An all-speed relaxation scheme for interface ows with surface tension
We consider interface ows where compressibility and capillary forces (surface tension) are signi-cant. These ows are described by a non-conservative, unconditionally hyperbolic multiphasemodel. The numerical approximation is based on nite-volume method for unstructured grids. At the discrete level, the surface tension is approximated by a volume force (CSF formulation). The interface physical properties are recovered by designing an appropriate linearized Riemann solver (Relaxation scheme) that prevents spurious oscillations near material interfaces. For low-speed ows, a preconditioning linearization is proposed and the low Mach asymptotic is formally recovered. Numerical computations, for a bubble equilibrium, converge to the required Laplace law and the dynamic of a drop, falling under gravity, is in agreement with experimental observations.
Journal of Computational Physics, no 228, pp. 5722-{5739, 2009
Benjamin BRACONNIER and Boniface NKONGA
On reliable triangular MITC6 shell elements
In engeneering practice we often deal with shell structures of complex geometry which forcely incorporate triangular elements when being meshed. Therefore, e ective triangular shell elements (namely locking free and consistent) are of utmost interest. The membrane locking is the main obstacle when developing e ective general shell nite elements that are supposed to well circumvent this problem without loss of consistency for membrane dominated shell problems. The MITC technique constitutes a good locking cure and it has already been implemented as a successful locking removal tool for quadrangular plate/shell nite elements, but spurious membrane modes may arise in membrane dominated shell problems. A numerical patch-test aimed at detecting membrane locking and the existence of membrane spuirous modes when designing MITC shell nite elements is presented. The MITC6a element (formulated by Bathe and Lee) seems to be one of the best candidates of the MITC6 family, but it features some non-physical displacement modes with vanishing membrane strain energy that might considerably deteriorate the numerical solution. We propose a remedy based on a stabilized bilinear form by adding an unreduced shear term. In view
of a detailed assessment, we advocate the use of some stabilization in the MITC6a formulation for engeneering practice.
Proceeding : Contribution for the International Conference on Mathematics and Continuum Mechanics (ICMCM) 2008, Porto (Portugal)
Iria PARIS SUAREZ
Detailed reliability assessment of triangular MITC elements for thin shells.
Effective shell finite elements are of utmost interest in engineering practice, and more particularly triangular shell elements are often needed to handle complex geometries. The quadrilateral elements of the MITC family have been shown to be effective for general asymptotic behaviors, but a triangular MITC shell finite element of comparable performance remains to be found. The main difficulty is to reduce the locking phenomenon arising in bending dominated situations without destroying the ability of the procedure to accurately capture membrane dominated and mixed behaviors. In this context, we have designed a simple numerical rank test aimed at assessing the reliability of MITC triangular elements. This test led to selecting some specific MITC6 tying schemes, which have been further assessed using some meaningful test problems. The assessment results showed that the MITC6a shell element is a most promising candidate, although it may feature some non-physical membrane spurious modes in some specific shell problems. !
2008 Elsevier Ltd. All rights reserved.
Keywords: Shells, Triangular MITC elements, Spurious modes, Numerical locking, Mixed formulations
Computers and Structures, 86 (2008) 2192–2202
journal homepage: www.elsevier.com/locate/compstruc
- D. Chapelle, INRIA, MACS Team, Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France
- I. Paris Suarez, Glaizer Group, 32 Rue Guy Môquet, 92240 Malakoff, France
The singularity expansion method applied to the transient motions of a oating elastic plate
In this paper we propose an original approach for the simulation of the time-dependent response of a oating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles of the analytic continuation called resonances of the system, and a low frequency component associated to a branch point at frequency zero.We present the mathematical analysis of this method
for the two-dimensional sea-keeping problem of a thin elastic plate (ice oe, oating runway, . . . )and provide some numerical results to illustrate and discuss its efficiency.
Revue : M2AN, vol 41, no 5, pp. 925-943, 2007.
Christophe HAZARD and Françcois LORET