate the shear effect, especially with respect to the ratio of the in-plane extensional over shear modulus and with respect to the ratio of plate length over thickness. It is seen that transverse shear can affect largely the displacement profiles, rendering the structure more compliant, and can promote growth by increasing the energy release rate, but this latter effect is moderate and mainly noticable only at the later stages in the postbuckling regime.

POST-BUCKLING OF AN ELASTIC COLUMN WITH VARIOUS ROTATIONAL END RESTRAINTS

2005 ◽  
Vol 05 (01) ◽  
pp. 113-123 ◽  
Author(s):  
B. PHUNGPAINGAM ◽  
S. CHUCHEEPSAKUL
Keyword(s):  
Shooting Method ◽  
Nonlinear Differential Equations ◽  
Compressive Force ◽  
Limit Load ◽  
Technical Note ◽  
Buckling Behavior ◽  
End Conditions ◽  
Post Buckling ◽  
Secondary Bifurcation ◽  
Elastic Column

In this technical note, the post-buckling behavior of a simply supported elastic column with various rotational end conditions of the supports is investigated. The compressive force is applied at the tip of the column. The characteristic equation for solving the critical loads is obtained from the boundary value problem of linear systems. In the post-buckling state, a set of nonlinear differential equations with boundary conditions is established and numerically solved by the shooting method. The interesting features associated with this problem such as the limit load point, snap-through phenomenon and the secondary bifurcation point will be highlighted herein.

Post-Buckling Analysis of Stiffened Laminated Panel

1988 ◽  
Vol 55 (3) ◽  
pp. 635-640 ◽  
Author(s):  
Izhak Sheinman ◽  
Yeoshua Frostig
Keyword(s):  
Variational Principle ◽  
Finite Difference ◽  
Difference Scheme ◽  
Lateral Displacement ◽  
Numerical Procedure ◽  
Stiffened Panel ◽  
Airy Stress Function ◽  
Buckling Behavior ◽  
Plate Elements ◽  
Post Buckling

An analytical-numerical procedure is applied to investigate the post-buckling behavior of a composite laminated stiffened panel. The panel is modeled by plate elements for which the nonlinear equations are derived (via a variational principle) in terms of the lateral displacement and Airy stress function, and treated by resolving the variables into eigenfunctions in conjunction with a finite-difference scheme.

Initial Post-buckling Behavior of Thick Rings Under Uniform External Hydrostatic Pressure

1995 ◽  
Vol 62 (2) ◽  
pp. 338-345 ◽  
Author(s):  
Lei Fu ◽  
A. M. Waas
Keyword(s):  
Hydrostatic Pressure ◽  
Shear Deformation ◽  
Buckling Load ◽  
Deformation Analysis ◽  
Two Dimensional ◽  
Composite Ring ◽  
Buckling Behavior ◽  
Buckling Stability ◽  
Post Buckling ◽  
Beam Type

The initial post-buckling behavior of thick rings under external uniform hydrostatic pressure is investigated. In the analysis, no assumptions are placed upon the relative magnitudes of the elongations and rotations, and the ring is assumed to be elastic and extensional. The importance of including certain nonlinear terms in the initial post-buckling stability analysis and the effects of nonzero shearing strains on the buckling load and the initial post-buckling stability are examined. It is shown that the classical Kirchhoff assumptions, when employed for a ring lead to nonvanishing through thickness strains, εzz and εzθ, with the latter being proportional to the through thickness coordinate z. An approximate first order shear deformation analysis and a two-dimensional elasticity analysis (without beam-type kinematical assumptions) of the initial post-buckling behavior of thick rings are presented and the thickness effects on the buckling load and the initial post-buckling behavior are examined. The formulation for the composite ring was reduced to that of an isotropic ring and the results thus obtained were compared with published one-dimensional results in the literature. It is found from both the shear deformation and the two-dimensional analysis that the initial post-buckling behavior of the isotropic ring and the composite rings studied are stable. The influence of thickness on the degree of stability in the immediate post-buckling response is characterized.

