Mathematical Models for Suspension Bridges

Mathematical Models for Suspension Bridges

Author: Filippo Gazzola

Publisher: Springer

Published: 2015-05-29

Total Pages: 274

ISBN-13: 3319154346

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This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.


Nonlinear Equations for Beams and Degenerate Plates with Piers

Nonlinear Equations for Beams and Degenerate Plates with Piers

Author: Maurizio Garrione

Publisher: Springer Nature

Published: 2019-10-31

Total Pages: 115

ISBN-13: 3030302180

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This book develops a full theory for hinged beams and degenerate plates with multiple intermediate piers with the final purpose of understanding the stability of suspension bridges. New models are proposed and new tools are provided for the stability analysis. The book opens by deriving the PDE’s based on the physical models and by introducing the basic framework for the linear stationary problem. The linear analysis, in particular the behavior of the eigenvalues as the position of the piers varies, enables the authors to tackle the stability issue for some nonlinear evolution beam equations, with the aim of determining the “best position” of the piers within the beam in order to maximize its stability. The study continues with the analysis of a class of degenerate plate models. The torsional instability of the structure is investigated, and again, the optimal position of the piers in terms of stability is discussed. The stability analysis is carried out by means of both analytical tools and numerical experiments. Several open problems and possible future developments are presented. The qualitative analysis provided in the book should be seen as the starting point for a precise quantitative study of more complete models, taking into account the action of aerodynamic forces. This book is intended for a two-fold audience. It is addressed both to mathematicians working in the field of Differential Equations, Nonlinear Analysis and Mathematical Physics, due to the rich number of challenging mathematical questions which are discussed and left as open problems, and to Engineers interested in mechanical structures, since it provides the theoretical basis to deal with models for the dynamics of suspension bridges with intermediate piers. More generally, it may be enjoyable for readers who are interested in the application of Mathematics to real life problems.


Multiscale Modeling and Uncertainty Quantification of Materials and Structures

Multiscale Modeling and Uncertainty Quantification of Materials and Structures

Author: Manolis Papadrakakis

Publisher: Springer

Published: 2014-07-02

Total Pages: 303

ISBN-13: 3319063316

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This book contains the proceedings of the IUTAM Symposium on Multiscale Modeling and Uncertainty Quantification of Materials and Structures that was held at Santorini, Greece, September 9 – 11, 2013. It consists of 20 chapters which are divided in five thematic topics: Damage and fracture, homogenization, inverse problems–identification, multiscale stochastic mechanics and stochastic dynamics. Over the last few years, the intense research activity at micro scale and nano scale reflected the need to account for disparate levels of uncertainty from various sources and across scales. As even over-refined deterministic approaches are not able to account for this issue, an efficient blending of stochastic and multiscale methodologies is required to provide a rational framework for the analysis and design of materials and structures. The purpose of this IUTAM Symposium was to promote achievements in uncertainty quantification combined with multiscale modeling and to encourage research and development in this growing field with the aim of improving the safety and reliability of engineered materials and structures. Special emphasis was placed on multiscale material modeling and simulation as well as on the multiscale analysis and uncertainty quantification of fracture mechanics of heterogeneous media. The homogenization of two-phase random media was also thoroughly examined in several presentations. Various topics of multiscale stochastic mechanics, such as identification of material models, scale coupling, modeling of random microstructures, analysis of CNT-reinforced composites and stochastic finite elements, have been analyzed and discussed. A large number of papers were finally devoted to innovative methods in stochastic dynamics.


Structural and Civil Engineering Design

Structural and Civil Engineering Design

Author: William Addis

Publisher: Taylor & Francis

Published: 2016-12-05

Total Pages: 410

ISBN-13: 1351897470

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The importance of design has often been neglected in studies considering the history of structural and civil engineering. Yet design is a key aspect of all building and engineering work. This volume brings together a range of articles which focus on the role of design in engineering. It opens by considering the principles of design, then deals with the application of these to particular subjects including bridges, canals, dams and buildings (from Gothic cathedrals to Victorian mills) constructed using masonry, timber, cast and wrought iron.


Advances in Mathematical Modeling and Scientific Computing

Advances in Mathematical Modeling and Scientific Computing

Author: Firuz Kamalov

Publisher: Springer Nature

Published: 2023

Total Pages: 933

ISBN-13: 3031414209

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This volume collects the proceedings of the International Conference on Recent Developments in Mathematics (ICRDM), held at Canadian University Dubai, UAE, in August 2022. This is the second of two volumes, with this volume focusing on more applied topics, particularly mathematical modeling and scientific computing, and the first covering recent advances in algebra and analysis. Each chapter identifies existing research problems, the techniques needed to solve them, and a thorough analysis of the obtained results. Advances in Mathematical Modeling and Scientific Computing will appeal to a range of postgraduate students, researchers, and industry professionals interested in exploring recent advancements in applied mathematics.