Dual reciprocity BEM for time-stepping approach to the transient heat conduction problem in nonlinear materials

• Published in: Computer methods in applied mechanics and engineering Vol. 195; no. 37; pp. 4953 - 4961
• Main Authors: Tanaka, Masataka, Matsumoto, Toshiro, Takakuwa, Susumu
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2006; Elsevier
• Subjects: Computational mechanics; Computational techniques; Dual reciprocity method; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat conduction; Heat transfer; Mathematical methods in physics; Physics; Temperature-dependent material; Time-stepping boundary element method; Transient heat conduction; Computational mechanics; Dual reciprocity method; Temperature-dependent material; Time-stepping boundary element method; Transient heat conduction; Temperature- dependent material; Transient response; Laplace equations; Non linear material; Step method; Boundary integral method; Duality; Homogeneous material; Integral transformations; Radial basis function; Temperature effects; Integral equations; Meshless method; Reciprocity theorem; Modelling; Boundary element method; Heat transfer; Thermal conduction
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2005.04.025

This paper presents a dual reciprocity boundary element method (DRBEM) applied to the transient heat conduction problem in temperature-dependent materials. The integral equation formulation employs the fundamental solution of the Laplace equation for homogeneous materials, and hence 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 in the governing differential equation is approximated by the time-stepping method, and the domain integral also appears from this approximation. The domain integral corresponding to the so-called “pseudo initial condition” at each time step is also transformed into boundary integrals 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 results by a finite difference scheme, the usefulness of the present DRBEM is demonstrated.