The First International Conference on Finite Elements in Biomechanics was held in Tucson, Ariz. February 18-20, 1980. This conference, which was sponsored by the United States National Science Foundation and the College of Engineering of the University of Arizona, contained about 60 presentations which covered a wide variety of finite element applications in biomechanics. The conference organizers (editors of this book) invited the authors of 18 of these presentations to prepare manuscripts for publication in this book. The book starts with the introduction of a clinician's view and then a finite element specialist view of the method. G. T. Rab presents his views on the finite element method, special model problems with biologic materials, and problem of clinician-engineer collaboration. O. C. Zienkiewicz and D. W. Kelley then present the basic outline of the finite element process, its historical development, present trends, and its impact on the field of bioengineering. The remainder of the book presents a diverse array of finite element applications in biomechanics. Two chapters address the mechanics of biologic fluid flow. Normal mechanics of capillary flow, arterial flow, blood cell deformation, and peristaltic flow are discussed. Special problems of pulsatile flow through a stenosis and through an aneurysm are also considered. The application of the finite element method in soft tissue mechanics is demonstrated in an introductory chapter and a subsequent series of chapters dealing with the mechanics of the lungs and heart. Analyses of the role of interfacial forces in lung deformation, lung parenchyma, and the heart's left ventricle are discussed. The remainder of the book, and by far the most indepth treatment of a subject, is devoted to the finite element method applied to solid mechanics, predominantly orthopaedic problems. After a survey chapter on the role of finite element models in orthopaedics, subsequent chapters address specific orthopaedic applications. An application of the finite method to external fracture fixation devices is followed by studies of stress-morphology relationships in trabecular bone, stress distributions in the femoral head, intervertebral disk function, the mechanics of artificial joint fixation, cement-bone failure, the function of femoral endoprostheses, and head and neck injury mechanisms. This book assembles the highlights of what was a very interesting biomechanics conference. The presentations chosen for inclusion in this book survey well the diverse application of the finite element method to biomechanics problems and illustrate important problems unique to finite element modeling of biologic systems. The reader is introduced to problems associated with biologic variability, growth and maturation, nonlinear materials, anisotropic materials, incompressible materials, viscoelastic materials, and structural pathology. The book as a whole serves as an excellent introduction for the experienced finite element programmer to the applications and special problems of biologic sy...

The focus of this paper is the optimization of complex multi-parameter systems. We consider systems in which the objective function is not known explicitly, and can only be evaluated through computationally intensive numerical simulation or through costly physical experiments. The objective function may also contain many local extrema which may be of interest. Given objective function values at a scattered set of parameter values, we develop a response surface model that can dramatically reduce the required computation time for parameter optimization runs. The response surface model is developed using radial basis functions, producing a model whose objective function values match those of the original system at all sampled data points. Interpolation to any other point is easily accomplished and generates a model which represents the system over the entire parameter space. This paper presents the details of the use of radial basis functions to transform scattered data points, obtained from a complex continuum mechanics simulation of explosive materials, into a response surface model of a function over the given parameter space. Response surface methodology and radial basis functions are discussed in general and are applied to a global optimization problem for an explosive oil well penetrator.

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This paper considers the optimization of complex multi-parameter systems in which the objective function is not known explicitly, and can only be evaluated either through costly physical experiments or through computationally intensive numerical simulation. Furthermore, the objective function of interest may contain many local extrema. Given a data set consisting of the value of the objective function at a scattered set of parameter values, we are interested in developing a response surface model to reduce dramatically the required computation time for parameter optimization runs.To accomplish these tasks, a response surface model is developed using radial basis functions. Radial basis functions provide a way of creating a model whose objective function values match those of the original system at all sampled data points. Interpolation to any other point is easily accomplished and generates a model which represents the system over the entire parameter space. This paper presents the details of the use

Abstract. Dul~g's equation with sinusoidal forcing produces chaos for certain combinations of the forcing amplitude and frequency. To determine the most chaotic response achieveable for given bounds on the input force, an optimal control problem was investigated to maximize the largest Lyapunov exponent, which in this case also corresponds to maximizing the Kaplan-Yorke Lyapunov fractal dimension. The resulting bang-bang optimal feedback controller yielded a bounded attractor with a positive largest Lyapunov exponent and a fractional Lyapunov dimension, indicating a chaotic strange attractor. Indeed, the largest Lyapunov exponent was approximately twice as large as that achieved with sinusoidal forcing at the same amplitude. However, the resulting attractor is just a stable limit cycle and is not chaotic or fractal at all! This contradicts the basic idea that a bounded attractor with at least one positive Lyapunov exponent must be chaotic and fractal.This article provides details of this chaotic limit cycle paradox and the resolution of the paradox. In particular, for systems of differential equations with only pieeewise differentiable right-hand sides, a jump discontinuity condition must be imposed on the state perturbations in order to compute correct Lyapunov exponents.