Using fredholm integral equation of the second kind to solve the vertical vibration of elastic plate on an elastic half space

1998 ◽  
Vol 19 (2) ◽  
pp. 157-162
Author(s):  
Jin Bo
Keyword(s):  
Integral Equation ◽  
Half Space ◽  
Elastic Plate ◽  
Fredholm Integral Equation ◽  
Elastic Half Space ◽  
Vertical Vibration

scholarly journals The ring delamination between bodies under the action of heat sinks distributed along a circle

2017 ◽  
pp. 55-62
Author(s):  
Maryana Mykytyn ◽  
Kristina Serednytska ◽  
Bohdan Monastyrskyy ◽  
Rostyslav Martynyak
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Half Space ◽  
Singular Integral ◽  
Elastic Half Space ◽  
Heat Sinks ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Normal Contact ◽  
Frictionless Contact

The frictionless contact an elastic half-space and a rigid thermo-insulated base with a local delamination between them on a ring domain under the action of heat sinks distributed uniformly along a circle and located in the half-space some distance away from its surface, is considered. The corresponding contact thermos-elasticity problem is reduced to a singular integral equation for a height of a ring gap. The solution of the singular integral equation and the internal and external radius of the ring are numerically determined using the method of collocation and the method of successive approximations. The dependence of the form of gap and normal contact stresses on the distance between the heat sinks and the surface of the half-space and the intensity of the heat sink are analyzed.

Stresses in a Thin Piezoelectric Element Bonded to a Half-Space

1997 ◽  
Vol 50 (11S) ◽  
pp. S204-S209 ◽  
Author(s):  
Wolfgang E. Seemann
Keyword(s):  
Integral Equation ◽  
Shear Stress ◽  
Half Space ◽  
Piezoelectric Element ◽  
Elastic Half Space ◽  
Bonding Layer ◽  
Rigid Substrate ◽  
Stress Concentrations ◽  
Piezoceramic Element

In this paper, a thin piezoceramic element is considered which is bonded to an elastic or a rigid half-space. Such a model may be an approximation of the interaction between piezoceramic elements and elastic structures like beams and plates. For an elastic half-space, the determination of the shear stress in the bonding layer leads to a singular integral equation. A half-space which is very stiff may be modeled as a rigid substrate. For this case, displacement functions are introduced. Hamilton’s principle for electromechanical systems allows the use of Lagrange multipliers to incorporate the condition of a stress free upper surface of the piezoceramic element. The stresses in the bonding layer and in the piezoceramic element are estimated by this method and compared with Finite Element results. Though the singularity near the ends of the piezoceramic element cannot be modeled by both methods, stress concentrations can clearly be seen for the shear stress as well as for the normal stress. As infinite stresses due to the singularity do not occur in reality, the results allow an estimation of the bonding stresses except in the near vicinity of the edges. The knowledge of these stresses is important to prevent failure due to delamination.

Sign in / Sign up

Export Citation Format

Share Document