244 - PPGMNE - Universidade Federal do Paraná

ABSTRACT
Together with the development of engineering, also the methods for solving
problems related to that applied science presented a remarkable development during the last
decades. Due to the difficulty of obtaining analytical solutions to the differential equations
that govern the physical problems, the numerical methods were developed in order to
overtake such a difficulty. Among them, the Boundary Element Method has demonstrated to
be very effective in solving many problems in the field of engineering. In this work, a BEM
formulation was developed to the solution of heat conduction problems in one-dimensional
problems.
Due to the use of the static fundamental solution, a domain integral, whose integrand
is equal to the product of fundamental solution with the first derivative of potential, appears in
the BEM equations. Because this integral is kept in the equation, the result formulation is
named D-BEM (D meaning domain). Beside the traditional D-BEM formulation, a new BEM
formulation, based on sub-domain weighting residuals presented. For validation of results,
four examples are presented and compared with the analytic solutions.
Computer codes in Fortran 2003, were developed for the numerical analyses.
xiv