Suddenly heated sphere

The transient 3D problem of a sphere suddenly heated at its surface is further considered (Park & Banerjee, 2002). The sphere has unit radius and initial null temperature, while its surface is free from tractions. At t = 0 the surface is set to T = 1 and this temperature is kept fixed.

Physical properties are: ρ = 1, E = 1, ν = 0.3, α = 0.02, k = 1, and c = 1.

The sphere is resolved with a mesh of 0.05 average element size. The time step is 0.01.

Results on temperature, deformations and stress are depicted in the following Figures.

Reference

Park, K.-H., & Banerjee, P. (2002). Two- and three-dimensional transient thermoelastic analysis by bem via particular integrals.
International Journal of Solids and Structures, 39 (10), 2871-2892.