Different solution strategies to the relaxed Saint-Venant problem are presented and comparatively discussed from a mechanical and computational point of view. Three approaches are considered; namely, the displacement approach, the mixed approach, and the modified potential stress approach. The different solution strategies lead to the formulation of two-dimensional Neumann and Dirichlet boundary-value problems. Several solution strategies are discussed in general, namely, the series approach, the reformulation of the boundary-value problems for the Laplace's equations as integral boundary equations, and the finite-element approach. In particular, the signatures of the finite-element weak solutions-the computational costs, the convergence, the accuracy-are discussed considering elastic cylinders whose cross sections are represented by piece-wise smooth domains. (c) 2006 Elsevier B.V. All rights reserved.
On solution strategies to Saint-Venant problem / Lacarbonara, Walter; Paolone, Achille. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - STAMPA. - 206:1(2007), pp. 473-497. [10.1016/j.cam.2006.08.008]
On solution strategies to Saint-Venant problem
LACARBONARA, Walter;PAOLONE, ACHILLE
2007
Abstract
Different solution strategies to the relaxed Saint-Venant problem are presented and comparatively discussed from a mechanical and computational point of view. Three approaches are considered; namely, the displacement approach, the mixed approach, and the modified potential stress approach. The different solution strategies lead to the formulation of two-dimensional Neumann and Dirichlet boundary-value problems. Several solution strategies are discussed in general, namely, the series approach, the reformulation of the boundary-value problems for the Laplace's equations as integral boundary equations, and the finite-element approach. In particular, the signatures of the finite-element weak solutions-the computational costs, the convergence, the accuracy-are discussed considering elastic cylinders whose cross sections are represented by piece-wise smooth domains. (c) 2006 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.