×

Distribution of stresses in a heated nonhomogeneous rod. (English) Zbl 0612.73007

The present paper is devoted to the study of the distribution of stress, displacement and temperature in an elasic inhomogeneous semi-infinite rod, one end of which is heated non-uniformly for a finite interval of time. Three types of temperature functions viz. (i) linear, (ii) periodic and (iii) exponential are considered. The elastic moduli and the density are considered to be functions of position. The modified heat conduction equation has been used. The problem is treated by using Laplace transforms. Since it is not possible to obtain a closed form solution, Laplace inversion is carried out by using short time range approximations and by using the complex inversion formula.

MSC:

74F05 Thermal effects in solid mechanics
74G70 Stress concentrations, singularities in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74E05 Inhomogeneity in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
35A22 Transform methods (e.g., integral transforms) applied to PDEs
PDFBibTeX XMLCite