https://hal.archives-ouvertes.fr/hal-01513346/document

Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement

Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

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Numerical solution of saddle point problems

Introduction to linear and nonlinear programming

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

This paper describes modern techniques used to solve contact problems within Computational Mechanics. On the basis of a continuum description of contact, the mathematical structure of the contact formulation for finite element methods is derived. Emphasis is also placed on the constitutive behavior at the contact interface for normal and tangential (frictional) contact. Furthermore, different discretization schemes currently applied to solve engineering problems are formulated for small and finite strain problems. These include isoparametric interpolations, node-to-segment discretizations and also mortar and Nitsche techniques. Furthermore, several algorithms related to spatial contact search and fulfillment of the inequality constraints at the contact interface are discussed. Here, especially the penalty and Lagrange multiplier schemes are considered and also SQP- and linear-programming methods are reviewed.


Keywords:

contact mechanics;
friction;
penalty method;
Lagrange multiplier method;
contact algorithms;
finite element method;
finite deformations;
discretization methods

Computational Contact Mechanics

Realistic modeling of 3D fragmentation procedures with minimal incorporation of restrictions to the crack path is still a challenge in modern computational engineering simulations. The presented approach is used to model failure and cracking in concrete structures, applying an explicit finite element integration scheme. Within this model the Strong Discontinuity Approach (SDA) is used to handle the failure process until the material is fully damaged. At stage an adaptive refinement technique is incorporated in ordner to introduce real cracks which are suitable for DEM / FEM coupling or contact formulations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

One fragmentation procedure for brittle material cracking

A finite deformation homogenization framework is developed to predict the macroscopic thermal response of contact interfaces between rough surface topographies. The overall homogenization framework transfers macroscopic contact variables such as surfacial stretch, pressure and heat flux as boundary conditions on a test sample within a micromechanical interface testing procedure. An analysis of the thermal dissipation within the test sample reveals a thermodynamically consistent identification for the macroscopic thermal contact conductance parameter that enables the solution of a homogenized thermomechanical contact boundary value problem based on standard computational approaches. The homogenized contact response effectively predicts a temperature jump across the macroscale contact interface.

Finite Deformation Thermomechanical Contact Homogenization Framework

Bei zahlreichen Bauteilen sind die Abmessungen der Querschnitte klein gegen die Lange. Sie konnen dann naherungsweise als linienhafte Korper betrachtet werden. Zwei solcher Tragwerke haben wir schon kennengelernt, namlich Stabe (gerade Achse, Last in Richtung der Stabachse, vgl. Band 1, Kap. 6) und Balken (gerade Achse, Last senkrecht zur Balkenachse, vgl. Band 1, Kap. 7). Weitere Linientragwerke sind Seile (gekrummte Achse, nehmen nur Zugkrafte auf) und Bogen (gekrummte Achse, Last beliebig). Daruber hinaus gibt es flachenformige Tragwerke, bei denen die Dicke klein ist gegenuber den Abmessungen in der Flache. Nach der Art der Belastung und der Geometrie solcher Flachentragwerke unterscheidet man Scheiben (ebene Mittelflache, Last in der Mittelflache, vgl. Abschnitt 2.5), Platten (ebene Mittelflache, Last senkrecht zur Mittelflache) und Schalen (gekrummte Mittelflache, Last beliebig). Bei den genannten Tragwerken konnen die Spannungszustande in guter Naherung bei Linientragwerken auf eindimensionale, bei Flachentragwerken auf zweidimensionale Probleme zuruckgefuhrt werden. In diesem Kapitel werden wir zeigen, wie man bei den verschiedenen Tragwerken vorgeht und durch welche Beziehungen die bei ihnen auftretenden Spannungen und Verformungen beschrieben werden.

Statik spezieller Tragwerke

Computational chemo-mechano-biological remodelling of arterial tissue constituents

Mooring systems of offshore wind turbines have to be designed to resist cyclic tension and bending. In order to take into account bending for the computation of the fatigue damage, local phenomena of fretting have to be properly predicted by means of a new numerical model.

Toward a two-scale modeling of spiral strand wire rope for floating offshore wind turbine topredict fatigue damage: possibilities and difficulties in using a legacy code

Peter Wriggers

Papers

One fragmentation procedure for brittle material cracking

Finite Deformation Thermomechanical Contact Homogenization Framework

Statik spezieller Tragwerke

Computational chemo-mechano-biological remodelling of arterial tissue constituents

Toward a two-scale modeling of spiral strand wire rope for floating offshore wind turbine topredict fatigue damage: possibilities and difficulties in using a legacy code