[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

Modeling of the evolution of distributed damage such as microcracking, void formation, and softening frictional slip necessitates strain-softening constitutive models. The nonlocal continuum concept has emerged as an effective means for regularizing the boundary value problems with strain softening, capturing the size effects and avoiding spurious localization that gives rise to pathological mesh sensitivity in numerical computations. A great variety of nonlocal models have appeared during the last two decades. This paper reviews the progress in the nonlocal models of integral type, and discusses their physical justifications, advantages, and numerical applications.

Nonlocal integral formulations of plasticity and damage: Survey of progress

The aim of the present chapter is to provide an in-depth survey of arbitrary Lagrangian–Eulerian (ALE) methods, including both conceptual aspects of the mixed kinematical description and numerical implementation details. Applications are discussed in fluid dynamics, nonlinear solid mechanics and coupled problems describing fluid–structure interaction. The need for an adequate mesh-update strategy is underlined, and various automatic mesh-displacement prescription algorithms are reviewed. This includes mesh-regularization methods essentially based on geometrical concepts, as well as mesh-adaptation techniques aimed at optimizing the computational mesh according to some error indicator. Emphasis is then placed on particular issues related to the modeling of compressible and incompressible flow and nonlinear solid mechanics problems. This includes the treatment of convective terms in the conservation equations for mass, momentum, and energy, as well as a discussion of stress-update procedures for materials with history-dependent constitutive behavior.


Keywords:

ALE description;
convective transport;
finite elements;
stabilization techniques;
mesh regularization and adaptation;
fluid dynamics;
nonlinear solid mechanics;
stress-update procedures;
fluid–structure interaction

https://onlinelibrary.wiley.com/doi/pdf/10.1002/0470091355.ecm009

Arbitrary Lagrangian–Eulerian Methods

http://users.auth.gr/~akonsta/2011_Gradient%20elasticity%20in%20statics%20and%20dynamics.pdf

Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results

Resumen Los modelos de gradiente basados en desplazamientos suavizados son una alternativa a los modelos estandares para simular numericamente el proceso de fallo de materiales. En esta formulacion alternativa coexisten los campos de desplazamientos mecanicos u con los desplazamientos suavizados u ˜ , que se obtienen de solucionar una ecuacion de difusion-reaccion. Analogamente a los modelos de regularizacion estandares, prescribir condiciones de contorno en esta formulacion alternativa es un problema abierto. Sin embargo, imponer estas condiciones para el campo de desplazamientos (en lugar de la variable de estado interna) presenta ciertas facilidades. El objetivo de este trabajo es estudiar la influencia de dichas condiciones: ni las condiciones de Dirichlet (prescritas en un principio) ni las condiciones de Neumann homogeneas (reminiscencia de los modelos de gradiente estandares) permiten obtener resultados numericos realistas; mediante las condiciones de contorno de Neumann no homogeneas, en cambio, los resultados son fisicamente admisibles. Sin embargo, estas condiciones no aseguran conservacion de volumen, que es una propiedad interesante en algunos modelos constitutivos. Por este motivo, se proponen unas nuevas condiciones de contorno (condiciones combinadas) que satisfacen las propiedades necesarias para la regularizacion: (a) reproducibilidad de orden 1 ( u = u ˜ si u es un campo lineal), (b) desplazamientos suavizados a lo largo del contorno y (c) conservacion de volumen. En este trabajo se han llevado a cabo varios ensayos numericos bidimensionales con el fin de ilustrar la influencia de las distintas condiciones de contorno.

/pdf/condiciones-de-contorno-en-modelos-de-gradiente-con-3u0n6t0f1h.pdf

Condiciones de contorno en modelos de gradiente con desplazamientos suavizados

Study of grain-scale effects in bulk handling using discrete element simulations

A wide range of bulk materials with different physical properties are nowadays handled in the packaging industry using different material conveying techniques. Nevertheless, experimental methodologies to characterise flowability of granular materials in actual handling conditions are still under development. This paper presents a new fully instrumented device for flowability assessment by granular column collapse of bulk materials. The generated granular flow is monitored by load cells that register the flow heights and by a high-speed video camera that captures the bulk flow kinematics through particle image velocimetry analysis. The 3D surface morphology of the final condition is determined with a 2D laser profile scanner. Results show the effect of varying the initial column aspect ratio on flow response.

A New Granular Column Collapse Device to Characterise Flowability of Bulk Materials

The solution of vibroacoustic linear systems as a finite sum of transmission paths

A generic non-local approach to regularise strain-softening continua is presented. The key idea is to introduce the gradient-type enrichment at the level of displacements [1, 2] (rather than some internal variable), so the model is formulated with two distinct displacement fields: the standard displacements ua and the gradient-enriched displacements ug. In fact, gradient models based on two displacement fields are usual in non-local elasticity, where the goal is to avoid the shortcomings of classical (local) elasticity (i.e. strain singularities in statics, non-dispersive behaviour in dynamics). We show that such a gradient elasticity backbone model can be combined with any standard nonlinear constitutive driver to render a regularised model for softening inelasticity. This generic continuous framework is subsequently enriched with discontinuities in the displacement fields.

Antonio Rodríguez-Ferran

Papers

Condiciones de contorno en modelos de gradiente con desplazamientos suavizados

Study of grain-scale effects in bulk handling using discrete element simulations

A New Granular Column Collapse Device to Characterise Flowability of Bulk Materials

The solution of vibroacoustic linear systems as a finite sum of transmission paths

A continuous-discontinuous model for softening and cracking based on non-local gradient elasticity