Cosserat Plate Theory

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Cosserat Plate Theory

Author : Lev Steinberg
Publisher : CRC Press
ISBN 13 : 1000608093
Total Pages : 183 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Cosserat Plate Theory by : Lev Steinberg

Download or read book Cosserat Plate Theory written by Lev Steinberg and published by CRC Press. This book was released on 2022-09-15 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the foundation and validation of the Cosserat Plate Theory, numerical experiments of deformation and vibration, and the unique properties of the Cosserat plates. Our approach incorporates the high accuracy assumptions of the Cosserat plate deformation consistent with the Cosserat Elasticity equilibrium equations, constitutive formulas, strain-displacement and torsion-microrotation relations. The Cosserat Plate Theory is parametric, where the "splitting parameter" minimizes the Cosserat plate energy. The validation of the theory is based on the comparison with the three-dimensional Cosserat Elastostatics and Elastodynamics. The numerical results are obtained using the Finite Element Method (FEM) specifically developed to solve the parametric system of equations. The analysis of deformation of a variety of Cosserat plates shows the stress concentration reduction, higher stiffness of Cosserat plates, and the size-effect related to the microstructure. The analysis of vibration of Cosserat plates predicts size-related properties of the plate vibration, the existence of the additional so-called Cosserat plate resonances, and the dynamic anisotropy, related to the dependency of the resonances on the microelement's shapes and orientations.

Cosserat Plate Theory

Author : Lev Steinberg
Publisher : CRC Press
ISBN 13 : 1000608107
Total Pages : 134 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Cosserat Plate Theory by : Lev Steinberg

Download or read book Cosserat Plate Theory written by Lev Steinberg and published by CRC Press. This book was released on 2022-09-15 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the foundation and validation of the Cosserat Plate Theory, numerical experiments of deformation and vibration, and the unique properties of the Cosserat plates. Our approach incorporates the high accuracy assumptions of the Cosserat plate deformation consistent with the Cosserat Elasticity equilibrium equations, constitutive formulas, strain-displacement and torsion-microrotation relations. The Cosserat Plate Theory is parametric, where the "splitting parameter" minimizes the Cosserat plate energy. The validation of the theory is based on the comparison with the three-dimensional Cosserat Elastostatics and Elastodynamics. The numerical results are obtained using the Finite Element Method (FEM) specifically developed to solve the parametric system of equations. The analysis of deformation of a variety of Cosserat plates shows the stress concentration reduction, higher stiffness of Cosserat plates, and the size-effect related to the microstructure. The analysis of vibration of Cosserat plates predicts size-related properties of the plate vibration, the existence of the additional so-called Cosserat plate resonances, and the dynamic anisotropy, related to the dependency of the resonances on the microelement's shapes and orientations.

Cosserat Continuum Mechanics

Author : Ioannis Vardoulakis (Deceased)
Publisher : Springer
ISBN 13 : 3319951564
Total Pages : 183 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Cosserat Continuum Mechanics by : Ioannis Vardoulakis (Deceased)

Download or read book Cosserat Continuum Mechanics written by Ioannis Vardoulakis (Deceased) and published by Springer. This book was released on 2018-08-01 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores the theory of Cosserat continuum mechanics, and covers fundamental tools, general laws and major models, as well as applications to the mechanics of granular media. While classical continuum mechanics is based on the axiom that the stress tensor is symmetric, theories such as that expressed in the seminal work of the brothers Eugène and François Cosserat are characterized by a non-symmetric stress tensor. The use of von Mises motor mechanics is introduced, for the compact mathematical description of the mechanics and statics of Cosserat continua, as the Cosserat continuum is a manifold of oriented “rigid particles” with 3 dofs of displacement and 3 dofs of rotation, rather than a manifold of points with 3 dofs of displacement. Here, the analysis is restricted to infinitesimal particle displacements and rotations. This book is intended as a valuable supplement to standard Continuum Mechanics courses, and graduate students as well as researchers in mechanics and applied mathematics will benefit from its self-contained text, which is enriched by numerous examples and exercises.

