Thermoelastic stress due to a rectangular heat source in a semi-infinite medium. Derivation of an analytical solution

摘要

The solution for a time-dependent heat source is obtained from the corresponding instantaneous heat source by a Duhamel superposition. The thermoelastic problem for the instantaneous rectangular heat source in an infinite surrounding is solved exactly. An important step is the introduction of so called quadrantal heat sources. The solution for the rectangle is obtained for four quadrantal solutions. The solution for the quadrantal heat source depends on the three dimensionless coordinates only. Time occurs in the scale factors only. The condition of zero normal and shear stresses at the ground surface is fulfilled by using a mirror heat source and a boundary solution. The boundary solution accounts for the residual normal stress at the ground surface. Using a Hertzian potential, a surprisingly simple solution is obtained. The final analytical solution is quite tractable, considering the complexity of the initial problem. The solution may be used to test numerical models for coupled thermoelastic processes. It may also be used in more detailed numerical simulations of the process near the heat sources as boundary conditions to account for the three-dimensional global process. 11 refs. (Atomindex citation 28:022165)