Imperfection Sensitivity of Laminated Cylindrical Shells by Full and Initial Post-Buckling Analyses

Aerospace ◽  
2004 ◽  
Author(s):  
Izhak Sheinman ◽  
Mahmood Jabareen
Keyword(s):  
Structural Engineering ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Test Results ◽  
Imperfection Sensitivity ◽  
Buckling Behavior ◽  
Load Carrying ◽  
Post Buckling ◽  
Linear Buckling Analysis ◽  
Laminated Cylindrical Shells

Laminated cylindrical shells are already commonly used in structural engineering, and their buckling and post-buckling behavior is of vital importance in the design of such structures. The validity of linear buckling analysis in this context, has been questioned because of the discrepancy observed between theoretical prediction and test results. The cause of this discrepancy is the fact that the nonlinear behavior of shell-like structures is generally characterized by a limit point rather than by a bifurcation point. For such structures, the load-carrying capacity depends on the level of imperfection (hence the concept “imperfection sensitivity”). The motivation is, therefore, to reduce the sensitivity rather than preventing the imperfection. For that purpose insight into the post-buckling state is called for.

Koiter-Based Solution for the Initial Post-buckling Behavior of Moderately Thick Orthotropic and Shear Deformable Cylindrical Shells Under External Pressure

1997 ◽  
Vol 64 (4) ◽  
pp. 885-896 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
External Pressure ◽  
Isotropic Case ◽  
Imperfection Sensitivity ◽  
Buckling Behavior ◽  
Load Carrying ◽  
Geometrical Imperfections ◽  
Post Buckling ◽  
Shear Deformable

The initial post-buckling behavior of moderately thick orthotropic shear deformable cylindrical shells under external pressure is studied by means of Koiter’s general post-buckling theory. To this extent, the objective is the calculation of imperfection sensitivity by relating to the initial post-buckling behavior of the perfect structure, since it is generally recognized that the presence of small geometrical imperfections in some structures can lead to significant reductions in their buckling strengths. A shear deformation theory, which accounts for transverse shear strains and rotations about the normal to the shell midsurface, is employed to formulate the shell equations. The initial post-buckling analysis indicates that for several combinations and geometric dimensions, the shell under external pressure will be sensitive to small geometrical imperfections and may buckle at loads well below the bifurcation predictions for the perfect shell. On the other hand, there are extensive ranges of geometrical dimensions for which the shell is insensitive to imperfections, and, therefore it would exhibit stable post-critical behavior and have a load-carrying capacity beyond the bifurcation point. The range of imperfection sensitivity depends strongly on the material anisotropy, and also on the shell thickness and whether the end pressure loading is included or not. For example, for the circumferentially reinforced graphite/epoxy example case studied, it was found that the structure is not sensitive to imperfections for values of the Batdorf length parameter z˜ above ≃270, whereas for the axially reinforced case the structure is imperfection-sensitive even at the high range of length values; for the isotropic case, the structure is not sensitive to imperfections above z˜ ≃ 1000.

Post-buckling Behavior of Stiffened Cross-Ply Cylindrical Shells

1994 ◽  
Vol 61 (4) ◽  
pp. 998-1000 ◽  
Author(s):  
M. Savoia ◽  
J. N. Reddy
Keyword(s):  
Axial Compression ◽  
Carrying Capacity ◽  
Shell Theory ◽  
Load Carrying Capacity ◽  
Imperfection Sensitivity ◽  
Buckling Modes ◽  
Geometric Imperfection ◽  
Buckling Behavior ◽  
Load Carrying ◽  
Post Buckling

The post-buckling of stiffened, cross-ply laminated, circular determine the effects of shell lamination scheme and stiffeners on the reduced load-carrying capacity. The effect of geometric imperfection is also included. The analysis is based on the layerwise shell theory of Reddy, and the “smeared stiffener” technique is used to account for the stiffener stiffness. Nu cylinders under uniform axial compression is investigated to merical results for stiffened and unstiffened cylinders are presented, showing that imperfection-sensitivity is strictly related to the number of nearly simultaneous buckling modes.

scholarly journals Displacement-based multi-modal formulation of Koiter's method applied to cylindrical shells

2021 ◽  
Author(s):  
Saullo G. P. Castro ◽  
Eelco Jansen
Keyword(s):  
Degrees Of Freedom ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Imperfection Sensitivity ◽  
Data Set ◽  
Collaborative Software ◽  
Close Relationship ◽  
Out Of Plane ◽  
Post Buckling ◽  
Displacement Based

