International Journal of Computational Engineering ScienceVol. 02, No. 02, pp. 249-266 (2001) No AccessNUMERICAL DIFFICULTIES AT HIGH ELASTICITY FOR VISCOELASTIC FLOW PAST A CONFINED CYLINDERHUA-SHU DOU and NHAN PHAN-THIENHUA-SHU DOUSchool of Aeronautical, Mechanical & Mechatronic Engineering, The University of Sydney, NSW 2006, Australia Search for more papers by this author and NHAN PHAN-THIENDepartment of Mechanical Engineering, The National University of Singapore, Singapore 119260, Singapore Search for more papers by this author https://doi.org/10.1142/S1465876301000313Cited by:1 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThe viscoelastic flow around a circular cylinder in a channel with geometry h/R = 2 (h the channel half width, R the cylinder radius) has been simulated by a few research groups for the Oldroyd-B fluid. All encountered numerical difficulties at a Deborah number of O(1) – the cause of this problem is poorly understood. In this paper, the numerical problems encountered at high Deborah are studied, and a reasonable explanation is provided. It is concluded that the numerical difficulties in calculating the flow around a cylinder at large Deborah numbers are due to the extensional flow near the rear (and/or front) stagnation point. It is the extensional stress gradients which directly limit the simulations at high elasticity for the Oldroyd-B fluid, rather than the shear stress around the cylinder. However, the shear flow region upstream of the wake in the narrow gap between the cylinder and the channel needs to be carefully evaluated with finer mesh in order to understand the flow behaviour. FiguresReferencesRelatedDetailsCited By 1The rheology of polymer solution elastic strands in extensional flowSimon J. Haward, Jeffrey A. Odell, Zhuo Li and Xue-Feng Yuan5 May 2010 | Rheologica Acta, Vol. 49, No. 7 Recommended Vol. 02, No. 02 Metrics History PDF download

Simple engineering analysis based on stress and momentum correspondence principles and the Rayleigh quotient approximation is used to derive error convergence rates and estimates for dynamic beam models based on the Timoshenko beam theory. These predictions are verified by carrying out numerical computations.

A new thick shell element is used to study the thermoelastic behavior of functionally graded structures made from shells and plates. The element accounts for the varying elastic and thermal properties across its thickness. It also accounts for the thickness change, normal stresses and strains. The nonlinear heat transfer equations governing the through-thickness thermal distribution are treated using the Rayleigh-Ritz method. Prescribed temperatures as well as convection conditions are imposed on both faces of the shell. Three examples involving functionally graded beams, circular plates and spherical shells are examined. The effect of the volume fraction of the constituent materials and the through-thickness integration order are also investigated.