(1) Research Title:

STATIC DEFORMATION OF AN  IRREGULAR INITIALLY STRESSED MEDIUM

  Dr. M. M. Selim         Department of Natural and Applied Sciences      Al-Aflaj Community College

Period: 10 Months                                                                               Budget :  15000 SR

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Summary:

   v            Research Problem:  

     The study of static deformation is of great interest to many scientists in the last three decades due to its varied applications. Specially, in seismology, geophysics and earthquake engineering to find a logic interpretation for slow earth motion. In the previous studies, the classic theory was used. The effect of initial stresses not considered.  In fact, the Earth is   

An initially stressed medium due to many physical factors. So, it is very interesting to study the static deformation of elastic medium with irregular thickness under initial stresses case which will give new closed form expressions of stresses and displacements in the considered medium. To find the new equilibrium equations, Biot's incremental deformation theory is employed.

   v            Research Significance:

     In the present paper, an attempt will be done to apply the theory of Biot's incremental deformation to find the closed form expressions of stresses and displacements due to normal line-load acting inside an irregular to static deformation of an initially stressed elastic half-space of irregular thickness which in turn,  help geophysicists to understand the response of media at continental boundaries and mountain roots. Finally, will get new closed form expressions of stresses and displacements which can be applied on any initial stressed medium.  

   v            Research Objectives:

1- Using Biot's incremental deformation theory to find a new equilibrium 

     equations for the considered medium.

2- Deriving a new closed form expressions of displacements and

    stresses at any point of an infinite initially stressed, irregular medium

    due to a normal line load .

3- Numerical applications will be done, for particular model, to show the

   effect of irregularity and initial stresses present in the medium on the

   displacement components due to static deformation.

   v            Research Methodology:

-Abstract-an introduction including the importance of studies of static deformation for elastic medium- applying Biot's theory and deriving a new equilibrium equations taking the effect of initial stresses and irregularity into    account- numerical applications- References. 

(2) Research Title:

Reflection and Refraction of Plane Waves at Free Surface of an Initially Stressed Dissipative Medium

Dr. M. M. Selim      Department of Natural and Applied Sciences      Al-Aflaj Community College

Period: 10 Months                                                       Budget :  15000 SR

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Summary

   v            Research Problem:  

     One of the most interesting but yet interesting is the study of reflection and refraction of plane waves because of their possible application in geological and seismic prospecting. In the previous studies, the classic theory was used. The effect of initial stresses not considered.  In fact, the Earth is an initially stressed medium due to many physical factors. So, it is very interesting to study the phenomenon of reflection and refraction of plane waves under initial stresses in the dissipative medium. Anew closed form expressions of stresses and displacements in the considered medium will be obtained. To find the new dynamical equations, Biot's incremental deformation theory is employed.

   v            Research Significance:

     In the present paper, an attempt will be done to apply the theory of Biot's incremental deformation to find the effects of Initial stresses and damping on the reflection and refraction of plane wave at the free surface of the medium, which in turn, will help geophysicists to understand the phenomenon of reflection and refraction of plane waves under initial stresses in the dissipative medium. Finally, will get new closed form expressions of stresses and displacements which can be applied on any initial stressed medium.

   v            Research Objectives:

1- Using Biot's incremental deformation theory to find a new dynamical

    equations for the considered medium.

2- Deriving a new closed form expressions of displacements and stresses at

    any point of an infinite initially stressed, dissipative  medium.

3- Numerical applications will be done, for particular model, to show the

   effects of Initial  stresses and damping on the reflection and refraction of

    plane wave at the free surface of the medium.

    v            Research Methodology:

-Abstract-an introduction including the importance of studies of reflection and refraction of plane wave at the free surface of the medium - applying Biot's theory and deriving a new dynamical equations taking the effect of initial stresses and dissipation into account- numerical applications- References.