A TIME-STEPPING BOUNDARY-ELEMENT METHOD FOR TRANSIENT HEAT-CONDUCTION IN ORTHOTROPIC BODIES

The paper proposes a boundary element method (BEM) for analysis of transient heat conduction problems in orthotropic bodies. A time derivative in the governing equation is approximated by the time-stepping scheme. The reduced differential equation is transformed into a regularised boundary integral equation which involves no integrals to be evaluated in the Cauchy principal-value sense. Although the formulation is presented for two-dimensional problems, it is also applicable to three-dimensional problems if the three-dimensional fundamental solution is used. A new computer program is developed and applied to several example problems. The computational aspects of the proposed time-stepping BEM are investigated first for the case where the principal axes of orthotropy coincide with the coordinates, and then for the other more general cases. It is concluded that there is a suitable time-step and a suitable element size for each problem to be investigated, and that the optimal computational conditions for an arbitrary case can be estimated from the numerical results obtained for some of the sample problems for which the exact solutions are known.