Ivan Hlavacek - Böcker
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3 produkter
3 produkter
1 064 kr
Skickas inom 10-15 vardagar
This book deals with approximation and numerical realization of variational inequalities of elliptic type, having applications in mechanics of solids. Emphasis is devoted to the study of contact problems of elastic bodies and problems of plasticity. The main feature of the book is that problems are treated in all their complexity - from the analysis of the continuous models, existence and uniqueness results, to finite element models and the study of their mutual relation, error estimates, convergence results. Special attention is given to contact problems with friction, where some new results are presented, concerning Coulombs model of friction.
Del 46 - North-Holland Series in Applied Mathematics and Mechanics
Uncertain Input Data Problems and the Worst Scenario Method
Inbunden, Engelska, 2004
1 809 kr
Skickas inom 5-8 vardagar
This book deals with the impact of uncertainty in input data on the outputs of mathematical models. Uncertain inputs as scalars, tensors, functions, or domain boundaries are considered. In practical terms, material parameters or constitutive laws, for instance, are uncertain, and quantities as local temperature, local mechanical stress, or local displacement are monitored. The goal of the worst scenario method is to extremize the quantity over the set of uncertain input data.A general mathematical scheme of the worst scenario method, including approximation by finite element methods, is presented, and then applied to various state problems modeled by differential equations or variational inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling, plate buckling, contact problems in elasticity and thermoelasticity with and without friction, and various models of plastic deformation, to list some of the topics. Dozens of examples, figures, and tables are included.Although the book concentrates on the mathematical aspects of the subject, a substantial part is written in an accessible style and is devoted to various facets of uncertainty in modeling and to the state of the art techniques proposed to deal with uncertain input data.A chapter on sensitivity analysis and on functional and convex analysis is included for the reader's convenience.�Rigorous theory is established for the treatment of uncertainty in modeling� Uncertainty is considered in complex models based on partial differential equations or variational inequalities � Applications to nonlinear and linear problems with uncertain data are presented in detail: quasilinear steady heat flow, buckling of beams and plates, vibration of beams, frictional contact of bodies, several models of plastic deformation, and more �Although emphasis is put on theoretical analysis and approximation techniques, numerical examples are also present�Main ideas and approaches used today to handle uncertainties in modeling are described in an accessible form�Fairly self-contained book
Del 12 - Wiley Series in Bioinformatics
Mathematical and Computational Methods in Biomechanics of Human Skeletal Systems
An Introduction
Inbunden, Engelska, 2011
1 489 kr
Skickas inom 7-10 vardagar
Cutting-edge solutions to current problems in orthopedics, supported by modeling and numerical analysisDespite the current successful methods and achievements of good joint implantations, it is essential to further optimize the shape of implants so they may better resist extreme long-term mechanical demands. This book provides the orthopedic, biomechanical, and mathematical basis for the simulation of surgical techniques in orthopedics. It focuses on the numerical modeling of total human joint replacements and simulation of their functions, along with the rigorous biomechanics of human joints and other skeletal parts. The book includes: An introduction to the anatomy and biomechanics of the human skeleton, biomaterials, and problems of alloarthroplastyThe definition of selected simulated orthopedic problemsConstructions of mathematical model problems of the biomechanics of the human skeleton and its partsReplacement parts of the human skeleton and corresponding mathematical model problemsDetailed mathematical analyses of mathematical models based on functional analysis and finite element methodsBiomechanical analyses of particular parts of the human skeleton, joints, and corresponding replacementsA discussion of the problems of data processing from nuclear magnetic resonance imaging and computer tomographyThis timely book offers a wealth of information on the current research in this field. The theories presented are applied to specific problems of orthopedics. Numerical results are presented and discussed from both biomechanical and orthopedic points of view and treatment methods are also briefly addressed. Emphasis is placed on the variational approach to the investigated model problems while preserving the orthopedic nature of the investigated problems. The book also presents a study of algorithmic procedures based on these simulation models.This is a highly useful tool for designers, researchers, and manufacturers of joint implants who require the results of suggested experiments to improve existing shapes or to design new shapes. It also benefits graduate students in orthopedics, biomechanics, and applied mathematics.