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

The paper proposes a boundary element method (BEM) for analysis of tra nsient heat conduction problems in orthotropic bodies. A time derivati ve in the governing equation is approximated by the time-stepping sche me. The reduced differential equation is transformed into a regularise d boundary integral equation which involves no integrals to be evaluat ed in the Cauchy principal-value sense. Although the formulation is pr esented for two-dimensional problems, it is also applicable to three-d imensional problems if the three-dimensional fundamental solution is u sed. A new computer program is developed and applied to several exampl e problems. The computational aspects of the proposed time-stepping BE M are investigated first for the case where the principal axes of orth otropy coincide with the coordinates, and then for the other more gene ral cases. It is concluded that there is a suitable time-step and a su itable element size for each problem to be investigated, and that the optimal computational conditions for an arbitrary case can be estimate d from the numerical results obtained for some of the sample problems for which the exact solutions are known.