Download or read book Anisotropic Doubly Curved Shells written by Francesco Tornabene and published by Società Editrice Esculapio. This book was released on 2019-11-01 with total page 1199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for the mechanical analysis of doubly-curved shell structures made of anisotropic and composite materials. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the structural behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are developed to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are presented, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. Finally, two numerical techniques, named Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are developed to deal with multi-element domains characterized by arbitrary shapes and discontinuities.

Download or read book Hygro Thermo Magneto Electro Elastic Theory of Anisotropic Doubly Curved Shells written by Francesco Tornabene and published by Società Editrice Esculapio. This book was released on 2023-10-13 with total page 1073 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for studying the Hygro-Thermo-Magneto-Electro- Elastic Theory of Anisotropic Doubly-Curved Shells. In particular, a general coupled multifield theory regarding anisotropic shell structures is provided. The three-dimensional multifield problem is reduced in a two-dimensional one following the principles of the Equivalent Single Layer (ESL) approach and the Equivalent Layer-Wise (ELW) approach, setting a proper configuration model. According to the adopted configuration assumptions, several Higher-order Shear Deformation Theories (HSDTs) are obtained. Furthermore, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the physical behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are used to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are considered, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. The Theory of Composite Thin Shells is derived in a simple and intuitive manner from the theory of thick and moderately thick shells (First-order Shear Deformation Theory or Reissner- Mindlin Theory). In particular, the Kirchhoff-Love Theory and the Membrane Theory for composite shells are shown. Furthermore, the Theory of Composite Arches and Beams is also exposed. In particular, the equations of the Timoshenko Theory and the Euler-Bernoulli Theory are directly deducted from the equations of singly-curved shells of translation and of plates.

Download or read book Generalized Differential and Integral Quadrature written by Francesco Tornabene and published by Società Editrice Esculapio. This book was released on 2023-10-17 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of this book is to analyze the mathematical fundamentals and the main features of the Generalized Differential Quadrature (GDQ) and Generalized Integral Quadrature (GIQ) techniques. Furthermore, another interesting aim of the present book is to shown that from the two numerical techniques mentioned above it is possible to derive two different approaches such as the Strong and Weak Finite Element Methods (SFEM and WFEM), that will be used to solve various structural problems and arbitrarily shaped structures. A general approach to the Differential Quadrature is proposed. The weighting coefficients for different basis functions and grid distributions are determined. Furthermore, the expressions of the principal approximating polynomials and grid distributions, available in the literature, are shown. Besides the classic orthogonal polynomials, a new class of basis functions, which depend on the radial distance between the discretization points, is presented. They are known as Radial Basis Functions (or RBFs). The general expressions for the derivative evaluation can be utilized in the local form to reduce the computational cost. From this concept the Local Generalized Differential Quadrature (LGDQ) method is derived. The Generalized Integral Quadrature (GIQ) technique can be used employing several basis functions, without any restriction on the point distributions for the given definition domain. To better underline these concepts some classical numerical integration schemes are reported, such as the trapezoidal rule or the Simpson method. An alternative approach based on Taylor series is also illustrated to approximate integrals. This technique is named as Generalized Taylor-based Integral Quadrature (GTIQ) method. The major structural theories for the analysis of the mechanical behavior of various structures are presented in depth in the book. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. Generally speaking, two formulations of the same system of governing equations can be developed, which are respectively the strong and weak (or variational) formulations. Once the governing equations that rule a generic structural problem are obtained, together with the corresponding boundary conditions, a differential system is written. In particular, the Strong Formulation (SF) of the governing equations is obtained. The differentiability requirement, instead, is reduced through a weighted integral statement if the corresponding Weak Formulation (WF) of the governing equations is developed. Thus, an equivalent integral formulation is derived, starting directly from the previous one. In particular, the formulation in hand is obtained by introducing a Lagrangian approximation of the degrees of freedom of the problem. The need of studying arbitrarily shaped domains or characterized by mechanical and geometrical discontinuities leads to the development of new numerical approaches that divide the structure in finite elements. Then, the strong form or the weak form of the fundamental equations are solved inside each element. The fundamental aspects of this technique, which the author defined respectively Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are presented in the book.

