Attilio Frangi

Bio: Attilio Frangi is an academic researcher from Polytechnic University of Milan. The author has contributed to research in topics: Finite element method & Boundary element method. The author has an hindex of 29, co-authored 178 publications receiving 2792 citations. Previous affiliations of Attilio Frangi include Northwestern University & Instituto Politécnico Nacional.

The finite element method in solid mechanics

Abstract: The book focuses on topics that are at the core of the Finite Element Method (FEM) for the mechanics of deformable solids and structures.Its main objective is to provide the reader, who is assumed to be familiar with standard continuum solid mechanics, with a clear grasp of the essentials, sufficient background for reading and exploiting the research literature on computational solid mechanics, and a working knowledge of the main implementational issues of the FEM.This book arises from a course taught since 2004 to last-year students of Ecole Polytechnique (France). It is intended for Master and PhD students, as well as scientists and engineers looking for a rigorous introduction to FEM theory and programming for linear and non-linear analyses in solid mechanics.As a distinguishing feature, in addition to sections devoted to theory and concepts presented in general terms, each chapter also features other sections (interspersed with the former) devoted to detailed description of specific features (e.g. the construction of a specific finite element), annotated Matlab code and/or numerical examples produced with it, or worked-out analytical examples.

Recent Advances and Emerging Applications of the Boundary Element Method

Abstract: Sponsored by the U.S. National Science Foundation, a workshop on the boundary element method (BEM) was held on the campus of the University of Akron during September 1–3, 2010 (NSF, 2010, “Workshop on the Emerging Applications and Future Directions of the Boundary Element Method,” University of Akron, Ohio, September 1–3). This paper was prepared after this workshop by the organizers and participants based on the presentations and discussions at the workshop. The paper aims to review the major research achievements in the last decade, the current status, and the future directions of the BEM in the next decade. The review starts with a brief introduction to the BEM. Then, new developments in Green's functions, symmetric Galerkin formulations, boundary meshfree methods, and variationally based BEM formulations are reviewed. Next, fast solution methods for efficiently solving the BEM systems of equations, namely, the fast multipole method, the pre-corrected fast Fourier transformation method, and the adaptive cross approximation method are presented. Emerging applications of the BEM in solving microelectromechanical systems, composites, functionally graded materials, fracture mechanics, acoustic, elastic and electromagnetic waves, time-domain problems, and coupled methods are reviewed. Finally, future directions of the BEM as envisioned by the authors for the next five to ten years are discussed. This paper is intended for students, researchers, and engineers who are new in BEM research and wish to have an overview of the field. Technical details of the BEM and related approaches discussed in the review can be found in the Reference section with more than 400 papers cited in this review.

Mechanical characterization of polysilicon through on-chip tensile tests

Abstract: Two new types of on-chip tests have been designed in order to evaluate the elastic Young modulus and the fracture strength of polysilicon used in microelectromechanical systems (MEMS). The former is a pure tension test, while the latter is a single-edge-notched tension test. The actuation in both tests is obtained by means of an ad hoc designed layout of parallel plates capacitors applying sufficiently high forces to reach significant strains in the tensile specimens and complete failure of the notched specimens. The pure tension tests on 20 specimens showed a low dispersion and gave a Young modulus for the polysilicon of 143 GPa. A total of 92 notched specimens were tested up to failure. The experimental results, supported by finite-element simulations, gave a value of the maximum stress for the notched specimens in the range 4144-4568 MPa.

Anchor Losses in AlN Contour Mode Resonators

Abstract: In this paper, we analyze possible sources of dissipation in aluminium nitride (AlN) contour mode resonators for three different resonance frequency devices ( ${f} _{\!r}$ ) (220 MHz, 370 MHz, and 1.05 GHz). For this purpose, anchors of different widths ( ${W} _{\!a}$ ) and lengths ( ${L} _{\!a}$ ) proportional to the acoustic wavelength ( $\lambda $ ) are designed as supports for resonators in which the dimensions of the vibrating body are kept fixed. The ${Q}$ extracted experimentally confirms that anchor losses are the dominant source of damping for most anchor designs when ${f} _{\!r}$ is equal to 220 and 370 MHz. For specific anchor dimensions ( ${W} _{\!a}$ / $\lambda $ is in the range of 1/4–1/2) that mitigate energy leakage through the supports, a temperature-dependent dissipation mechanism dominates as seen in higher ${f} _{\!r}$ resonators operating close to 1.05 GHz. To describe the ${Q}$ due to anchor losses, we use a finite-element method with absorbing boundary conditions. We also propose a simple analytical formulation for describing the dependence of the temperature-dependent damping mechanism on frequency. In this way, we are able to quantitatively predict ${Q}$ due to anchor losses and qualitatively describe the trends observed experimentally. [2014-0232]

Photonic crystals

Abstract: The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

Electrostatic pull-in instability in MEMS/NEMS: A review

Abstract: Pull-in instability as an inherently nonlinear and crucial effect continues to become increasingly important for the design of electrostatic MEMS and NEMS devices and ever more interesting scientifically. This review reports not only the overview of the pull-in phenomenon in electrostatically actuated MEMS and NEMS devices, but also the physical principles that have enabled fundamental insights into the pull-in instability as well as pull-in induced failures. Pull-in governing equations and conditions to characterize and predict the static, dynamic and resonant pull-in behaviors are summarized. Specifically, we have described and discussed on various state-of-the-art approaches for extending the travel range, controlling the pull-in instability and further enhancing the performance of MEMS and NEMS devices with electrostatic actuation and sensing. A number of recent activities and achievements methods for control of torsional electrostatic micromirrors are introduced. The on-going development in pull-in applications that are being used to develop a fundamental understanding of pull-in instability from negative to positive influences is included and highlighted. Future research trends and challenges are further outlined.

Fast multipole boundary element method : theory and applications in engineering

Abstract: 1. Introduction 2. Conventional BEM for potential problems 3. Fast multipole BEM for potential problems 4. Elastostatic problems 5. Stokes flow problems 6. Acoustic wave problems.