Virtual Work Approach To Mechanical Modeling

This book is centred about the Principle of virtual work and the related method for mechanical modelling. It aims at showing and enhancing the polyvalence and versatility of the virtual work approach in the mechanical modelling process. The virtual work statement is set as the principle at the root of a force modelling method that can be implemented on any geometrical description. After experimentally induced hypotheses have been made on the geometrical parameters that describe the concerned system and subsystems, the method provides a unifying framework for building up consistently associated force models where external and internal forces are introduced through their virtual rates of work. Systems described as three-dimensional, curvilinear or planar continua are considered: force models are established with the corresponding equations of motion; the validation process points out that enlarging the domain of relevance of the model for practical applications calls for an enrichment of the geometrical description that takes into account the underlying microstructure.

Outstanding approach to continuum mechanics. Its high mathematical level of teaching together with abstracts, summaries, boxes of essential formulae and numerous exercises with solutions, makes this handbook one of most complete books in the area. Students, lecturers, and practitioners will find this handbook a rich source for their studies or daily work.

This book evaluates the importance of various historical sources and discusses their role in the creation and transmission of scientific knowledge. It presents an annotated translation of the introductory words given by Johan Ludvig Heiberg to his translation of the works of Archimedes. Further, it offers English translations of and commentaries on selected fundamental works by Ernst Hellinger and Gabrio Piola, which lay the groundwork for the modern theory of advanced materials, and also examines the criteria used to evaluate scientific works.

Presents a Systematic Approach for Modeling Mechanical Models Using Variational Formulation—Uses Real-World Examples and Applications of Mechanical Models Utilizing material developed in a classroom setting and tested over a 12-year period, Computational Solid Mechanics: Variational Formulation and High-Order Approximation details an approach that establishes a logical sequence for the treatment of any mechanical problem. Incorporating variational formulation based on the principle of virtual work, this text considers various aspects of mechanical models, explores analytical mechanics and their variational principles, and presents model approximations using the finite element method. It introduces the basics of mechanics for one-, two-, and three-dimensional models, emphasizes the simplification aspects required in their formulation, and provides relevant applications. Introduces Approximation Concepts Gradually throughout the Chapters Organized into ten chapters, this text provides a clear separation of formulation and finite element approximation. It details standard procedures to formulate and approximate models, while at the same time illustrating their application via software. Chapter one provides a general introduction to variational formulation and an overview of the mechanical models to be presented in the other chapters. Chapter two uses the concepts on equilibrium that readers should have to introduce basic notions on kinematics, duality, virtual work, and the PVW. Chapters three to ten present mechanical models, approximation and applications to bars, shafts, beams, beams with shear, general two- and three-dimensional beams, solids, plane models, and generic torsion and plates. Learn Theory Step by Step In each chapter, the material profiles all aspects of a specific mechanical model, and uses the same sequence of steps for all models. The steps include kinematics, strain, rigid body deformation, internal loads, external loads, equilibrium, constitutive equations, and structural design. The text uses MATLAB® scripts to calculate analytic and approximated solutions of the considered mechanical models. Computational Solid Mechanics: Variational Formulation and High Order Approximation presents mechanical models, their main hypothesis, and applications, and is intended for graduate and undergraduate engineering students taking courses in solid mechanics.

Elastic, Plastic and Yield Design of Reinforced Structures presents a whole set of new results which have been published by the authors over the last 30 years in the field of continuum solid mechanics applied to the analysis and design of reinforced civil engineering structures. The focus is on the development and application of up-scaling/homogenization methods in the design of such composite structures, with a special emphasis on the plastic behavior and ultimate strength of materials. The specificity of the book is highlighted by at least two completely innovative concepts which lie at the very heart of the book’s originality: the elaboration of a fully comprehensive homogenization-based method for the design of reinforced structures (and not only materials), through the study of macroscopic behavior, and the development of a multiphase model for materials reinforced by linear inclusions, which considerably extends the range of applicability of the classical homogenization procedure. Sums up almost thirty years of original research in the field of mechanics applied to the analysis and design of reinforced civil engineering structures Focuses on the application of upscaling/homogenization methods to the design of civil engineering structures Highlights the elaboration of a fully comprehensive homogenization-based method for the design of reinforced structures (and not only materials), through the concept of macroscopic behavior Features development of a multiphase model for materials reinforced by linear inclusions, which considerably extends the range of applicability of the classical homogenization procedure.

Automation in the Virtual Testing of Mechanical Systems: Theories and Implementation Techniques provides a practical understanding of Knowledge-Based Engineering (KBE), an approach that is driving automation in engineering. Companies are using the technology to automate engineering tasks, achieving gains in output, and saving time. This book will be the main source of information available for implementing KBE systems, integrating KBE with the finite element methods, and showing how KBE is used to automate engineering and analysis of mechanical systems. The process of combining KBE with optimization techniques is explored, and the use of software tools is presented in some detail. Features Introduces automation with Knowledge-Based Engineering (KBE) in generic mechanical design Develops a framework for generic mechanism modeling including a library format Explores a KBE environment for generic design automation Includes design cases in KBE Gives a presentation of the interwoven technologies used in modern design environments

Thematerialsusedinmanufacturingtheaerospace,aircraft,automobile,andnuclear parts have inherent aws that may grow under uctuating load environments during the operational phase of the structural hardware. The design philosophy, material selection, analysis approach, testing, quality control, inspection, and manufacturing are key elements that can contribute to failure prevention and assure a trouble-free structure. To have a robust structure, it must be designed to withstand the envir- mental load throughout its service life, even when the structure has pre-existing aws or when a part of the structure has already failed. If the design philosophy of the structure is based on the fail-safe requirements, or multiple load path design, partial failure of a structural component due to crack propagation is localized and safely contained or arrested. For that reason, proper inspection technique must be scheduled for reusable parts to detect the amount and rate of crack growth, and the possible need for repairing or replacement of the part. An example of a fail-sa- designed structure with crack-arrest feature, common to all aircraft structural parts, is the skin-stiffened design con guration. However, in other cases, the design p- losophy has safe-life or single load path feature, where analysts must demonstrate that parts have adequate life during their service operation and the possibility of catastrophic failure is remote. For example, all pressurized vessels that have single load path feature are classi ed as high-risk parts. During their service operation, these tanks may develop cracks, which will grow gradually in a stable manner.