Buckling of an Elastic Plate/Layer Along a Rigid Base With Adhesion

2019 ◽  
Vol 87 (2) ◽  
Author(s):  
George G. Adams
Keyword(s):  
Elastic Plate ◽  
Cohesive Zone ◽  
Elastic Layer ◽  
Buckling Load ◽  
Rigid Base ◽  
Sufficient Condition ◽  
Euler Buckling ◽  
Elastic Film ◽  
Zone Parameter ◽  
Unbonded Length

Abstract An infinitely long elastic plate/layer is under uniaxial compression with its long dimension held by adhesion to a flat rigid base without friction. A prescribed length of the plate/layer is free of adhesion. This configuration is similar to a pre-stressed elastic film for which buckling of an unbonded section is a necessary, but not sufficient, condition for delamination. For that configuration, buckling occurs at the Euler buckling load of a fixed–fixed plate. Although the present study does not include friction or tangential interface stresses, the onset of buckling should be similar for these two cases. For the case of an elastic plate, a cohesive zone is used and it is found that the fixed–fixed buckling load is not attained except for extremely large values of a cohesive zone parameter. For realistic values, the buckling load is about half of that value. For the situation of an elastic layer with adhesion (without a cohesive zone), the buckling load approaches the fixed–fixed value only for very large values of the ratio of the unbonded length to the thickness.

scholarly journals Contact Stress of an Elastic Layer Pressed on a Rigid Base with a Smooth Protrusion

1983 ◽  
Vol 26 (219) ◽  
pp. 1481-1487
Author(s):  
Toshikazu SHIBUYA ◽  
Takashi KOIZUMI ◽  
Toshimitsu TAKAGI
Keyword(s):  
Contact Stress ◽  
Elastic Layer ◽  
Rigid Base

Tubular Conical Columns for Offshore Structures

1993 ◽  
Vol 115 (4) ◽  
pp. 219-222
Author(s):  
S. J. Cox
Keyword(s):  
Hydrostatic Pressure ◽  
Offshore Structures ◽  
Buckling Load ◽  
Tubular Columns ◽  
Euler Buckling ◽  
Effect Of Hydrostatic Pressure ◽  
Volume Preserving

We examine submerged nonlinear tubular columns with slenderness ratios between 40 and 160 and ratios of diameter to thickness between 20 and 50. We demonstrate that the column’s Euler buckling load can be increased nearly 30 percent by a volume preserving taper of only a few degrees. We determine the effect of hydrostatic pressure and self-weight on such conical columns and offer some preliminary remarks on the role played by model imperfections.

scholarly journals Vibration modes characterized by Rayleigh waves propagating in an elastic layer on a rigid base.

1987 ◽  
pp. 191-199
Author(s):  
Shigeaki MORICHI ◽  
Tatuso OHMACHI ◽  
Takumi TOSHINAWA ◽  
Akiyo MIYAI
Keyword(s):  
Rayleigh Waves ◽  
Elastic Layer ◽  
Rigid Base ◽  
Vibration Modes

Wrinkling of Wide Sandwich Panels∕Beams With Orthotropic Phases by an Elasticity Approach

2004 ◽  
Vol 72 (6) ◽  
pp. 818-825 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Compressive Loading ◽  
Sandwich Panels ◽  
Wave Mode ◽  
Buckling Load ◽  
Face Sheet ◽  
Beam Model ◽  
Elasticity Solution ◽  
Short Side ◽  
Euler Buckling ◽  
Sandwich Construction

There exist many formulas for the critical compression of sandwich plates, each based on a specific set of assumptions and a specific plate or beam model. It is not easy to determine the accuracy and range of validity of these rather simple formulas unless an elasticity solution exists. In this paper, we present an elasticity solution to the problem of buckling of sandwich beams or wide sandwich panels subjected to axially compressive loading (along the short side). The emphasis on this study is on the wrinkling (multi-wave) mode. The sandwich section is symmetric and all constituent phases, i.e., the facings and the core, are assumed to be orthotropic. First, the pre-buckling elasticity solution for the compressed sandwich structure is derived. Subsequently, the buckling problem is formulated as an eigen-boundary-value problem for differential equations, with the axial load being the eigenvalue. For a given configuration, two cases, namely symmetric and anti-symmetric buckling, are considered separately, and the one that dominates is accordingly determined. The complication in the sandwich construction arises due to the existence of additional “internal” conditions at the face sheet∕core interfaces. Results are produced first for isotropic phases (for which the simple formulas in the literature hold) and for different ratios of face-sheet vs core modulus and face-sheet vs core thickness. The results are compared with the different wrinkling formulas in the literature, as well as with the Euler buckling load and the Euler buckling load with transverse shear correction. Subsequently, results are produced for one or both phases being orthotropic, namely a typical sandwich made of glass∕polyester or graphite∕epoxy faces and polymeric foam or glass∕phenolic honeycomb core. The solution presented herein provides a means of accurately assessing the limitations of simplifying analyses in predicting wrinkling and global buckling in wide sandwich panels∕beams.

scholarly journals Contact Stresses of an Elastic Plate Pressed onto a Rigid Base with a Cylindrical Protrusion or Pit

1981 ◽  
Vol 24 (198) ◽  
pp. 2067-2073 ◽  
Author(s):  
Toshikazu SHIBUYA ◽  
Takashi KOIZUMI ◽  
Katsuhiko IIDA ◽  
Toshiaki HARA
Keyword(s):  
Elastic Plate ◽  
Contact Stresses ◽  
Rigid Base ◽  
Cylindrical Protrusion

Plane Contact and Partial Slip Behaviors of Elastic Layers With Randomly Rough Surfaces

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
Fan Jin ◽  
Qiang Wan ◽  
Xu Guo
Keyword(s):  
Rough Surface ◽  
Contact Area ◽  
Elastic Layer ◽  
Partial Slip ◽  
Real Contact Area ◽  
Rigid Base ◽  
Slip Model ◽  
Normal Contact ◽  
Real Contact ◽  
Plane Contact

A plane contact and partial slip model of an elastic layer with randomly rough surface were established by combining the Greenwood–Williamson (GW) rough contact model and the Cattaneo–Mindlin partial slip model. The rough surface of the elastic layer bonded to a rigid base is modeled as an ensemble of noninteracting asperities with identical radius of curvature and Gaussian-distributed heights. By employing the Hertzian solution and the Cattaneo–Mindlin solution to each individual asperity of the rough surface, we derive the total normal force, the real contact area, and the total tangential force for the rough surface, respectively, and then examine the normal contact and partial slip behaviors of the layer. An effective Coulomb coefficient is defined to account for interfacial friction properties. Furthermore, a typical stick–slip transition for the rough surface was also captured by distinguishing the stick and slip contacting asperities according to their respective indentation depths. Our analysis results show that an increasing layer thickness may result in a larger real contact area, a lower mean contact pressure, and a higher effective Coulomb coefficient.

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