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.

/pdf/numerical-solution-of-saddle-point-problems-l583iob5c2.pdf

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

On practical integration of semi-discretized nonlinear equations of motion. Part 1: reasons for probable instability and improper convergence

Within this contribution the mechanical behavior of dry frictional granular material is modeled by a three-dimensional discrete element method (DEM). The DEM uses a superquadric particle geometry which allows to vary the elongation and angularity of the particles and therefore enables a better representation of real grain shapes compared to standard spherical particles. To reduce computation times an efficient parallelization scheme is developed which is based on the Verlet list concept and the sorting of particles according to their spatial position. The macroscopic mechanical behavior of the particle model is analyzed through standard triaxial tests of periodic cubical samples. A technique to accurately apply stress boundary conditions is presented in detail. Finally, the triaxial tests are used to analyze the influence of the sample size and the particle shape on the resulting stress-strain behavior.

Homogenization of Granular Material Modeled by a 3D DEM

In engineering problems like shrink fitting, deep drawing or hot rolling the effects of heat generation and heat transfer have to be considered during the process. Since many of these simulations involve contact problems with dry friction it is of interest to develop contact laws which are able to predict besides normal and tangential stresses also the amount of heat generated due to friction and the heat transfer across the contact surface.

On the Treatment of Contact Contraints within Coupled Thermomechanical Analysis

Zusammenfassung Für die langfristige Nutzung von Offshore-Windenergieanlagen ist das Verhalten von Hochleistungsbetonen unter Wasser von Bedeutung. In dieser Arbeit wird ein numerisches Simulationsmodell entwickelt, das es erlaubt, Mikrostruktursimulationen des Schädigungsverhaltens von trockenen und wassergesättigten Hochleistungsbetonen durchzuführen. Dabei spielt die Ermüdung aufgrund der zyklischen Beanspruchung der Strukturen eine wesentliche Rolle. Es zeigt sich, dass sich die numerische Prädiktion der entwickelten Simulationsmodelle mit den Ergebnissen aus Experimenten deckt und so gut für die Konstruktion von Betonstrukturen im Offshore-Bereich eingesetzt werden kann.

Wasserinduzierte Schädigungsmechanismen zyklisch beanspruchter Hochleistungsbetone/Water-induced damage mechanisms of cyclically loaded High-performance concretes

Peter Wriggers

Papers

On practical integration of semi-discretized nonlinear equations of motion. Part 1: reasons for probable instability and improper convergence

Homogenization of Granular Material Modeled by a 3D DEM

On the Treatment of Contact Contraints within Coupled Thermomechanical Analysis

Wasserinduzierte Schädigungsmechanismen zyklisch beanspruchter Hochleistungsbetone/Water-induced damage mechanisms of cyclically loaded High-performance concretes

Contact Modeling for Solids and Particles