The Omega-Theory

Author : Jure Žalohar
Publisher : Elsevier
ISBN 13 : 0128145811
Total Pages : 572 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis The Omega-Theory by : Jure Žalohar

Download or read book The Omega-Theory written by Jure Žalohar and published by Elsevier. This book was released on 2018-05-10 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Omega-Theory: A New Physics of Earthquakes, Second Edition offers a unifying, mathematical framework to describe and answer the most pressing and unexamined dilemmas of earthquake sequences. Those in the fields of seismology and geology are currently faced with a vast and complex mathematical structure, involving many new, natural laws and theorems. This book interprets this structure as a new physical theory and paradigm, helping users understand the tectonic and seismic processes within the Earth. As such, it is an essential resource for future researchers in the fields of structural geology, physics of the Earth, and seismology. In the last decades, generations of seismologists, geophysicists, and geologists have accumulated enough knowledge and information to allow for the reformulation and solution of this essential problem. Hence, this book provides a great resource for researchers and professionals. - Brings together twenty years of research in the field of geophysics and attacks the problem within the framework of the Cosserat continuum theory - Heavily tested on tens of natural examples and numerical tests - Includes 350 color figures and graphs - Spans across many fields of theoretical physics and geology, such as plate tectonics, synchronization of chaotic systems, solitons and fractals, mathematical set theory, and quantum mechanics

Theories of Plates and Shells

Author : Reinhold Kienzler
Publisher : Springer Science & Business Media
ISBN 13 : 3540399054
Total Pages : 258 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Theories of Plates and Shells by : Reinhold Kienzler

Download or read book Theories of Plates and Shells written by Reinhold Kienzler and published by Springer Science & Business Media. This book was released on 2013-06-01 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plate and shell theories experienced a renaissance in recent years. The potentials of smart materials, the challenges of adaptive structures, the demands of thin-film technologies and more on the one hand and the availability of newly developed mathematical tools, the tremendous increase in computer facilities and the improvement of commercial software packages on the other caused a reanimation of the scientific interest. In the present book the contributions of the participants of the EUROMECH Colloquium 444 "Critical Review of the Theories of Plates and Shells and New Applications" have been collected. The aim was to discuss the common roots of different plate and shell approaches, to review the current state of the art, and to develop future lines of research. Contributions were written by scientists with civil and mechanical engineering as well as mathematical and physical background.

Thin Plates and Shells

Author : Eduard Ventsel
Publisher : CRC Press
ISBN 13 : 9780203908723
Total Pages : 688 pages
Book Rating : 4.9/5 (87 download)

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Book Synopsis Thin Plates and Shells by : Eduard Ventsel

Download or read book Thin Plates and Shells written by Eduard Ventsel and published by CRC Press. This book was released on 2001-08-24 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting recent principles of thin plate and shell theories, this book emphasizes novel analytical and numerical methods for solving linear and nonlinear plate and shell dilemmas, new theories for the design and analysis of thin plate-shell structures, and real-world numerical solutions, mechanics, and plate and shell models for engineering appli

Modern Trends in Structural and Solid Mechanics 2

Author : Noel Challamel
Publisher : John Wiley & Sons
ISBN 13 : 1119831849
Total Pages : 306 pages
Book Rating : 4.1/5 (198 download)

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Book Synopsis Modern Trends in Structural and Solid Mechanics 2 by : Noel Challamel

Download or read book Modern Trends in Structural and Solid Mechanics 2 written by Noel Challamel and published by John Wiley & Sons. This book was released on 2021-06-08 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprised of three separate volumes presents the recent developments and research discoveries in structural and solid mechanics; it is dedicated to Professor Isaac Elishakoff. This second volume is devoted to the vibrations of solid and structural members. Modern Trends in Structural and Solid Mechanics 2 has broad scope, covering topics such as: exact and approximate vibration solutions of rods, beams, membranes, plates and three-dimensional elasticity problems, Bolotins dynamic edge effect, the principles of plate theories in dynamics, nano- and microbeams, nonlinear dynamics of shear extensible beams, the vibration and aeroelastic stability behavior of cellular beams, the dynamic response of elastoplastic softening oscillators, the complex dynamics of hysteretic oscillators, bridging waves, and the three-dimensional propagation of waves. This book is intended for graduate students and researchers in the field of theoretical and applied mechanics.

