Buckling and Post-buckling of Composite Plates and Shells Subjected to Elevated Temperature

1993 ◽  
Vol 60 (2) ◽  
pp. 514-519 ◽  
Author(s):  
V. Birman ◽  
C. W. Bert
Keyword(s):  
Thermal Field ◽  
Axial Loading ◽  
Composite Plates ◽  
Simultaneous Action ◽  
Algebraic Equations ◽  
Equilibrium Equations ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Plates And Shells ◽  
Effects Of Temperature

Effects of temperature on buckling and post-buckling behavior of reinforced and unstiffened composite plates or cylindrical shells are considered. First, equilibrium equations are formulated for a shell subjected to the simultaneous action of a thermal field and an axial loading. These equations are used to predict a general form of the algebraic equations describing the post-buckling response of a shell. Conditions for the snap-through of a shell subjected to thermomechanical loading are formulated. As an example, the theory is applied to prediction of post-buckling response of flat large-aspect-ratio panels reinforced in the direction of their short edges.

On the Post-Buckling Behavior of Reinforced Composite Shells

1990 ◽  
Vol 34 (03) ◽  
pp. 207-211
Author(s):  
Victor Birman
Keyword(s):  
Sufficient Conditions ◽  
Axial Loading ◽  
Dynamic Buckling ◽  
General Analysis ◽  
Composite Shells ◽  
Stiffened Shells ◽  
Reinforced Composite ◽  
Buckling Behavior ◽  
Axisymmetric Buckling ◽  
Post Buckling

The problem of post-buckling behavior of composite cylindrical shells reinforced in the axial and circumferential directions and subject to axial loading is considered. The equations of equilibrium of an imperfect shell are formulated in terms of displacements. Then the sufficient conditions of imperfection in sensitivity for both static and dynamic buckling problems are formulated. This general analysis is applied to a particular case of axisymmetric buckling of ring-stiffened shells which appear to be practically imperfection-insensitive.

scholarly journals The Instability Improvement of the Symmetric Angle-Ply and Cross-Ply Composite Plates with Shape Memory Alloy Using Finite Element Method

2014 ◽  
Vol 6 ◽  
pp. 632825 ◽  
Author(s):  
Zainudin A. Rasid ◽  
Rizal Zahari ◽  
Amran Ayob
Keyword(s):  
Finite Element ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Element Formulation ◽  
Recovery Stress ◽  
Buckling Behavior ◽  
Post Buckling

Shape memory alloy (SMA) wires were embedded within laminated composite plates to take advantage of the shape memory effect property of the SMA in improving post-buckling behavior of composite plates. A nonlinear finite element formulation was developed for this study. The plate-bending formulation used in this study was developed based on the first order shear deformation theory, where the von Karman's nonlinear moderate strain terms were added to the strain equations. The effect of the SMA was captured by adding recovery stress term in the constitutive equation of the SMA composite plates. Values of the recovery stress of the SMA were determined using Brinson's model. Using the principle of virtual work and the total Lagrangian approach, the final finite element nonlinear governing equation for the post-buckling of SMA composite plates was derived. Buckling and post-buckling analyses were then conducted on the symmetric angle-ply and cross-ply SMA composite plates. The effect of several parameters such as the activation temperature, volume fraction, and the initial strain of the SMA on the post-buckling behavior of the SMA composite plates were studied. It was found that significant improvements in the post-buckling behavior for composite plates can be attained.

Thermal post buckling behavior of rectangular antisymmetric cross-ply composite plates

1993 ◽  
Vol 98 (1-4) ◽  
pp. 39-50 ◽  
Author(s):  
G. Singh ◽  
G. Venkateswara Rao ◽  
N. G. R. Iyengar
Keyword(s):  
Composite Plates ◽  
Buckling Behavior ◽  
Post Buckling

Post-buckling Analysis of Multiply Delaminated Composite Plates

1997 ◽  
Vol 64 (4) ◽  
pp. 842-846 ◽  
Author(s):  
Haiying Huang ◽  
G. A. Kardomateas
Keyword(s):  
External Load ◽  
Perturbation Technique ◽  
Linear Equations ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Internal Load ◽  
Nonlinear Beam ◽  
Buckling Behavior ◽  
Beam Equations ◽  
Post Buckling

This paper presents an elastic post-buckling analysis of an axially loaded beam-plate with two central across-the-width delaminations located at arbitrary depths. The analysis is based on the nonlinear beam equations, combined with the appropriate kinematic continuity and equilibrium conditions. A perturbation technique is employed, which transforms the nonlinear equations into a sequence of linear equations. An asymptotic solution of the post-buckling behavior of the plate is thus obtained. It is shown that with two delaminations, both the maximum deflection and the internal load of the first buckled (top) subplate increase as the external load increases. Of particular interest is the redistribution of load among subplates, which keeps the increase rate of internal load of the top buckled subplate much less than that of the external load. In other words, the load of the buckled subplate is close to the critical value even though the externally applied load is much larger than the critical load. In addition to the two-delamination configuration, a single delamination case is studied based on the present approach in order to verify the accuracy of the method. Also, a comparison with available finite element results is performed.

