STATE-SPACE APPROACH ON GENERALIZED
THERMOELASTICITY FOR AN INFINITE
MATERIAL WITH A SPHERICAL CAVITY AND
VARIABLE THERMAL CONDUCTIVITY
SUBJECTED TO RAMP-TYPE HEATING

H. M. YOUSSEF

Abstract. The present paper is concerned with a homo-geneous and isotropic unbounded body with a spherical cavity subjected to ramp-type heating. The Lord and Shulman model of thermoelasticity is employed with variable thermal conductivity. The closed form solutions for distributions of displacement, temperature, strain and stresses are obtained by using the Laplace transform and the state-space approach. Numerical results applicable to a copper-like material are also presented graphically and the nature of variations of the physical quantities with radial coordinate and with the thermal conductivity.