[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

This is the peer reviewed version of the following article: This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Geelen, R., Liu, Y., Dolbow, J., Rodriguez-Ferran, A. An optimization-based phase-field method for continuous-discontinuous crack propagation. "International journal for numerical methods in engineering", 5 Octubre 2018, vol. 116, num. 1, p. 1-20, which has been published in final form at https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5911.

An optimization‐based phase‐field method for continuous‐discontinuous crack propagation

An experimental testing campaign on tensile bolted joints between straps is reported. Two dominant failure modes are identified: (1) tilting, bearing and tearing of the sheets (TS) and (2) tilting, bearing and net-section failure (NSF). The analysis in terms of ductility and strength shows that bolted connections are less adequate than screwed connections (reported in Part 1 of this paper) for the seismic design of X-braced shear walls in lightweight structures. NSF joints are more ductile than TS joints in the sense that they undergo larger displacements before failure. However, if washers are not used, both types of connections fail before energy dissipation through yielding of the diagonal straps can occur. Some design recommendations to improve the seismic performance of bolted joints, including the use of washers, are given. The accuracy of Eurocode 3 formulas to predict the ultimate load is also analyzed.

/pdf/experimental-testing-of-joints-for-seismic-design-of-277uuhxutt.pdf

Experimental testing of joints for seismic design of lightweight structures. Part 1. Screwed joints in straps

Steel studs are used in double walls to provide structural stability. This creates a vibration transmission path between leaves that can often be more critical than the airborne path through the cavity. Some of the existing models for sound transmission consider the studs as elastic springs. The spring stiff ness may be taken as the cross-section elastic stiff ness of the stud, but this leads to an underestimation of the vibration transmission. A procedure to obtain more accurate parameters to be used in vibration and sound insulation models is presented. The results show that they must be obtained from dynamic models and/or experiments.

/pdf/the-role-of-studs-in-the-sound-transmission-of-double-walls-21g35sbt3x.pdf

The Role of Studs in the Sound Transmission of Double Walls

A new adaptive refinement strategy for phase-field models of brittle fracture is proposed. The approach provides a computationally efficient solution to the high demand in spatial resolution of phase-field models. The strategy is based on considering two types of elements: h-refined elements along cracks, where more accuracy is needed to capture the solution, and standard elements in the rest of the domain. Continuity between adjacent elements of different type is imposed in weak form by means of Nitsche’s method. The weakly imposition of continuity leads to a very local refinement in a simple way, for any degree of approximation and both in 2D and 3D. The performance of the strategy is assessed for several scenarios in the quasi-static regime, including coalescence and branching of cracks in 2D and a twisting crack in 3D.

/pdf/adaptive-refinement-for-phase-field-models-of-brittle-4duav24995.pdf

Adaptive refinement for phase-field models of brittle fracture based on Nitsche’s method

An adaptive scheme is proposed in which the domain is split into two subdomains. One subdomain consists of regions where the discretization is refined with an h-adaptive approach, whereas in the other subdomain node relocation or r-adaptivity is used. Through this subdivision the advantageous properties of both remeshing strategies (accuracy and low computer costs, respectively) can be exploited in greater depth. The subdivision of the domain is based on the formulation of a desired element size, which renders the approach suitable for coupling with various error assessment tools. Two-dimensional linear examples where the analytical solution is known illustrate the approach. It is shown that the combined rh-adaptive approach is superior to its components r- and h-adaptivity, in that higher accuracies can be obtained compared to a purely r-adaptive approach, while the computational costs are lower than that of a purely h-adaptive approach. As such, a more flexible formulation of adaptive strategies is given, in which the relative importance of attaining a pre-set accuracy and speeding-up the computational process can be set by the user. Copyright © 2001 John Wiley & Sons, Ltd.

/pdf/a-combined-rh-adaptive-scheme-based-on-domain-subdivision-5a1sdjda51.pdf

Antonio Rodríguez-Ferran

Papers

An optimization‐based phase‐field method for continuous‐discontinuous crack propagation

Experimental testing of joints for seismic design of lightweight structures. Part 1. Screwed joints in straps

The Role of Studs in the Sound Transmission of Double Walls

Adaptive refinement for phase-field models of brittle fracture based on Nitsche’s method

A combined rh‐adaptive scheme based on domain subdivision. Formulation and linear examples