Dynamic Response of Circular Rigid-Plastic Plates Resting on Fluid

1976 ◽  
Vol 43 (1) ◽  
pp. 102-106 ◽  
Author(s):  
D. Krajcinovic
Keyword(s):  
Integral Equation ◽  
Dynamic Response ◽  
Integral Transform ◽  
Specific Problem ◽  
Integral Equation Method ◽  
Dual Integral Equation ◽  
Inviscid Fluid ◽  
Rigid Plastic ◽  
Interaction Problem ◽  
Integral Transform Technique

Paper concerns a specific problem in the study of dynamic response of rigid-plastic plates in contact with incompressible and inviscid fluid. The dynamic load is assumed to be of high intensity and short duration. Employing integral transform technique in conjunction with the dual integral equation method this interaction problem is reduced to the problem of plate deforming in vacuum for which the solution is well known.

An Integral Equation Approach to the Semi-Infinite Strip Problem

1973 ◽  
Vol 40 (4) ◽  
pp. 948-954 ◽  
Author(s):  
G. D. Gupta
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Laminate Composite ◽  
Integral Transform ◽  
Stress Singularity ◽  
Infinite Strip ◽  
Integral Equation Approach ◽  
Fixed End ◽  
Integral Transform Technique

A semi-infinite strip held rigidly on its short end is considered. Loads in the strip at infinity (far away from the fixed end) are prescribed. Integral transform technique is used to provide an exact formulation of the problem in terms of a singular integral equation. Stress singularity at the strip corner is obtained from the singular integral equation which is then solved numerically. Stresses along the rigid end are determined and the effect of the material properties on the stress-intensity factor is presented. The method can also be applied to the problem of a laminate composite with a flat inclusion normal to the interfaces.

scholarly journals The dual integral equation method in hydromechanical systems

2004 ◽  
Vol 2004 (6) ◽  
pp. 447-460 ◽  
Author(s):  
N. I. Kavallaris ◽  
V. Zisis
Keyword(s):  
Integral Equation ◽  
Potential Function ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Integral Equation Method ◽  
Equation Method ◽  
Dual Integral Equation ◽  
Spherical Coordinates ◽  
Steady State Heat

Some hydromechanical systems are investigated by applying the dual integral equation method. In developing this method we suggest from elementary appropriate solutions of Laplace's equation, in the domain under consideration, the introduction of a potential function which provides useful combinations in cylindrical and spherical coordinates systems. Since the mixed boundary conditions and the form of the potential function are quite general, we obtain integral equations withmth-order Hankel kernels. We then discuss a kind of approximate practicable solutions. We note also that the method has important applications in situations which arise in the determination of the temperature distribution in steady-state heat-conduction problems.

scholarly journals On a Method in Dynamic Elasticity Problems for Heterogeneous Wedge-Shaped Medium

2021 ◽  
Vol 273 ◽  
pp. 04002
Author(s):  
Vyacheslav Berkovich ◽  
Viсtor Poltinnikov
Keyword(s):  
Integral Equation ◽  
Wave Field ◽  
Boundary Integral Equation ◽  
Integral Transform ◽  
Boundary Integral ◽  
Geometric Characteristics ◽  
Dynamic Elasticity ◽  
Elasticity Problems ◽  
Steady Oscillations ◽  
Integral Transform Technique

The method of analysis of steady oscillations arising in the piecewise homogeneous wedge-shaped medium composed by two homogeneous elastic wedges with different mechanical and geometric characteristics is presented. Method is based on the distributions’ integral transform technique and allows reconstructing the wave field in the whole medium by displacement oscillations given in the domain on the boundary of the medium. The problem in question is reduced to a boundary integral equation (BIA). Solvability problems of the BIA are examined and the structure of its solution is established.

Response of Nonlinearly Supported Spherical Boundaries to Shock Waves

1957 ◽  
Vol 24 (4) ◽  
pp. 501-505
Author(s):  
M. L. Baron
Keyword(s):  
Integral Equation ◽  
Integral Transform ◽  
Boundary Value ◽  
Acoustic Medium ◽  
Plane Shock ◽  
Linear Boundary ◽  
Influence Coefficients ◽  
Pressure Time ◽  
Elastically Supported ◽  
Integral Transform Technique

Abstract An integral transform technique is used to solve a boundary-value problem in which the partial differential equation is linear but the associated boundary condition is nonlinear. A spherical cavity in an infinite acoustic medium has an elastically supported boundary such that the pressure-displacement relation on the boundary is nonlinear. The response of the boundary to a plane shock wave which progresses across the cavity and envelops it is obtained by solving two auxiliary boundary-value problems with linear boundary conditions. Using influence coefficients obtained from these solutions, a nonlinear integral equation for the response of the actual boundary is obtained. The integral equation is solved numerically for a set of parameters, and curves for the pressure-time and displacement-time responses of the boundary are presented.

Axisymmetric Singular Stresses in a Thick-Walled Spherical Shell With an Internal Edge Crack

1983 ◽  
Vol 50 (1) ◽  
pp. 37-42 ◽  
Author(s):  
A. Atsumi ◽  
Y. Shindo
Keyword(s):  
Integral Equation ◽  
Spherical Shell ◽  
Edge Crack ◽  
Integral Transform ◽  
Crack Opening ◽  
Cauchy Kernel ◽  
Opening Displacement ◽  
Inner Surface ◽  
Dominant Part ◽  
Integral Transform Technique

The paper considers the elastostatic axisymmetric problem for a thick-walled spherical shell containing a circumferential edge crack on the inner surface. The ring-shaped edge crack and the inner surface of the spherical shell are subjected to internal pressure. Using an integral transform technique we obtain a singular integral equation of the first kind which has a generalized Cauchy kernel as the dominant part. The integral equation is solved numerically, and the influence of the geometrical configuration on the stress-intensity factor and the crack-opening displacement is shown graphically in detail.

Sign in / Sign up

Export Citation Format

Share Document