Instability of a Fiber-Reinforced Elastic Slab Subjected to Axial Loads

1979 ◽  
Vol 46 (4) ◽  
pp. 839-843 ◽  
Author(s):  
M. Kurashige
Keyword(s):  
Elastic Material ◽  
Fiber Reinforced ◽  
Axial Loads ◽  
Foam Rubber ◽  
Instability Problem ◽  
Isotropic Elastic Material ◽  
Shear Buckling ◽  
Elastic Slab

Following the derivation of the relations of incremental stresses and strains for an idealized fiber-reinforced isotropic elastic material, the instability problem stated in the title is analyzed on the basis of Biot’s mechanics of incremental deformations. The analysis indicates that the slab reinforced by fibers along the direction of its thickness under axial loads becomes unstable in a manner different from the case of an unreinforced slab. In the course of the analysis the material was specified as the so-called Blatz-Ko rubber, solid and foam. It was found that the slab of solid rubber buckled only under compression, while that of foam rubber became unstable under tension as well as under compression. There exist two types of buckling for foam rubber under tension: a shear buckling and an internal buckling. However, the latter does not manifest itself physically since the former always occurs first.

Instability of a Transversely Isotropic Elastic Slab Subjected to Axial Loads

1981 ◽  
Vol 48 (2) ◽  
pp. 351-356 ◽  
Author(s):  
M. Kurashige
Keyword(s):  
Critical Load ◽  
Transverse Direction ◽  
Transversely Isotropic ◽  
Axial Direction ◽  
Axial Loads ◽  
Instability Problem ◽  
Wrong Direction ◽  
Elastic Slab ◽  
Anisotropic Slab ◽  
Anisotropy Strength

After obtaining the relations between incremental stresses and incremental strains, we analyzed the instability problem stated in the title on the basis of Biot’s mechanics of incremental deformations. The slab, made of a hypothetical transversely isotropic compressible elastic material, is assumed to be stronger in its transverse direction than in its axial direction. The analysis shows that, no matter what the anisotropy strength of the slab is or its thickness is, it can become unstable under tension as well as under compression. The critical load is higher for the stronger anisotropy in the compressive case, while it is lower for the stronger anisotropy in the tensile case. In other words, the reinforcement in the “wrong” direction weakens the slab under tension with respect to its stability. Furthermore, the weakly anisotropic slab can become unstable only after the axial resultant force reaches its maximum, while the strongly anisotropic slab can lose its stability before the force reaches its maximum.

General theory of small elastic deformations superposed on finite elastic deformations

1952 ◽  
Vol 211 (1104) ◽  
pp. 128-154 ◽  
Keyword(s):  
General Theory ◽  
Elastic Material ◽  
Finite Deformation ◽  
Plane Surface ◽  
Thin Sheet ◽  
Potential Functions ◽  
Homogeneous Deformation ◽  
Infinitesimal Deformation ◽  
Elastic Deformations ◽  
Isotropic Elastic Material

Using tensor notations a general theory is developed for small elastic deformations, of either a compressible or incompressible isotropic elastic body, superposed on a known finite deformation, without assuming special forms for the strain-energy function. The theory is specialized to the case when the finite deformation is pure homogeneous. When two of the principal extension ratios are equal the changes in displacement and stress due to the small superposed deformation are expressed in terms of two potential functions in a manner which is analogous to that used in the infinitesimal deformation of hexagonally aeolotropic materials. The potential functions are used to solve the problem of the infinitesimally small indentation, by a spherical punch, of the plane surface of a semi-infinite body of incompressible isotropic elastic material which is first subjected to a finite pure homogeneous deformation symmetrical about the normal to the force-free plane surface. The general theory is also applied to the infinitesimal deformation of a thin sheet of incompressible isotropic elastic material which is first subjected to a finite pure homogeneous deformation by forces in its plane. A differential equation is obtained for the small deflexion of the sheet due to small forces acting normally to its face. This equation is solved completely in the case of a clamped circular sheet subjected to a pure homogeneous deformation having equal extension ratios in the plane of the sheet, the small bending force being uniformly distributed over a face of the sheet. Finally, equations are obtained for the homogeneously deformed sheet subjected to infinitesimal generalized plane stress, and a method of solution by complex variable technique is indicated.

Optimum Elastic Restraint for Pressurised Circular Plates

1963 ◽  
Vol 67 (632) ◽  
pp. 525-526
Author(s):  
Charles W. Bert
Keyword(s):  
Effective Stress ◽  
Elastic Material ◽  
Unit Volume ◽  
List Type ◽  
Maximum Deflection ◽  
Type Number ◽  
Circular Plates ◽  
Uniform Thickness ◽  
Isotropic Elastic Material ◽  
Elastically Restrained

SummaryFor uniform-thickness, solid circular plates made of isotropic elastic material and elastically restrained at the edge, expressions are derived for the optimum support stiffness to minimise the following quantities: 1.The largest effective stress based on several different strength theories.2.The largest effective stress per unit of maximum deflection or per unit volume displaced.

Sign in / Sign up

Export Citation Format

Share Document