Classical and Advanced Theories of Thin Structures


Book Description

The book presents an updated state-of-the-art overview of the general aspects and practical applications of the theories of thin structures, through the interaction of several topics, ranging from non-linear thin-films, shells, junctions, beams of different materials and in different contexts (elasticity, plasticity, etc.). Advanced problems like the optimal design and the modeling of thin films made of brittle or phase-transforming materials will be presented as well.




Beam Structures


Book Description

Beam theories are exploited worldwide to analyze civil, mechanical, automotive, and aerospace structures. Many beam approaches have been proposed during the last centuries by eminent scientists such as Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc. Most of these models are problem dependent: they provide reliable results for a given problem, for instance a given section and cannot be applied to a different one. Beam Structures: Classical and Advanced Theories proposes a new original unified approach to beam theory that includes practically all classical and advanced models for beams and which has become established and recognised globally as the most important contribution to the field in the last quarter of a century. The Carrera Unified Formulation (CUF) has hierarchical properties, that is, the error can be reduced by increasing the number of the unknown variables. This formulation is extremely suitable for computer implementations and can deal with most typical engineering challenges. It overcomes the problem of classical formulae that require different formulas for tension, bending, shear and torsion; it can be applied to any beam geometries and loading conditions, reaching a high level of accuracy with low computational cost, and can tackle problems that in most cases are solved by employing plate/shell and 3D formulations. Key features: compares classical and modern approaches to beam theory, including classical well-known results related to Euler-Bernoulli and Timoshenko beam theories pays particular attention to typical applications related to bridge structures, aircraft wings, helicopters and propeller blades provides a number of numerical examples including typical Aerospace and Civil Engineering problems proposes many benchmark assessments to help the reader implement the CUF if they wish to do so accompanied by a companion website hosting dedicated software MUL2 that is used to obtain the numerical solutions in the book, allowing the reader to reproduce the examples given in the book as well as to solve other problems of their own www.mul2.com Researchers of continuum mechanics of solids and structures and structural analysts in industry will find this book extremely insightful. It will also be of great interest to graduate and postgraduate students of mechanical, civil and aerospace engineering.




Stability and Vibrations of Thin-Walled Composite Structures


Book Description

Stability and Vibrations of Thin-Walled Composite Structures presents engineering and academic knowledge on the stability (buckling and post buckling) and vibrations of thin walled composite structures like columns, plates, and stringer stiffened plates and shells, which form the basic structures of the aeronautical and space sectors. Currently, this knowledge is dispersed in several books and manuscripts, covering all aspects of composite materials. The book enables both engineers and academics to locate valuable, up-to-date knowledge on buckling and vibrations, be it analytical or experimental, and use it for calculations or comparisons. The book is also useful as a textbook for advanced-level graduate courses. - Presents a unified, systematic, detailed and comprehensive overview of the topic - Contains contributions from leading experts in the field - Includes a dedicated section on testing and experimental results




Shell-like Structures


Book Description

The book presents mathematical and mechanical aspects of the theory of plates and shells, applications in civil, aero-space and mechanical engineering, as well in other areas. The focus relates to the following problems:• comprehensive review of the most popular theories of plates and shells,• relations between three-dimensional theories and two-dimensional ones,• presentation of recently developed new refined plates and shells theories (for example, the micropolar theory or gradient-type theories),• modeling of coupled effects in shells and plates related to electromagnetic and temperature fields, phase transitions, diffusion, etc.,• applications in modeling of non-classical objects like, for example, nanostructures,• presentation of actual numerical tools based on the finite element approach.




Thin Plates and Shells


Book Description

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




Nonlinear Mechanics of Thin-Walled Structures


Book Description

This book presents a hybrid approach to the mechanics of thin bodies. Classical theories of rods, plates and shells with constrained shear are based on asymptotic splitting of the equations and boundary conditions of three-dimensional elasticity. The asymptotic solutions become accurate as the thickness decreases, and the three-dimensional fields of stresses and displacements can be determined. The analysis includes practically important effects of electromechanical coupling and material inhomogeneity. The extension to the geometrically nonlinear range uses the direct approach based on the principle of virtual work. Vibrations and buckling of pre-stressed structures are studied with the help of linearized incremental formulations, and direct tensor calculus rounds out the list of analytical techniques used throughout the book. A novel theory of thin-walled rods of open profile is subsequently developed from the models of rods and shells, and traditionally applied equations are proven to be asymptotically exact. The influence of pre-stresses on the torsional stiffness is shown to be crucial for buckling analysis. Novel finite element schemes for classical rod and shell structures are presented with a comprehensive discussion regarding the theoretical basis, computational aspects and implementation details. Analytical conclusions and closed-form solutions of particular problems are validated against numerical results. The majority of the simulations were performed in the Wolfram Mathematica environment, and the compact source code is provided as a substantial and integral part of the book.




Higher Gradient Materials and Related Generalized Continua


Book Description

This book discusses recent findings and advanced theories presented at two workshops at TU Berlin in 2017 and 2018. It underlines several advantages of generalized continuum models compared to the classical Cauchy continuum, which although widely used in engineering practice, has a number of limitations, such as: • The structural size is very small. • The microstructure is complex. • The effects are localized. As such, the development of generalized continuum models is helpful and results in a better description of the behavior of structures or materials. At the same time, there are more and more experimental studies supporting the new models because the number of material parameters is higher.




Advances in Predictive Models and Methodologies for Numerically Efficient Linear and Nonlinear Analysis of Composites


Book Description

This book gathers contributions addressing issues related to the analysis of composite structures, whose most relevant common thread is augmented numerical efficiency, which is more accurate for given computational costs than existing methods and methodologies. It first presents structural theories to deal with the anisotropy of composites and to embed multifield and nonlinear effects to extend design capabilities and provide methods of augmenting the fidelity of structural theories and lowering computational costs, including the finite element method. The second part of the book focuses on damage analysis; the multiscale and multicomponent nature of composites leads to extremely complex failure mechanisms, and predictive tools require physics-based models to reduce the need for fitting and tuning based on costly and lengthy experiments, and to lower computational costs; furthermore the correct monitoring of in-service damage is decisive in the context of damage tolerance. The third part then presents recent advances in embedding characterization and manufacturing effects in virtual testing. The book summarizes the outcomes of the FULLCOMP (FULLy integrated analysis, design, manufacturing, and health-monitoring of COMPosite structures) research project.




Theories of Plates and Shells


Book Description

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.




Advanced Topics Of Thin-walled Structures


Book Description

This unique compendium presents some new topics related to thin-walled structures, like beams, plates and shells used in aerospace structures. It highlights their dynamic behaviors and also the correlation between compressive loading and natural frequency to enable a correlation between the two, yielding a valuable non-destructive tool, to predict buckling for thin-walled structures.This useful reference text combines valuable data on metal materials and composite materials together with new adaptive and smart materials like piezoelectricity, shape memory alloys and optic fibers, which form the present state of the art in thin-walled structure domain.