321 非定常熱伝導問題の時間ステップ BEM への二重相反法の適用 : 3 次元問題の検討

Abstract

This paper presents a dual reciprocity boundary element method (DRBEM) applied to the transient heat conduction problem of functionally graded materials. The functionally graded material can be modeled as an inhomogeneous one where the thermal conductivity is a continuous function of coordinates. The integral equation formulation employs the fundamental solution of the Laplace equation for homogeneous materials, and hence from the inhomogeneous part of the governing differential equation a domain integral arises in the boundary integral equation. This domain integral is transformed into boundary integrals by using a new set of radial basis functions. Furthermore, time derivative is approximated by the time-stepping method, and the domain integral also appears from this approximation. The domain integral concerning the "pseudo" initial condition at each time step is also transformed into a boundary integral via the same dual reciprocity method. The details of the proposed DRBEM are presented, and a computer code is developed for three-dimensional problems. Through comparison of the results obtained by the computer code with the result of collocation method, the usefulness of the present DRBEM is demonstrated.