IOSR Journal of Mathematics (IOSRJM) ISSN: 2278-5728 Volume 2, Issue 1 (July-Aug 2012), PP 46-54 www.iosrjournals.org www.iosrjournals.org 46 | Page Strees Analysis in Elastic Half Space Due To a Thermoelastic Strain Ayaz Ahmad Department of Mathematics NIT Patna Bihar India 800005 Abstract: The stress distribution on elastic space due to nuclei of thermo elastic strain distributed uniformly on the circumference of a circle of radius R situated in the place z= λ of the elastic semi space of Hookean model has been discussed by Nowacki: The Force stress and couple stress have been determined . The fore stress reduces to the one obtained by Nowacki for classical elasticity. I. Introduction: Analysis of stress distribution in elastic space due to nuclei of thermoelastic strain distributed uniformly on the circumference of a circle of radius r situated in the plane Z = h of the elastic semi space of Hookean model has been discussed by Nowacki. This note is an extension of the analysis of above problem for micropolar elastic semi-space. Force stress  ji and couple stress  ji have been determined due to presence of nuclei of thermoelastic strain situated in the place Z = h inside the semi space. The force stress reduces to the one obtained by Nowascki for classical elasticity. II. Basic Equations: We consider a homogenous isotropic elastic material occupying the sami infinite region Z  O in cylindrical polar coordinate system (r, , Z). It has been shown by Nowacki [64] that is in the case when the 2 macrodisplacement vector u  and microrotation w  depend only on r and z the basic equations of equilibrium of micro-polar theory of elasticity are decomposed into two mutually independent sets. Here we shall be concerned with the set u  = (u r , O, u z ) and the rotation vector w  = (O,   ,O): 2 1 ( )( ) ( ) 2 2 r r e T u r z r                       2 1 ( )( ( ) 2. ( ) z u e T r r r r z                       …..(6.1) 2 1 ( )( 2 ( ) 4 0 2 r z r u u z r                  Where e = 1 ( ) z r u r r r z        2 = 2 2 1 r r z r     = (3λ + 2)  t u r , u z = displacement components   = Component of rotation vector λ, , , ,  = elastic constants T (r, z) = temperature distribution  t = coefficient of thermal expansion.