scholarly journals In-Plane Stress and Displacement Distributions in a Spinning Annular Disk Under Stationary Edge Loads

1997 ◽  
Vol 64 (4) ◽  
pp. 897-904 ◽  
Author(s):  
Jen-San Chen ◽  
Jhi-Lu Jhu
Keyword(s):  
Plane Stress ◽  
Rotational Speed ◽  
Stress Function ◽  
Classical Solutions ◽  
Airy Stress Function ◽  
Displacement Fields ◽  
Centrifugal Effect ◽  
Annular Disk ◽  
Spinning Disk ◽  
Stress And Displacement Fields

It is well known that the in-plane stress and displacement distributions in a stationary annular disk under stationary edge tractions can be obtained through the use of Airy stress function in the classical theory of linear elasticity. By using Lame’s potentials, this paper extends these solutions to the case of a spinning disk under stationary edge tractions. It is also demonstrated that the problem of stationary disk-spinning load differs from the problem of spinning disk-stationary load not only by the centrifugal effect, but also by additional terms arising from the Coriolis effect. Numerical simulations show that the amplitudes of the stress and displacement fields grow unboundedly as the rotational speed of the disk approaches the critical speeds. As the rotational speed approaches zero, on the other hand, the in-plane stresses and displacements are shown, both numerically and analytically, to recover the classical solutions derived through the Airy stress function.

Bending Due to Ring Loading of a Cylindrical Shell With an Elastic Core

1965 ◽  
Vol 32 (1) ◽  
pp. 99-103 ◽  
Author(s):  
John C. Yao
Keyword(s):  
Cylindrical Shell ◽  
Stress Function ◽  
Shell Theory ◽  
Soft Core ◽  
Thin Cylindrical Shell ◽  
Displacement Fields ◽  
Material Constants ◽  
The Core ◽  
Stress And Displacement Fields ◽  
Classical Shell Theory

The problem of a long, thin cylindrical shell with a soft core and subjected to a radial ring load is solved with the use of the Boussinesq-Neuber stress function for the core in conjunction with classical shell theory. Numerical results for stress and displacement fields are given for various values of the cylinder geometry parameters and material constants.

scholarly journals A Cauchy like problem in plane elasticity

2007 ◽  
Vol 29 (3) ◽  
pp. 245-248
Author(s):  
Dang Dinh Ang ◽  
Nguyen Dung
Keyword(s):  
Harmonic Function ◽  
Stress Field ◽  
Elastic Body ◽  
Bounded Domain ◽  
Plane Stress ◽  
Stress Function ◽  
Plane Elasticity ◽  
Airy Stress Function ◽  
Surface Stresses

Let \(\Omega \) be a bounded domain in the plane, representing an elastic body. Let \(\Gamma_0 \) be a portion of the boundary \(\Gamma\) of \(\Omega \), \(\Gamma_0 \) being assumed to be paralled to the \(x\)-axis. It is proposed to determine the stress field in \(\Omega \) from the displacements and surface stresses given on \(\Gamma_0 \). Under the assumption of plane stress, it is shown that \(u_x + u_y\) is a harmonic function. An Airy stress function is introduced, from which the stress field is computed.

Generalized plane stress in a semi-infinite strip under arbitrary end-load

1964 ◽  
Vol 281 (1385) ◽  
pp. 184-206 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Plane Stress ◽  
Stress Function ◽  
Infinite Strip ◽  
Order Ordinary Differential Equation ◽  
Orthogonal Functions

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.

A Stress Singularity Parameter Approach for Evaluating the Interfacial Reliability of Plastic Encapsulated LSI Devices

1989 ◽  
Vol 111 (4) ◽  
pp. 243-248 ◽  
Author(s):  
T. Hattori ◽  
S. Sakata ◽  
G. Murakami
Keyword(s):  
Adhesive Strength ◽  
Evaluation Method ◽  
Stress Singularity ◽  
The Finite Element Method ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
Ni Alloy ◽  
Base Resin ◽  
Interfacial Reliability ◽  
Parameter Approach

Since the stress and displacement fields near a bonding edge show singularity behaviors, the adhesive strength evaluation method, using maximum stresses calculated by a numerical stress analysis such as the finite element method, is generally not valid. In this paper, a new method, which uses two stress singularity parameters, is presented for evaluating adhesive strength. This method is applied to several kinds of molded models, composed of epoxy base resin and Fe-Ni alloy sheets, and plastic encapsulated LSI models. Predictions about the initiation and extension of delamination are compared with the results of observations made by scanning acoustic tomography on these models.

Axisymmetric Solution of a Flexible Disk Rotating Near a Rigid Surface

1988 ◽  
Vol 110 (4) ◽  
pp. 674-677 ◽  
Author(s):  
M. Carpino ◽  
G. A. Domoto
Keyword(s):  
Plane Stress ◽  
Asymptotic Expansions ◽  
Reynolds Equation ◽  
Flat Surface ◽  
Inertial Effects ◽  
Rigid Surface ◽  
Axisymmetric Solution ◽  
Spinning Disk ◽  
Rotating Flexible Disk ◽  
Flexible Disk

A rotating flexible disk separated from a rigid flat surface by a gas film is addressed. The gas film between the disk and the plate is represented by an incompressible Reynolds equation. Inertial effects are included. The disk is treated as a membrane where the tension is found from the plane stress solution for a spinning disk. Two different methods for the axisymmetric solution of this system are developed. The first uses the method of matched asymptotic expansions. The second method is a mixed numerical/perturbation procedure.

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