The main objective of the presented study is an evaluation of the effectiveness of various methods for estimating statistics of rotor-shaft vibration responses. The computational effectiveness as well as the
accuracy of statistical moment estimation are essential for efficient robust design optimization of the rotor-shaft systems. The compared methods include sampling techniques, the perturbation approach, the
dimension reduction method and the polynomial chaos expansion method. For comparison, two problems of the rotor-shaft vibration analysis are considered: a typical single-span rotor-shaft of the eight-stage
centrifugal compressor driven by the electric motor and a large multi-bearing rotor-shaft system of the steam turbo-generator. The most important reason for the observed scatter of the rotor-shaft vibration
responses is the inherently random nature of residual unbalances as well as stiffness and damping properties of the journal bearings. A proper representation of these uncertain parameters leads to multidimensional
stochastic models. It was found that methods that provide a satisfactory balance between the estimation accuracy and computational effectiveness are sampling techniques. On the other hand, methods based
on Taylor series expansion in most of the analyzed cases fail to approximate the rotor-shaft response statistics.

*Keywords:* stochastic moment estimation, Latin hypercube sampling, polynomial chaos expansion, rotor-
shaft system, lateral vibration analysis.

Markus Kraus, Paul Steinmann. Finite element formulations for 3D convex polyhedra in nonlinear continuum mechanics. CAMES 2012 (19)

In this paper, we present finite element formulations for general three-dimensional convex polyhedra for use
in a common finite element framework that are well suited, e.g., for modeling complex granular materials
and for mesh refinements. Based on an universally applicable interpolant for any convex polyhedron,
different interpolation schemes are investigated in the context of nonlinear elastostatics.
The modeling benefits and the numerical performance regarding the mechanical response and the
computational cost are analyzed by several examples.

*Keywords:* nonlinear finite elements, polyhedral elements, 3D interpolation, finite elasticity.

Caroline Vanmaele, Karel Vergote, Dirk Vandepitte, Wim Desmet. Simulation of in-plane vibrations of 2D structural solids with singularities using an efficient wave based prediction technique. CAMES 2012 (19)

This paper proposes the wave based method for the steady-state dynamic analysis of the in-plane behaviour
of 2D structural solids. This novel prediction technique relaxes the frequency limitations of the commonly
used finite element method through an improved computational efficiency. This efficiency is obtained by
selecting basis functions which satisfy the governing equations a priori, in accordance with the indirect
Trefftz approach. Special attention is paid to problems in which singularities appear in the problem
solution. For these problems, the conventional set of basis functions is extended with functions which can
represent the singularity accurately. The capabilities of this novel method for mid-frequency applications,
as compared to the standard finite element method, are demonstrated by means of two numerical examples.

*Keywords:* structural dynamics, wave based method, indirect Trefftz method, plate membrane, stress
singularities, corner functions.

Etienne Vergnault, Olivier Allix, Serge Maison-le-Poëc. A mixed, scalable domain decomposition method for incompressible flow. CAMES 2012 (19)

This work deals with the construction of a mixed and extensible domain decomposition method for incompressible
flows. In the scheme proposed here, the solution is sought at the intersection of two spaces, one
containing the solution of the Navier-Stokes equations considered separately in each subdomain, and the
other one containing the solutions of the compatibility equations on the interfaces. A solution verifying all
the equations of the two spaces is achieved iteratively. One difficulty is that the interface problem is large
and dense. In order to reduce its cost while maintaining the extensibility of the method, we defined an
interface macroproblem in terms of a few interface macro unknowns. The best option takes advantage of
the incompressibility condition to prescribe an interface macroproblem which propagates the information
to the whole domain by making use of only two unknowns per interface. Several examples are used to
illustrate the main properties of the method.

*Keywords:* Navier-Stokes, Domain Decomposition Method, Multiscale Method.

ECCOMAS. 2013/2014- Announcements. CAMES 2012 (19)

IACM. 2013- Announcements. CAMES 2012 (19)

CISM. 2013- Announcements. CAMES 2012 (19)