The multi-modal formulation of Koiter's asymptotic method provides a systematic and efficient procedure to evaluate the initial post-buckling behaviour and to assess the nonlinear behavior of structures. This manuscript presents a displacement-based multi-modal formulation of Koiter's method for cylindrical shells, which are structures known for their high imperfection sensitivity and for having clustered bifurcation modes that highly interact. A third-order interpolation is used for the in-plane and out-of-plane displacements by means of the Bogner-Fox-Schmit-Castro (BFSC) element, with 4 nodes and 10 degrees-of-freedom per node, aiming at an accurate representation of the second-order fields required in the initial post-buckling analysis. The single-curvature of the shell is considered in the finite element kinematics and the study includes nonlinear kinematics from Von Kármán and Sanders. The mesh is obtained by closing the circumferentially oriented coordinate at the position where the mesh completes one revolution about the shell perimeter. The proposed formulation and implementation is verified in detail by comparing results for composite shells against established literature for multi-mode asymptotic expansions. A fast convergence of the proposed formulation is observed for linear buckling, pre-buckling state and the initial post-buckling coefficients. The developed formulation enables a close relationship between formulae and the implemented code, and is implemented using state-of-the-art collaborative software. The authors made the implemented routines in a publicly available data set with the aim to popularize Koiter's method.

Buckling Behavior of Elliptical Shells of Changing Thickness under Uniform Axial Compression

2013 ◽  
Vol 351-352 ◽  
pp. 492-496 ◽  
Author(s):  
Li Wan ◽  
Lei Chen
Keyword(s):  
Axial Compression ◽  
Cylindrical Shells ◽  
Imperfection Sensitivity ◽  
Buckling Mode ◽  
Buckling Strength ◽  
Shell Buckling ◽  
Buckling Behavior ◽  
Structural Applications ◽  
Post Buckling ◽  
Shell Geometry

Many elliptical shells are used in structural applications in which the dominant loading condition is axial compression. Due to the fact that the radius varies along the cross-section midline, the buckling behavior is more difficult to identify than those of cylindrical shells. The general concerned aspects in cylindrical shell buckling analyses such as the buckling mode, the pre-buckling deformation and post-buckling deformation are all quite different related to specific elliptical shell geometry. The buckling behavior of elliptical cylindrical shells with uniform thickness has been widely studied by many researchers. However, the thickness around the circumference may change for some specific structural forms, the femoral neck for example, which makes the buckling behavior more complex. It is known that the buckling strength of thin cylindrical shells is quite sensitive to imperfections, so it is natural to explore the imperfection sensitivity of elliptical shells. This paper explores the buckling behavior of imperfect elliptical shells under axial compression. It is hoped that the results will make a useful contribution in this field.

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.

Geometric Imperfection Sensitivity and Effect of Constraint Conditions of H-Section Columns under Compression

2010 ◽  
Vol 102-104 ◽  
pp. 140-144
Author(s):  
Yi Ping Wang ◽  
Yong Zang ◽  
Di Ping Wu
Keyword(s):  
Carrying Capacity ◽  
Steel Structures ◽  
Load Carrying Capacity ◽  
Imperfection Sensitivity ◽  
Geometric Imperfection ◽  
Manufacture Process ◽  
Buckling Behavior ◽  
Load Carrying ◽  
Thin Walled ◽  
Tolerance Control

The buckling behavior of thin-walled steel structures under load is still imperfectly understood, in spite of much research over the past 50 years. In this paper, the buckling behaviors of H-section columns under compression have been simulated with ANSYS. In the analysis, contact pairs between column ends and end blocks have been introduced into the model, and the load carrying capacity of the columns with four kinds of end constraint conditions and various typical initial geometric imperfections has been calculated and discussed. The results indicate that the load carrying capacity is most sensitive to the flexural imperfection, and the constraint condition cannot change the imperfection sensitivity of a column under compression, but improving restrain condition can heighten the load carrying capacity. They are helpful to the use and the tolerance control in the manufacture process of thin-walled H-section steel structures.

scholarly journals Instability of Conical Shells with Multiple Dimples under Axial Compression

2020 ◽  
Vol 8 (5) ◽  
pp. 1022-1027 ◽  
Keyword(s):  
Axial Compression ◽  
Conical Shell ◽  
Numerical Data ◽  
Test Results ◽  
Conical Shells ◽  
Numerical Predictions ◽  
Test Models ◽  
Buckling Behavior ◽  
Shell Models ◽  
Load Carrying

Thin-walled conical shells are primary structures in offshore application. Presence of imperfection can considerably reduce the load carrying capacity of such structures when in use. This study examines the buckling behavior of axially compressed imperfect steel cones using the multiple perturbation load analysis (MPLA). This is both a numerical and experimental study. Eight conical shell test models were manufactured in pairs and collapsed under axial compression: two perfect, and the remaining six with MPLA imperfection amplitude, A, of 0.56, 1.12 and 1.68 having two equally-spaced dimples on each cones. Experimental test results for all the conical shell models and the accompanying numerical predictions are given in this paper. Repeatability of experimental data was good. The errors within each pair were 3%, 13%, 1% and 0%. In addition, there was a good comparison between experimental and numerical data. The ratio of experimental to numerical buckling loads varies from 0.91 to 1.13.

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