scholarly journals AN APPROXIMATE METHOD FOR DETERMINING THE PLANE STRESS OF ORTHOTROPIC MATERIAL

1957 ◽  
Vol 13 (6) ◽  
pp. 452
Author(s):  
HAO TUNG-SHENG
Keyword(s):  
Approximate Method ◽  
Plane Stress ◽  
Orthotropic Material

Orthotropic Characteristics of Glass-Fibre-Epoxy Laminates under Plane Stress

1973 ◽  
Vol 15 (2) ◽  
pp. 102-108 ◽  
Author(s):  
R. M. Ogorkiewicz
Keyword(s):  
Tensile Strength ◽  
Epoxy Resin ◽  
Uniaxial Tension ◽  
Plane Stress ◽  
Glass Fibre ◽  
Orthotropic Material ◽  
Glass Fibres ◽  
Degree Of Anisotropy

Deformational characteristics of laminates of unidirectionally arranged glass fibres and epoxy resin under plane stress are shown to correspond very closely under uniaxial tension and, to a lesser extent, under shear to the theroetical pattern of stiffness of an orthotropic material. The anisotropy in stiffness is also shown to be accompanied by an even greater degree of anisotropy in tensile strength.

The Affine Transformation for Orthotropic Plane-Stress and Plane-Strain Problems

1956 ◽  
Vol 23 (1) ◽  
pp. 1-6
Author(s):  
H. A. Lang
Keyword(s):  
Shear Modulus ◽  
Plane Strain ◽  
Elastic Constants ◽  
Plane Stress ◽  
Affine Transformation ◽  
Orthotropic Material ◽  
Elastic Symmetry ◽  
Concentrated Load ◽  
Plane Strain Problem ◽  
Orthotropic Plane

Abstract It is demonstrated that a single affine transformation of the type x = ax′, y = by′ immediately extends the solution of any isotropic plane-stress or plane-strain problem to the solution of an orthotropic plane problem where the orthotropic material is characterized by three independent constants. Since orthotropy, defined as elastic symmetry with respect to two orthogonal axes, implies four independent elastic constants, the affine transformation introduces a restriction upon the orthotropic shear modulus. The orthotropic shear modulus differs from that used by previous investigators. This difference alters the equation which the orthotropic stress function must satisfy and, therefore, directly affects the solution to every plane-stress or plane-strain problem. Some arguments are advanced to favor the shear modulus, as here defined, whenever orthotropy must be restricted to three elastic constants. The two solutions of the orthotropic half plane subjected to a normal concentrated load are contrasted to illustrate the effect of the two definitions of orthotropic shear modulus.

scholarly journals Some Plane Stress Problems of Orthotropic Material

1961 ◽  
Vol 4 (13) ◽  
pp. 11-16
Author(s):  
Takuo HAYASHI
Keyword(s):  
Plane Stress ◽  
Orthotropic Material

Some New Types of Orthotropic Plates Laminated of Orthotropic Material

1953 ◽  
Vol 20 (2) ◽  
pp. 286-288
Author(s):  
C. Bassel Smith
Keyword(s):  
Plane Stress ◽  
Orthotropic Material ◽  
Laminated Plates ◽  
The Other ◽  
Arbitrary Angle ◽  
Orthotropic Plates ◽  
Elastic Symmetry

Abstract Plywood plates are usually constructed so that the grain of adjacent plies is perpendicular. Such laminated plates possess two perpendicular axes of elastic symmetry. In this discussion plywood plates having other than 90 degree angles between the grain of adjacent plies are considered. First, a two-ply plate with the grain of one ply making any arbitrary angle with the grain of the other ply is discussed. It is shown that this plate, when in a state of plane stress or when subjected to small deflections, possesses the same two perpendicular axes of elastic symmetry. By making use of the formulas obtained for the two-ply plate, it is shown how to construct a plate of any number of plies (the adjacent plies not necessarily having their grain perpendicular) possessing the same type of elastic symmetry as the two-ply plate.

Computing cell tractions from particle displacements on silicone rubber substrata

1994 ◽  
Vol 52 ◽  
pp. 162-163
Author(s):  
Tim Oliver ◽  
Akira Ishihara ◽  
Ken Jacobsen ◽  
Micah Dembo
Keyword(s):  
Plane Stress ◽  
Linear Elasticity ◽  
Silicone Rubber ◽  
Mathematical Analysis ◽  
Elastic Recovery ◽  
Video Images ◽  
Cell Traction Forces ◽  
Latex Beads ◽  
Cell Traction ◽  
Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

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