The title, “Laminated Composite Doubly-Curved Shell Structures. Differential and Integral Quadrature. Strong Form Finite Elements” 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 numerical results reported in the present volume are compared to the one available in the literature, but also to the ones obtained through several codes based on the Finite Element Method (FEM). Furthermore, an advanced version of the DQ method, termed Strong Formulation Finite Element Method (SFEM), is presented. The SFEM solves the differential equations inside each element in the strong form and implements the mapping technique typical of the FEM.

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.

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.

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.

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.

The broad use of composite materials and shell structural members with complex geometries in technologies related to various branches of engineering has gained increased attention from scientists and engineers for the development of even more refined approaches and investigation of their mechanical behavior. It is well known that composite materials are able to provide higher values of strength stiffness, and thermal properties, together with conferring reduced weight, which can affect the mechanical behavior of beams, plates, and shells, in terms of static response, vibrations, and buckling loads. At the same time, enhanced structures made of composite materials can feature internal length scales and non-local behaviors, with great sensitivity to different staking sequences, ply orientations, agglomeration of nanoparticles, volume fractions of constituents, and porosity levels, among others. In addition to fiber-reinforced composites and laminates, increased attention has been paid in literature to the study of innovative components such as functionally graded materials (FGMs), carbon nanotubes (CNTs), graphene nanoplatelets, and smart constituents. Some examples of smart applications involve large stroke smart actuators, piezoelectric sensors, shape memory alloys, magnetostrictive and electrostrictive materials, as well as auxetic components and angle-tow laminates. These constituents can be included in the lamination schemes of smart structures to control and monitor the vibrational behavior or the static deflection of several composites. The development of advanced theoretical and computational models for composite materials and structures is a subject of active research and this is explored here for different complex systems, including their static, dynamic, and buckling responses; fracture mechanics at different scales; the adhesion, cohesion, and delamination of materials and interfaces.

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.

Veer Surendra Sai University of Technology (VSSUT), Burla is one among the foremost universities of India in the field of higher education, basic and applied research. The foundation of this iconic college was laid in 1956 to cater the maintenance and upkeep of the mighty Hirakud Dam (worlds longest earth dam) at Burla. The university now has sixteen academic departments ion various disciplines in engineering and sciences. The International Conference on Advances in Mechanics and Materials (ICRAMM-2016), was organized at the Veer Surendra Sai University of Technology, Burla, Odisha during 17-18 December, 2016. Over the years, tremendous progress has been made in the fields related to mechanics and materials due to rapid advancements in analytical, experimental and computational facilities. The outcome has immensely benefited the industries, research and academic organizations in numerous ways. The International Conference on Recent Advances in Mechanics and Materials (ICRAMM-2016) will provide a common platform for academicians, engineers, scientists and technologists to come together and discuss the progress made on various aspects of mechanics and materials. Realizing the importance of recent developments in the areas of recent advances in mechanics and materials, the conference ICRAMM 2016, focuses on following major themes: Computational mechanics, Experimental mechanics, Fluid mechanics, Geomechanics, Structural mechanics, Continuum mechanics, Coupled field problems, Structural and Soil Dynamics, Vibration Control, Structural Health Monitoring, Rehabilitation and Retrofitting of structures, Composite Materials, Cement Concrete Composites and Sustainable construction materials. The papers included in this conference proceeding reflect in general the need for emerging technologies and growing interest in structural mechanics and materials to tailor it to meet the requirements for the varying application.

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.

Challenges and Opportunities Selected, peer reviewed papers from the International Conference on Advanced Materials Processing – Challenges and Opportunities (AMPCO 2012), November 2-4, 2012, Roorkee, India