Creep Buckling and Post-Buckling Analyses of a Viscoelastic FGM Cylindrical Shell with Initial Deflection Subjected to a Uniform In-Plane Load

2012 ◽  
Vol 28 (2) ◽  
pp. 391-399 ◽  
Author(s):  
H.-L. Dai ◽  
H.-Y. Zheng
Keyword(s):  
Cylindrical Shell ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Volume Fraction ◽  
Superposition Principle ◽  
Functionally Graded ◽  
Initial Deflection ◽  
Transverse Shear Deformation ◽  
Creep Buckling ◽  
Post Buckling

AbstractIn this paper, based on the viscoelastic theory, the creep buckling and post-buckling behaviors of a viscoelastic functionally graded material (FGM) cylindrical shell with initial deflection subjected to a uniform in-plane load are investigated. The material properties of the viscoelastic FGM cylindrical shell are assumed to vary through the structural thickness according to a power law distribution of the volume fraction of constituent materials and Poisson's ratio is assumed as a constant. Considering the transverse shear deformation and geometric nonlinearity, the constitutive relation of the viscoelastic FGM cylindrical shell is established. By means of the Newton-Newmark method and the Boltzmann superposition principle, the problem for the creep buckling and post-buckling of the FGM cylindrical shell is solved. The numerical results reveal that the transverse shear deformation, volume fraction and geometric parameters have significant effects on the creep buckling and post-buckling of the viscoelastic FGM cylindrical shell.

Post-buckling and Snap-Through Behavior of Inclined Slender Beams

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
Jian Zhao ◽  
Jianyuan Jia ◽  
Xiaoping He ◽  
Hongxi Wang
Keyword(s):  
Large Deflection ◽  
Buckling Modes ◽  
Strongly Nonlinear ◽  
Elastic Beams ◽  
Buckling Behavior ◽  
Geometrical Nonlinear ◽  
Slender Beams ◽  
Post Buckling ◽  
Inclined Beam ◽  
Good Agreement

Based on the geometrical nonlinear theory of large deflection elastic beams, the governing differential equations of post-buckling behavior of clamped-clamped inclined beams subjected to combined forces are established. By using the implicit compatibility conditions to solve the nonlinear statically indeterminate problems of elastic beams, the strongly nonlinear equations formulated in terms of elliptic integrals are directly solved in the numerical sense. When the applied force exceeds the critical value, the numerical simulation shows that the inclined beam snaps to the other equilibrium position automatically. It is in the snap-through process that the accurate configurations of the post-buckling inclined beam with different angles are presented, and it is found that the nonlinear stiffness decreases as the midpoint displacement is increased according to our systematical analysis of the inward relations of different buckling modes. The numerical results are in good agreement with those obtained in the experiments.

Nonlinear analysis of stability for imperfect eccentrically stiffened FGM plates under mechanical and thermal loads based on FSDT. Part 2: Numerical results and discussions

2015 ◽  
Vol 37 (4) ◽  
pp. 251-262
Author(s):  
Dao Van Dung ◽  
Nguyen Thi Nga
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Buckling Load ◽  
Geometrical Parameters ◽  
Thermal Loads ◽  
First Order ◽  
Elastic Foundations ◽  
Buckling Behavior ◽  
Post Buckling

Based on the first-order shear deformation plate theory (FSDT), the smeared stiffeners technique and Galerkin method, the analytical expressions to determine the static critical buckling load and analyze the post-buckling load-deflection curves of FGM plates reinforced by FGM stiffeners resting on elastic foundations and subjected to in-plane compressive loads or thermal loads are established in part 1. In this part, we will use them to study the effects of temperature, stiffener, volume fraction index, geometrical parameters, elastic foundations on the buckling and post-buckling behavior of plates. In addition, the results in comparisons between the classical plate theory (CPT) and the first order shear deformation theory (FSDT) also are carried out and shown that the buckling and post-buckling behavior of more thick plate should be studied by FSDT.

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