Download or read book Mechanics of Laminated Composite Doubly Curved Shell Structures written by Francesco Tornabene and published by Società Editrice Esculapio. This book was released on 2021-12-01 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: This manuscript comes from the experience gained over ten years of study and research on shell structures and on the Generalized Differential Quadrature method. The title, Mechanics of Laminated Composite Doubly-Curved Shell Structures, illustrates the theme followed in the present volume. The present study aims to analyze the static and dynamic behavior of moderately thick shells made of composite materials through the application of the Differential Quadrature (DQ) technique. A particular attention is paid, other than fibrous and laminated composites, also to “Functionally Graded Materials” (FGMs). They are non-homogeneous materials, characterized by a continuous variation of the mechanical properties through a particular direction. The GDQ numerical solution is compared, not only with literature results, but also with the ones supplied and obtained through the use of different structural codes based on the Finite Element Method (FEM). Furthermore, an advanced version of GDQ method is also presented. This methodology is termed Strong Formulation Finite Element Method (SFEM) because it employs the strong form of the differential system of equations at the master element level and the mapping technique, proper of FEM. The connectivity between two elements is enforced through compatibility conditions.

Download or read book Theory of Laminated Composite Doubly Curved Shell Structures written by Francesco Tornabene and published by Società Editrice Esculapio. This book was released on 2017-01-09 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This manuscript comes from the experience gained over thirteen years of study and research on shell structures. The title, Theory of Laminated Composite Doubly-Curved Shell Structures, illustrates the theme followed in the present volume. The present study aims to analyze the static and dynamic behavior of moderately thick shells made of composite materials. A particular attention is paid, other than fibrous and laminated composites, also to “Functionally graded materials” (FGMs). They are non-homogeneous materials, characterized by a continuous varia on of the mechanical properties through a particular direction. In particular, the present manuscript was written as an attempt to show, in an easy way, the theoretical aspects of doubly-curved composite shell structures. Furthermore, it focuses only on the theoretical aspects related to laminated composite doubly-curved shell structures and represents a shortened version of the book entitled: Mechanics of Laminated Composite Doubly-Curved Shell Structures by the same authors, wherein also the numerical part has been presented. The present volume is aimed at Master degree and PhD students in structural and applied mechanics, as well as experts in these fields. The present volume is divided into six chapters, in which static and dynamic analyses of several structural elements are provided in detail. Furthermore, the results of the adopted numerical technique are presented for several problems such as different loading and boundary conditions.

Download or read book Mechanics of laminated Composite doubly curvel shell structures written by Francesco Tornabene and published by Società Editrice Esculapio. This book was released on 2014-03-01 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: This manuscript comes from the experience gained over ten years of study and research on shell structures and on the Generalized Differential Quadrature method. The title, Mechanics of Laminated Composite Doubly-Curved Shell Structures, illustrates the theme followed in the present volume. The present study aims to analyze the static and dynamic behavior of moderately thick shells made of composite materials through the application of the Differential Quadrature (DQ) technique. A particular attention is paid, other than fibrous and laminated composites, also to “Functionally Graded Materials” (FGMs). They are non-homogeneous materials, characterized by a continuous variation of the mechanical properties through a particular direction. The GDQ numerical solution is compared, not only with literature results, but also with the ones supplied and obtained through the use of different structural codes based on the Finite Element Method (FEM). Furthermore, an advanced version of GDQ method is also presented. This methodology is termed Strong Formulation Finite Element Method (SFEM) because it employs the strong form of the differential system of equations at the master element level and the mapping technique, proper of FEM. The connectivity between two elements is enforced through compatibility conditions.

Download or read book Structural Mechanics written by Alberto Carpinteri and published by CRC Press. This book was released on 2017-12-21 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a complete and unified treatment of the fundamental themes of structural mechanics, ranging from the traditional to the most advanced topics, covering mechanics of linear elastic solids, theory of beam systems, and phenomena of structural failure. The book considers explicitly all the static and kenetic operators of structural mechanics with their dual character. Topics relating to structural symmetry are covered in a single chapter while dynamics is dealt with at various points. The logical presentation allows the clear introduction of topics such as finite element methods, automatic calculation of framed beam systems, plate and shell theory, theory of plasticity, and fracture mechanics. Numerous worked examples, exercises with complete solutions and illustrations make it accessible both as a text for students and as a reference for research workers and practicing engineers.

