Development of a three-dimensional analytical method based on a boundary element approach for a thermal shock in the first wall of a fusion reactor

In order to analyze a thermal shock phenomenon which occurs in fusion reactor components, a three-dimensional elasto-dynamic calculational method has been developed, based on a boundary element approach. The calculational basis is Navier's equation which includes a thermal expansion term. The temperature distribution in the structure is calculated by an unsteady heat conduction equation. Navier's equation is discretized by using Kelvin's fundamental solution. In this case, a domain integral still remains in the acceleration term. This domain integral term is transformed to a boundary integral form by introducing an arbitrary function of the distance between the observation and source points. A general analytical boundary integration form of this term for the three-dimensional case is obtained, when the arbitrary function is approximated by a polynomial series of the distance between the observation and source points.Verification of the method was made on the longitudinal oscillation of a square column, when a sudden compression load was applied to the top surface. The solutions for displacement and frequency in the time domain agreed with the theoretical ones within 5%. The present method was also applied to the thermal shock problem of the first wall in which a surface is suddenly heated in contact with the plasma.