Nonlinear Theory of Elastic Plates

Author : Anh Le Van
Publisher : Elsevier
ISBN 13 : 0081023596
Total Pages : 214 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Nonlinear Theory of Elastic Plates by : Anh Le Van

Download or read book Nonlinear Theory of Elastic Plates written by Anh Le Van and published by Elsevier. This book was released on 2017-05-31 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Theory of Elastic Plates provides the theoretical materials necessary for the three plate models—Cosserat plates, Reissner-Mindlin plates and Kirchhoff-Love plates— in the context of finite elastic deformations. One separate chapter is devoted to the linearized theory of Kirchhoff-Love plates, which allows for the study of vibrations of a pre-stressed plate and the static buckling of a plate. All mathematical results in the tensor theory in curvilinear coordinates necessary to investigate the plate theory in finite deformations are provided, making this a self-contained resource. - Presents the tricky process of linearization, which is rarely dealt with, but explained in detail in a separate chapter - Organized in a mathematical style, with definitions, hypotheses, theorems and proofs clearly stated - Presents every theorem with its accompanying hypotheses, enabling the reader to quickly recognize the conditions of validity in results

Recent Developments in the Theory of Shells

Author : Holm Altenbach
Publisher : Springer Nature
ISBN 13 : 3030177475
Total Pages : 799 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Recent Developments in the Theory of Shells by : Holm Altenbach

Download or read book Recent Developments in the Theory of Shells written by Holm Altenbach and published by Springer Nature. This book was released on 2019-09-25 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book commemorates the 80th birthday of Prof. W. Pietraszkiewicz, a prominent specialist in the field of general shell theory. Reflecting Prof. Pietraszkiewicz’s focus, the respective papers address a range of current problems in the theory of shells. In addition, they present other structural mechanics problems involving dimension-reduced models. Lastly, several applications are discussed, including material models for such dimension-reduced structures.

Recent Approaches in the Theory of Plates and Plate-Like Structures

Author : Holm Altenbach
Publisher : Springer Nature
ISBN 13 : 3030871851
Total Pages : 326 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Recent Approaches in the Theory of Plates and Plate-Like Structures by : Holm Altenbach

Download or read book Recent Approaches in the Theory of Plates and Plate-Like Structures written by Holm Altenbach and published by Springer Nature. This book was released on 2022-01-01 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the various approaches in establishment the basic equations of one- and two-dimensional structural elements. In addition, the boundaries of validity of the theories and the estimation of errors in approximate theories are given. Many contributions contain not only new theories, but also new applications, which makes the book interesting for researcher and graduate students.

Advances in Engineering Materials, Structures and Systems: Innovations, Mechanics and Applications

Author : Alphose Zingoni
Publisher : CRC Press
ISBN 13 : 0429761171
Total Pages : 2435 pages
Book Rating : 4.4/5 (297 download)

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Book Synopsis Advances in Engineering Materials, Structures and Systems: Innovations, Mechanics and Applications by : Alphose Zingoni

Download or read book Advances in Engineering Materials, Structures and Systems: Innovations, Mechanics and Applications written by Alphose Zingoni and published by CRC Press. This book was released on 2019-08-21 with total page 2435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Engineering Materials, Structures and Systems: Innovations, Mechanics and Applications comprises 411 papers that were presented at SEMC 2019, the Seventh International Conference on Structural Engineering, Mechanics and Computation, held in Cape Town, South Africa, from 2 to 4 September 2019. The subject matter reflects the broad scope of SEMC conferences, and covers a wide variety of engineering materials (both traditional and innovative) and many types of structures. The many topics featured in these Proceedings can be classified into six broad categories that deal with: (i) the mechanics of materials and fluids (elasticity, plasticity, flow through porous media, fluid dynamics, fracture, fatigue, damage, delamination, corrosion, bond, creep, shrinkage, etc); (ii) the mechanics of structures and systems (structural dynamics, vibration, seismic response, soil-structure interaction, fluid-structure interaction, response to blast and impact, response to fire, structural stability, buckling, collapse behaviour); (iii) the numerical modelling and experimental testing of materials and structures (numerical methods, simulation techniques, multi-scale modelling, computational modelling, laboratory testing, field testing, experimental measurements); (iv) innovations and special structures (nanostructures, adaptive structures, smart structures, composite structures, bio-inspired structures, shell structures, membranes, space structures, lightweight structures, long-span structures, tall buildings, wind turbines, etc); (v) design in traditional engineering materials (steel, concrete, steel-concrete composite, aluminium, masonry, timber, glass); (vi) the process of structural engineering (conceptualisation, planning, analysis, design, optimization, construction, assembly, manufacture, testing, maintenance, monitoring, assessment, repair, strengthening, retrofitting, decommissioning). The SEMC 2019 Proceedings will be of interest to civil, structural, mechanical, marine and aerospace engineers. Researchers, developers, practitioners and academics in these disciplines will find them useful. Two versions of the papers are available. Short versions, intended to be concise but self-contained summaries of the full papers, are in this printed book. The full versions of the papers are in the e-book.