Download or read book Laminated Composite Doubly Curved Shell Structures written by Francesco Tornabene and published by Società Editrice Esculapio. This book was released on 2016-05-17 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: The title, “Laminated Composite Doubly-Curved Shell Structures. Differential al Geometry and Higher-order Theories” illustrates the theme treated and the prospective followed during the composition of the present work. The aim of this manuscript is to analyze the static and dynamic behavior of thick and moderately thick composite shells through the application of the Differential Quadrature (DQ) method. The book is divided into two volumes wherein the principal higher order structural theories are illustrated in detail and the mechanical behavior of doubly-curved structures are presented by several static and dynamic numerical applications. In particular, the first volume is mainly theoretical, whereas the second one is mainly related to the numerical DQ technique and its applications in the structural field. The starting point to analyze higher-order structural theories is given by the so-called Unified Formulation (UF), which allows to consider and study several kinematic models in a unified manner. Both the Equivalent Single Layer (ESL) and Layer-Wise (LW) approaches are presented. A particular attention is paid to composite materials, due to their increasing development and use in many engineering fields during the last years.

Download or read book Elements of Advanced Mathematical Analysis for Physics and Engineering written by Filippo Gazzola and published by Società Editrice Esculapio. This book was released on 2015-08-26 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deep comprehension of applied sciences requires a solid knowledge of Mathematical Analysis. For most of high level scientific research, the good understanding of Functional Analysis and weak solutions to differential equations is essential. This book aims to deal with the main topics that are necessary to achieve such a knowledge. Still, this is the goal of many other texts in advanced analysis; and then, what would be a good reason to read or to consult this book? In order to answer this question, let us introduce the three Authors. Alberto Ferrero got his degree in Mathematics in 2000 and presently he is researcher in Mathematical Analysis at the Università del Piemonte Orientale. Filippo Gazzola got his degree in Mathematics in 1987 and he is now full professor in Mathematical Analysis at the Politecnico di Milano. Maurizio Zanotti got his degree in Mechanical Engineering in 2004 and presently he is structural and machine designer and lecturer professor in Mathematical Analysis at the Politecnico di Milano. The three Authors, for the variety of their skills, decided to join their expertises to write this book. One of the reasons that should encourage its reading is that the presentation turns out to be a reasonable compromise among the essential mathematical rigor, the importance of the applications and the clearness, which is necessary to make the reference work pleasant to the readers, even to the inexperienced ones. The range of treated topics is quite wide and covers the main basic notions of the scientific research which is based upon mathematical models. We start from vector spaces and Lebesgue integral to reach the frontier of theoretical research such as the study of critical exponents for semilinear elliptic equations and recent problems in fluid dynamics. This long route passes through the theory of Banach and Hilbert spaces, Sobolev spaces, differential equations, Fourier and Laplace transforms, before which we recall some appropriate tools of Complex Analysis. We give all the proofs that have some didactic or applicative interest, while we omit the ones which are too technical or require too high level knowledge. This book has the ambitious purpose to be useful to a broad variety of readers. The first possible beneficiaries are of course the second or third year students of a scientific course of degree: in what follows they will find the topics that are necessary to approach more advanced studies in Mathematics and in other fields, especially Physics and Engineering. This text could be also useful to graduate students who want to start a Ph.D. course: indeed it contains the matter of a multidisciplinary Ph.D. course given by Filippo Gazzola for several years at Politecnico di Milano. Finally, this book could be addressed also to the ones who have already left education far-back but occasionally need to use mathematical tools: we refer both to university professors and their research, and to professionals and designers who want to model a certain phenomenon, but also to the nostalgics of the good old days when they were students. It is precisely for this last type of reader that we have also reported some elementary topics, such as the properties of numerical sets and of the integrals; moreover, every chapter is provided with examples and specific exercises aimed at the involvement of the reader.

Download or read book Library of Congress Catalogs written by Library of Congress and published by . This book was released on 1955 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The National Union Catalog written by and published by . This book was released on 1961 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book National Union Catalog written by and published by . This book was released on 1973 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes entries for maps and atlases.

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Download or read book Library of Congress Catalog written by Library of Congress and published by . This book was released on 1970 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: A cumulative list of works represented by Library of Congress printed cards.

Download or read book The National Union Catalog Pre 1956 Imprints written by and published by . This book was released on 1976 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Architecture Series Bibliography written by and published by . This book was released on 1985 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Annali di matematica pura ed applicata written by and published by . This book was released on 1901 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This journal, the oldest scientific periodical in Italy, publishes articles on virtually any subject of pure and applied mathematics.