eng Ansari Education and Research Society Journal of Ultra Scientist of Physical Sciences April 2010 22 1 71 78 jusps-A 1029 article P.K. Mathur 1 Madhvi Gupta 1 Saifia Science College, Bhopal (M.P.) INDIA) <p style="text-align: justify;">A solution of axisymmetric Boussinesq-type problem is derived for transient thermal stresses in a half-space under heating by using the Laplace and Hankel transforms. An analytical method is developed to predict the temperature field that satisfies the prescribed mechanical conditions. Several simple shapes of punches of arbitrary profile are considered and an expression for the total load is derived to achieve penetration. The numerical results for the temperature and the total load on the punch are shown graphically.<br /> &nbsp;</p> https://www.ultrascientist.org/paper/1029/ Operational Calculus (for fractional derivatives & integrals Integral & Series Equations Classical Linear Elasticity.