Nonlinear Mechanics Of Thin Walled Structures

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.

Mechanical engineering, an engineering discipline born of the needs of the Industrial Revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face the profound issues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series is a new series, featuring graduate texts and research monographs, intended to address the need for information in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that will cover a broad range of concentrations important to mechanical engineering graduate education and research. We are fortunate to have a distinguished roster of consulting editors, each an expert in one of the areas of concentration. The names of the consult ing editors are listed on page vi. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics of materials, processing, thermal science, and tribology. We are pleased to present Nonlinear Analysis of Thin-Walled Structures by James F. Doyle. Austin, Texas Frederick F. Ling Preface This book is concerned with the challenging subject of the nonlinear static, dynamic, and stability analyses of thin-walled structures. It carries on from where Static and Dynamic Analysis of Structures, published by Kluwer 1991, left off; that book concentrated on frames and linear analysis, while the present book is focused on plated structures, nonlinear analysis, and a greater emphasis on stability analysis.

This volume contains the papers presented at the Third International Conference on Thin-Walled Structures, Cracow, Poland on June 5-7, 2001. There has been a substantial growth in knowledge in the field of Thin-Walled Structures over the past few decades. Lightweight structures are in widespread use in the Civil Engineering, Mechanical Engineering, Aeronautical, Automobile, Chemical and Offshore Engineering fields. The development of new processes, new methods of connections, new materials has gone hand-in-hand with the evolution of advanced analytical methods suitable for dealing with the increasing complexity of the design work involved in ensuring safety and confidence in the finished products. Of particular importance with regard to the analytical process is the growth in use of the finite element method. This method, about 40 years ago, was confined to rather specialist use, mainly in the aeronautical field, because of its requirements for substantial calculation capacity. The development over recent years of extremely powerful microcomputers has ensured that the application of the finite element method is now possible for problems in all fields of engineering, and a variety of finite element packages have been developed to enhance the ease of use and the availability of the method in the engineering design process.

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

Thin-plated structures are used extensively in building construction, automobile, aircraft, shipbuilding and other industries because of a number of favourable factors such as high strength-weight ratio, development of new materials and processes and the availability of efficient analytical methods. This class of structure is made by joining thin plates together at their edges and they rely for their rigidity and strength upon the tremendous stiffness and load-carrying capacity of the flat plates from which they are made. Many of the problems encountered in these structures arise because of the effects of local buckling. The knowledge of various facets of this phenomenon has increased dramatically since the 1960s. Problem areas which were hitherto either too complex for rigorous analysis or whose subtleties were not fully realized have in these years been subjected to intensive study. Great advances have been made in the areas of inelastic buckling. The growth in use of lightweight strong materials, such as fibre-reinforced plastics has also been a contributory factor towards the need for advances in the knowledge of the far post-buckling range. The conference is a sequel to the international conference organised by the University of Strathclyde in December 1996 and this international gathering will provide the opportunity for discussion of recent developments and trends in design of thin-walled structures.

This book covers different topics of nonlinear mechanics in complex structures, such as the appearance of new nonlinear phenomena and the behavior of finite-dimensional and distributed nonlinear systems, including numerous systems directly connected with important technological problems.

This volume contains the papers presented at the Fourth International Conference of Thin-Walled Structures (ICTWS4), and contains 110 papers which, collectively, provide a comprehensive state-of-the-art review of the progress made in research, development and manufacture in recent years in thin-walled structures.The presentations at the conference had representation form 35 different countries and their topical areas of interest included aeroelastic response, structural-acoustic coupling, aerospace structures, analysis, design, manufacture, cold-formed structures, cyclic loading, dynamic loading, crushing, energy absorption, fatigue, fracture, damage tolerance, plates, stiffened panels, plated structures, polymer matrix composite members, sandwich structures, shell structures, thin-walled beams, columns and vibrational response. The range of applications of thin-walled structures has become increasingly diverse with a considerable deployment of thin-walled structural elements and systems being found in a wide range of areas within Aeronautical, Automotive, Civil, Mechanical, Chemical and Offshore Engineering fields. This volume is an extremely useful reference volume for researchers and designers working within a wide range of engineering disciplines towards the design, development and manufacture of efficient thin-walled structural systems.

Nonlinear Mechanics for Composite Heterogeneous Structures applies both classical and multi-scale finite element analysis to the non-linear, failure response of composite structures. These traditional and modern computational approaches are holistically presented, providing insight into a range of non-linear structural analysis problems. The classical methods include geometric and material non-linearity, plasticity, damage and contact mechanics. The cutting-edge formulations include cohesive zone models, the Extended Finite Element Method (XFEM), multi-scale computational homogenization, localization of damage, neural networks and data-driven techniques. This presentation is simple but efficient, enabling the reader to understand, select and apply appropriate methods through programming code or commercial finite element software. The book is suitable for undergraduate studies as a final year textbook and for MSc and PhD studies in structural, mechanical, aerospace engineering and material science, among others. Professionals in these fields will also be strongly benefited. An accompanying website provides MATLAB codes for two-dimensional finite element problems with contact, multi-scale (FE2) and non-linear XFEM analysis, data-driven and machine learning simulations.