Nonlinear finite element analysis of solids and structures by M.A. Crisfield

A quadratic manifold for model order reduction of nonlinear structural dynamics

This paper aims at reviewing nonlinear methods for model order reduction in structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear-based techniques by their use of a nonlinear mapping instead of adding new vectors to enlarge the projection basis. Invariant manifolds have been first introduced in vibration theory within the context of nonlinear normal modes and have been initially computed from the modal basis, using either a graph representation or a normal form approach to compute mappings and reduced dynamics. These developments are first recalled following a historical perspective, where the main applications were first oriented toward structural models that can be expressed thanks to partial differential equations. They are then replaced in the more general context of the parametrisation of invariant manifold that allows unifying the approaches. Then, the specific case of structures discretised with the finite element method is addressed. Implicit condensation, giving rise to a projection onto a stress manifold, and modal derivatives, used in the framework of the quadratic manifold, are first reviewed. Finally, recent developments allowing direct computation of reduced-order models relying on invariant manifolds theory are detailed. Applicative examples are shown and the extension of the methods to deal with further complications are reviewed. Finally, open problems and future directions are highlighted.

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Exact nonlinear model reduction for a von Kármán beam: Slow-fast decomposition and spectral submanifolds

Generalization of quadratic manifolds for reduced order modeling of nonlinear structural dynamics

A lean and efficient snapshot generation technique for the Hyper-Reduction of nonlinear structural dynamics

Model order reduction using an adaptive basis for geometrically nonlinear structural dynamics

Investigations on gas-liquid flows in horizontal pipes are of immanent importance for Reactor Safety Research. In case of a breakage of the main cooling circuit of a Pressurized Water Reactor (PWR), the pressure losses of the gas-liquid flow significantly govern the loss of coolant rate. The flow regime is largely determined by liquid and gas superficial velocities and contains slug flow that causes high-pressure pulsations to the infrastructure of the main cooling circuit.Experimental and numerical investigations on adiabatic slug flow of a water-air system were carried out in a horizontal pipe of about 10 m length and 54 mm diameter at atmospheric pressure and room temperature. Stereoscopic high-speed Particle Image Velocimetry in combination with Laser Induced Fluorescence was successfully applied on round pipe geometry to determine instantaneous three-dimensional water velocity fields of slug flows.After grid independence studies, numerical simulations were run with the open-source CFD program OpenFOAM. The solver uses the VOF method (Volume of Fluid) with phase-fraction interface capturing approach based on interface compression. It provides mesh refinement at the interfacial area to improve resolution of the interface between the two phases. Furthermore, standard k-e turbulence model was applied in an unsteady Reynolds averaged Navier Stokes (URANS) model to resolve self-induced slug formation.The aim of this work is to present the feasibility of both relatively novel possibilities of determining two-phase slug flows in pipes. Experimental and numerical results allow the comparison of the slug initiation and expansion process with respect to their axial velocities and cross-sectional void fractions.Copyright © 2012 by ASME

Johannes B. Rutzmoser

Papers

A quadratic manifold for model order reduction of nonlinear structural dynamics

Generalization of quadratic manifolds for reduced order modeling of nonlinear structural dynamics

A lean and efficient snapshot generation technique for the Hyper-Reduction of nonlinear structural dynamics

Model order reduction using an adaptive basis for geometrically nonlinear structural dynamics

Investigations on Slug Flow in a Horizontal Pipe Using Stereoscopic Particle Image Velocimetry and CFD Simulation With Volume of Fluid Method