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

Summary
The production of new composite laminates with variable stiffness within the surface of plies was enabled by tow-placement machines. Because of the variation of stiffness, these materials are called variable stiffness composite laminates (VSCL). Recently, many attempts were made to investigate their structural behaviour. In this contribution, a first-order shear deformation theory is selected to model the multilayered composite laminates. The adopted theory is enhanced by the extended finite element method (XFEM) to describe discontinuities at element level of any interface of interest. To predict the location of the delamination onset, a traction–separation law is developed that is consistent with the XFEM topology. An exponential softening behaviour is implemented within the interface to model the delamination growth in a mixed-mode direction. In order to solve the non-linear equations of the delamination propagation, an arc-length method is applied. The effect of the curvilinear fibre orientation on the location of the delamination onset is investigated. Subsequently, the structural response of the laminates is computed. According to the simplicity of the new approach using the XFEM; and based on the computational cost for calculating the stiffness of VSCL, the method is able to determine structural response of VSCL with less computational effort. Copyright © 2016 John Wiley & Sons, Ltd.

Delamination growth in composite laminates of variable stiffness

A plate theory as a mean to compute precise 3D-solutions including edge effects and related (O. Allix and C. Dupleix-Courdec) A fully nonlinear thin shell model of Kirchhoff-Love type (P.M. Pimenta, E.S. Almeida Neto and E.M.B. Campello) A beam finite element for nonlinear analysis of shape memory alloy devices (E. Artioli, F. Auricchio and R.L. Taylor) A unified approach for the nonlinear dynamics of rods and shells using an exact conserving integration algorithm (P.M. Pimenta and E.M.B. Campello) Advanced Numerical Methods for the Form Finding and Patterning of Membrane Structures (K.-U. Bletzinger, J. Linhard and R. Wuechner) Contact between beams and shells (P. Wriggers) Advances in computational fluid-thin-walled-structure interaction-formulations and solvers (W.A. Wall, U. Kuettler, A. Gerstenberger, M. Gee and Ch. Foerster) Advances in Subdivision Finite Elements for Thin Shells (F. Cirak and Q. Long)

New trends in thin structures : formulation, optimization and coupled problems

This paper aims to describe the application of the virtual element method (VEM) to contact problems between elastic bodies.,Polygonal elements with arbitrary shape allow a stable node-to-node contact enforcement. By adaptively adjusting the polygonal mesh, this methodology is extended to problems undergoing large frictional sliding.,The virtual element is well suited for large deformation contact problems. The issue of element stability for this specific application is discussed, and the capability of the method is demonstrated by means of numerical examples.,This work is completely new as this is the first time, as per the authors’ knowledge, the VEM is applied to large deformation contact.

https://www.emerald.com/insight/content/doi/10.1108/EC-02-2019-0043/full/pdf?title=a-virtual-element-method-for-frictional-contact-including-large-deformations

Peter Wriggers

Papers

Delamination growth in composite laminates of variable stiffness

New trends in thin structures : formulation, optimization and coupled problems

A virtual element method for frictional contact including large deformations

Adaptive methods for frictionless contact problems

Computational Contact Mechanics with the Finite Element Method