BOUNDARY ELEMENT FORMULATION TO ANALYZE TORSION PROBLEMS IN GENERIC COMPOSITE BARS
Palavras-chave:
Torsion problems, bars with generic composite cross-sections, generic subregioning technique, numerical quadratures for singular and nearly-singular integralsResumo
This paper applies the boundary-element subregion-by-subregion (BE SBS) technique to
solve torsion problems in general composite bars. One presents details of the BE formulation for primary
torsion in coupled domains, including the discussion on the Krylov solvers embedded in the coupling
algorithm. The general principles involved in the derivation of the preconditioned Krylov solvers are
presented, although particular emphasis will be given in the applications to the short-recurrence methods
as the BiCG (biconjugate gradient) and BiCGSTAB(l) (l-dimensional biconjugate gradient stabilized)
solvers. Discontinuous boundary elements, essential to alleviate the modeling process of coupled
domains, are also developed. In this respect, efficient (low-order) quadratures for integrating singular
and nearly-singular fundamental kernels over the boundary elements are proposed. In addition, in order
to accelerate the iterative solution process, the BE SBS matrix structure is used to form an efficient
sparse incomplete LU factorization (SILU) preconditioner. Bars with complex composite patterns (e.g.
with many different materials) are analyzed to attest the efficiency and robustness of the whole
boundary-element technique.
