关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves

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Electrodynamics Of Continuous Media

This research aims at introducing a new idea in the design of frames to eliminate or suppress the transmission of waves through the structure in a certain designated range of frequencies that is called hereinafter as frequency band gap. To achieve this goal, we apply a concept from the mechanics of metamaterials to the investigated structural system by proposing a new beam-column connection in a multistory 2D frame. Modal and harmonic analysis are carried out for both the new proposed frame and the ordinary one in order to investigate the response of both systems. A thorough time history analysis is applied, also we demonstrate the response of the new proposed model under the loading of 9 different earthquake loads and a comparison between the resulted displacement and base shear is performed. Furthermore, a realization of the new connection is demonstrated. Results, comparison, and discussion are presented. The results show that the new proposed frame exhibits the calculated frequency band gap and the effect of seismic waves with frequencies within the bandgap frequency range was significantly mitigated. The novelty of this research is the ability of the new proposed idea to generate and tailor a frequency band gap in order to prevent the transmission of waves in this range of frequencies through the structural system itself. Consequently, the bandgap range of frequencies for each structure can be tuned depending on the seismic risk of its region on the global scale. This new feature could have a great impact and significant application to mitigate the effects of seismic waves on a structure. 

Evaluation of the seismic response of frames implemented with metamaterials

Global response of experimental uniaxial tests cannot be homogeneous because of the in- evitable presence of localizations of deformation, that is always preferable from an energetic viewpoint. Accordingly one must introduce some characteristic lengths in order to penalize the too localized deforma- tions. That leads to the concept of non-local damage models. The non-local approach implies non-local terms in the internal energy for controlling the size of the localization zone, see the remarkable works by Marigo and his coworkers (1, 2, 3, 4). The introduction of a length scale in a fully non-local theory has been achieved in perydynamics, see e.g. (5, 6). In this work the non-local term is given by the dependence of the internal energy of the second gradient of the displacement field. Following a variational approach (7), one defines the state variables and the total energy of the system associated with them. This total energy includes the potential energy (due to internal and external consequences) as well as the dissipated energy, here in terms of a damage parameter; finally, one formulates the evolution problem on the basis of the irreversibility of the damage parameter and of the variational principle. The irreversibility is taken because it is assumed that the damage field can not decrease its value. The variational principle assures that, at each time, a local minimum of the total energy among all accessible close states, is reached and the boundary conditions are derived and not assumed a priori. Extended Abstract In this work the damage state of a material point x is charactrerized by a scalar internal variable a = a(x), that is assumed to be within the range a2 (0; 1), being a = 0 corresponding to the undameged state and being a = 1, on the other hand, corresponding to the broken material. At a given a the behaviour is elastic and defined by an internal energy U that now is not only a functional of the displacement field u(x) but also of the damage field a(x). If we interprete the damaged material as a microstructured material, we also let the internal energy to depend upon the second gradient of displacement in the following way,

/pdf/towards-a-second-gradient-damage-model-4edudheha3.pdf

Towards a second gradient damage model

https://link-springer-com-443.webvpn.jmu.edu.cn/content/pdf/10.1007%2F978-3-662-53605-6_200-1.pdf

Finite Dimensional Lagrangian Systems

A complete theoretical presentation of the Continuum-mechanical, Anisotropic Flow model, based on an anisotropic Flow Enhancement factor (CAFFE model) is given. The CAFFE model is an application of the theory of mixtures with continuous diversity for the case of large polar ice masses in which induced anisotropy occurs. The anisotropic response of the polycrystalline ice is described by a generalization of Glen's flow law, based on a scalar anisotropic enhancement factor. The enhancement factor depends on the orientation mass density, which is closely related to the orientation distribution function and describes the distribution of grain orientations (fabric). Fabric evolution is governed by the orientation mass balance, which depends on four distinct effects, interpreted as local rigid body rotation, grain rotation, rotation recrystallization (polygonization) and grain boundary migration (migration recrystallization), respectively. It is proven that the flow law of the CAFFE model is truly anisotropic despite the collinearity between the stress deviator and stretching tensors.

/pdf/continuum-mechanical-anisotropic-flow-model-for-polar-ice-1xyjtnxvqz.pdf

Continuum-mechanical, Anisotropic Flow model for polar ice masses, based on an anisotropic Flow Enhancement factor

https://link.springer.com/content/pdf/10.1007/s00161-023-01207-x.pdf

Luca Placidi

Papers

Evaluation of the seismic response of frames implemented with metamaterials

Towards a second gradient damage model

Finite Dimensional Lagrangian Systems

Continuum-mechanical, Anisotropic Flow model for polar ice masses, based on an anisotropic Flow Enhancement factor

Editorial for the IWCMM29 special issue