Mechanics of Generalized Continua

Author : Gérard A. Maugin
Publisher : Springer Science & Business Media
ISBN 13 : 1441956956
Total Pages : 337 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Mechanics of Generalized Continua by : Gérard A. Maugin

Download or read book Mechanics of Generalized Continua written by Gérard A. Maugin and published by Springer Science & Business Media. This book was released on 2010-03-24 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics and can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.

Dynamical Systems Theory

Author : Jan Awrejcewicz
Publisher : BoD – Books on Demand
ISBN 13 : 1838802290
Total Pages : 186 pages
Book Rating : 4.8/5 (388 download)

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Book Synopsis Dynamical Systems Theory by : Jan Awrejcewicz

Download or read book Dynamical Systems Theory written by Jan Awrejcewicz and published by BoD – Books on Demand. This book was released on 2020-03-25 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quest to ensure perfect dynamical properties and the control of different systems is currently the goal of numerous research all over the world. The aim of this book is to provide the reader with a selection of methods in the field of mathematical modeling, simulation, and control of different dynamical systems. The chapters in this book focus on recent developments and current perspectives in this important and interesting area of mechanical engineering. We hope that readers will be attracted by the topics covered in the content, which are aimed at increasing their academic knowledge with competences related to selected new mathematical theoretical approaches and original numerical tools related to a few problems in dynamical systems theory.

Generalized Continua - from the Theory to Engineering Applications

Author : Holm Altenbach
Publisher : Springer Science & Business Media
ISBN 13 : 3709113717
Total Pages : 403 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Generalized Continua - from the Theory to Engineering Applications by : Holm Altenbach

Download or read book Generalized Continua - from the Theory to Engineering Applications written by Holm Altenbach and published by Springer Science & Business Media. This book was released on 2012-10-17 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the roots of continuum mechanics in differential geometry -- a review.- Cosserat media.- Cosserat-type shells.- Cosserat-type rods.- Micromorphic media.- Electromagnetism and generalized continua.- Computational methods for generalized continua. The need of generalized continua models is coming from practice. Complex material behavior sometimes cannot be presented by the classical Cauchy continua. At present the attention of the scientists in this field is focused on the most recent research items • new models, • application of well-known models to new problems, • micro-macro aspects, • computational effort, and • possibilities to identify the constitutive equations The new research directions are discussed in this volume - from the point of view of modeling and simulation, identification, and numerical methods.

Cellular and Porous Materials in Structures and Processes

Author : Holm Altenbach
Publisher : Springer Science & Business Media
ISBN 13 : 3709102979
Total Pages : 334 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Cellular and Porous Materials in Structures and Processes by : Holm Altenbach

Download or read book Cellular and Porous Materials in Structures and Processes written by Holm Altenbach and published by Springer Science & Business Media. This book was released on 2011-01-27 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers the state-of-the-art treatment in modelling and experimental investigation of the mechanical behaviour of cellular and porous materials. Starting from the continuum mechanical modelling, to the numerical simulation, several important questions related to applications such as the fracture and impact behaviour are covered.

Applied Mechanics Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 276 pages
Book Rating : 4.:/5 (26 download)

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Book Synopsis Applied Mechanics Reviews by :

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1974 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Generalized Models and Non-classical Approaches in Complex Materials 1

Author : Holm Altenbach
Publisher : Springer
ISBN 13 : 3319724401
Total Pages : 799 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Generalized Models and Non-classical Approaches in Complex Materials 1 by : Holm Altenbach

Download or read book Generalized Models and Non-classical Approaches in Complex Materials 1 written by Holm Altenbach and published by Springer. This book was released on 2018-03-24 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of 2 special volumes dedicated to the memory of Gérard Maugin. Including 40 papers that reflect his vast field of scientific activity, the contributions discuss non-standard methods (generalized model) to demonstrate the wide range of subjects that were covered by this exceptional scientific leader. The topics range from micromechanical basics to engineering applications, focusing on new models and applications of well-known models to new problems. They include micro–macro aspects, computational endeavors, options for identifying constitutive equations, and old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.