Effects of symmetric imperfections on the behavior of bistable struts

2016 ◽  
Vol 22 (12) ◽  
pp. 2240-2252 ◽  
Author(s):  
Jianguo Cai ◽  
Xiaowei Deng ◽  
Jian Feng
Keyword(s):  
Virtual Work ◽  
Variable Geometry ◽  
Equilibrium Equations ◽  
Buckling Mode ◽  
Concentrated Load ◽  
Virtual Work Principle ◽  
Shallow Arches ◽  
Buckling Behavior ◽  
Nonlinear Equilibrium ◽  
Post Buckling

The behavior of a bistable strut for variable geometry structures was investigated in this paper. A three-hinged arch subjected to a central concentrated load was used to study the effect of symmetric imperfections on the behavior of the bistable strut. Based on a nonlinear strain–displacement relationship, the virtual work principle was adopted to establish both the pre-buckling and buckling nonlinear equilibrium equations for the symmetric snap-through buckling mode. Then the critical load for symmetric snap-through buckling was obtained. The results show that the axial force is in compression before the arch is buckled, but it becomes in tension after buckling. Thus, the previous formulas cannot be used for the analysis of post-buckling behavior of three-hinged shallow arches. Then, the principle of virtual work was also used to establish the post-buckling equilibrium equations of the arch in the horizontal and vertical directions as well as the static boundary conditions, which are very important for bistable struts.

Modeling for Initial Post-Buckling Analysis of Laminated Plates and Shells by FEM

2012 ◽  
Vol 166-169 ◽  
pp. 520-525
Author(s):  
Cheng Shuang Han ◽  
Hong Mei Zhang ◽  
Zai Ling Cheng
Keyword(s):  
Eigenvalue Problems ◽  
Buckling Analysis ◽  
Laminated Plates ◽  
Algebraic Equations ◽  
Nonlinear Eigenvalue Problems ◽  
Incremental Method ◽  
Plate And Shell ◽  
Classical Stability ◽  
Post Buckling ◽  
Plates And Shells

Nonlinear analysis of plate and shell structures can explain the phenomenon which cannot been explained by classical stability theory, and can obtain better validation of experimental results. Stability problems are essentially nonlinear and their nonlinear finite element solutions ultimately result in solving nonlinear algebraic equations and nonlinear eigenvalue problems. The solutions can define the shape of basic path and determine critical load by using the incremental method, The perturbation methods are used near the critical point, and the basic formulas are given for initial post-buckling analysis by FEM.

Relative Post-Buckling Stiffness Calculation of Symmetrically Laminated Composite Plates Using an Exact Finite Strip

2010 ◽  
Vol 123-125 ◽  
pp. 201-204 ◽  
Author(s):  
Seyyed Amir Mahdi Ghannadpour ◽  
Hamid Reza Ovesy
Keyword(s):  
Laminated Composite ◽  
Composite Plates ◽  
Unknown Coefficient ◽  
Laminated Composite Plates ◽  
Total Strain Energy ◽  
Finite Strip ◽  
Finite Strip Method ◽  
Buckling Behavior ◽  
Out Of Plane ◽  
Post Buckling

This paper presents the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of symmetrically laminated composite plates. The so-called exact finite strip is developed based on the concept that it is effectively a plate. The present method, which is designated by the name Full-analytical Finite Strip Method in this paper, provides an efficient and extremely accurate buckling solution. In the development process, the Von-Karman’s equilibrium equation is solved exactly to obtain the buckling loads and the corresponding form of out-of-plane buckling deflection modes. The investigation of thin flat plate buckling behavior is then extended to an initial post-buckling study with the assumption that the deflected form immediately after the buckling is the same as that obtained for the buckling. The post-buckling study is effectively a single-term analysis, which is attempted by utilizing the so-called semi-energy method. In this method, the Von-Karman’s compatibility equation governing the behavior of symmetrically laminated composite plates is used together with a consideration of the total strain energy of the plate. Through the solution of the compatibility equation, the in-plane displacement functions are developed in terms of the unknown coefficient in the assumed out-of-plane deflection function. These in-plane and out-of-plane deflected functions are then substituted in the total strain energy expressions and the theorem of minimum total potential energy is applied to solve for the unknown coefficient. The developed method is subsequently applied to analyze the initial post-buckling behavior of some representative thin flat plates for which the results are also obtained through the application of a semi-analytical finite strip method. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is significantly promoted.

Analysis of the Post-Buckling Response of Nonlocal Plates via Fractional Order Continuum Theory

2020 ◽  
pp. 1-22
Author(s):  
Sai Sidhardh ◽  
Sansit Patnaik ◽  
Fabio Semperlotti
Keyword(s):  
Long Range ◽  
Fractional Order ◽  
Constitutive Models ◽  
Continuum Theory ◽  
Path Following ◽  
Algebraic Equations ◽  
Nonlinear Buckling ◽  
Buckling Behavior ◽  
Long Range Interactions ◽  
Post Buckling

Abstract We present a comprehensive study on the post-buckling response of nonlocal structures performed by means of a frame-invariant fractional-order continuum theory to model the long-range (nonlocal) interactions. The use of fractional calculus facilitates an energy-based approach to nonlocal elasticity that plays a fundamental role in the present study. The underlying fractional framework enables mathematically, physically, and thermodynamically consistent integral-type constitutive models that, in contrast to the existing integer-order differential approaches, allow the nonlinear buckling and post-bifurcation analyses of nonlocal structures. Further, we present the first application of the Koiter's asymptotic method to investigate post-bifurcation branches of nonlocal structures. Finally, the theoretical framework is applied to study the post-buckling behavior of slender nonlocal plates. Both qualitative and quantitative analyses of the influence that long-range interactions bear on post-buckling response are undertaken. Numerical studies are carried out using a 2D fractional-order Finite Element Method (f-FEM) modified to include a combination of the Newton-Raphson and a path-following arc-length iterative methods in order to solve the system of nonlinear algebraic equations that govern the equilibrium beyond the critical points. The present framework provides a general foundation to investigate the post-buckling response of potentially any type of nonlocal structure.

Sign in / Sign up

Export Citation Format

Share Document