Mathematical Modeling of Dynamical Stress Field Problem for a Pre-stressed Bi-layered Plate-Strip

2014 ◽  
Vol 38 (2) ◽  
pp. 733-760 ◽  
Author(s):  
Ahmet Daşdemir ◽  
Mustafa Eröz
Keyword(s):  
Mathematical Modeling ◽  
Stress Field ◽  
Layered Plate ◽  
Field Problem ◽  
Plate Strip ◽  
Dynamical Stress

Dynamic response of a pre-stressed bi-layered plate-strip subjected to an arbitrary inclined time-harmonic force

2017 ◽  
Vol 26 (3) ◽  
pp. 255-262
Author(s):  
AHMET DASDEMIR ◽  
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Layered Plate ◽  
Field Problem ◽  
Time Harmonic ◽  
Governing System ◽  
Plate Strip ◽  
Linearized Theory ◽  
Complete Contact

Within the scope of the piecewise homogeneous body model with utilizing of the three dimensional linearized theory of elastic waves in initially stressed bodies the dynamical stress field problem in a bi-layered plate-strip with initial stress under the action of an arbitrary inclined timeharmonic force resting on a rigid foundation is investigated. The concrete materials such as a pair of Aluminum and Steel are selected. It is assumed that there exists a complete contact interaction between the layers. The mathematical modeling of the problem under consideration is carved out, and the governing system of the partial differential equations of motion is approximately solved by employing Finite Element Method. The numerical results related to the influence of certain parameters on the dynamic response of the plate-strip are presented.

Transient Response of an Interface-Crack in a Layered Plate

1986 ◽  
Vol 53 (3) ◽  
pp. 579-586 ◽  
Author(s):  
T. Kundu
Keyword(s):  
Stress Field ◽  
Interface Crack ◽  
Transient Response ◽  
Singular Integrals ◽  
Fortran Program ◽  
Numerical Results ◽  
New Method ◽  
Layered Plate ◽  
Improved Method ◽  
Sample Problem

In this paper, the transient response of an interface crack, in a two layered plate subjected to an antiplane stress field, is analytically computed. The problem is formulated in terms of semi-infinite integrals following the technique developed by Neerhoff (1979). It has been shown that the major steps of Neerhoff’s technique, which was originally developed for layered half-spaces, can also be applied to layered plate problems. An improved method for manipulation of semi-infinite singular integrals is also presented here. Finally, the new method is coded in FORTRAN program and numerical results for a sample problem are presented.

Extrusion of Polymer Melts and Melt Flow Instabilities. III. Theoretical Analysis of Extrusion through a Slit Die

1969 ◽  
Vol 42 (3) ◽  
pp. 691-699 ◽  
Author(s):  
James L. White
Keyword(s):  
Reynolds Number ◽  
Stress Field ◽  
Viscoelastic Fluid ◽  
Polymer Melts ◽  
Second Order ◽  
Secondary Flows ◽  
Newtonian Fluids ◽  
Creeping Flow ◽  
Flow Instabilities ◽  
Field Problem

Abstract In the previous sections of this paper we have discussed our own and other experimental studies of flow instabilities in the extrusion of polymer melts as well as various theories of the mechanism of initiation of the instability. It is our belief that one of the keys to a deeper understanding of this phenomenon is a fuller analytical understanding of the stress and velocity fields in the composite reservoir, capillary, and extrudate system. It is to this problem that we turn our attention here. The velocity, stress-field problem in the entrance region of a conduit being fed from a reservoir has received considerable attention for Newtonian fluids. Most authors have followed Schlichting and Goldstein in using boundary-layer theory to analyze this problem. While there are a number of such solutions for viscous non-Newtonian and viscoelastic fluids, they are of little interest for polymer melts. This is not only because they represent a high Reynolds number, inertia-dominated asymptote but because they neglect all phenomena occurring in the reservoir feeding the conduit. Of more interest are the low Reynolds number creeping flow solutions for Newtonian fluids which are based upon the work of Sampson (see also Roscoe and Weissberg). A decade ago Tomita published a pioneering analysis of the creeping flow of a viscous non-Newtonian (power-law) fluid into a sharp edge entrance of a capillary. More recently LaNieve and Bogue have analyzed the creeping flow of a Coleman-Noll second order into the capillary entrance. A recent study of the entry problem has been made by Metzner, Uebler, and Chan Man Fong. The related problem of creeping flow of a viscoelastic fluid in a converging channel or cone has been analyzed by Adams, Whitehead, and Bogue and Kaloni. While the former authors computed the stress field for a second-order fluid and an integral constitutive equation in a presumed velocity field, Kaloni actually evaluated velocity profiles and predicted the formation of secondary flows. A more intuitive, but far less rigorous approach to extrusion of a viscoelastic fluid has been taken by Dexter and Dienes and Smith. These authors presume a virgin material to enter a capillary die in fully developed flow and utilize the theory of linear viscoelasticity to evaluate the stress field.

scholarly journals Effect of Initial Stress on the Dynamic Response of a Multi-Layered Plate-Strip Subjected to an Arbitrary Inclined Time-Harmonic Force

2017 ◽  
Vol 22 (3) ◽  
pp. 521-537 ◽  
Author(s):  
A. Daşdemir
Keyword(s):  
Dynamic Response ◽  
Initial Stress ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Layered Plate ◽  
Harmonic Force ◽  
Time Harmonic ◽  
Governing System ◽  
Plate Strip ◽  
Complete Contact

AbstractThe forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

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