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Integration of theoretical developments offers complete description of linear theory of viscoelastic behavior of materials, with theoretical formulations derived from continuum mechanics viewpoint and discussions of problem solving. 1982 edition.
Describes general mathematical modeling of viscoelastic materials as systems with fading memory. Discusses the interrelation between topics such as existence, uniqueness, and stability of initial boundary value problems, variational and extremum principles, and wave propagation. Demonstrates the deep connection between the properties of the solution to initial boundary value problems and the requirements of the general physical principles. Discusses special techniques and new methods, including Fourier and Laplace transforms, extremum principles via weight functions, and singular surfaces and discontinuity waves.
Describes general mathematical modeling of viscoelastic materials as systems with fading memory. Discusses the interrelation between topics such as existence, uniqueness, and stability of initial boundary value problems, variational and extremum principles, and wave propagation. Demonstrates the deep connection between the properties of the solution to initial boundary value problems and the requirements of the general physical principles. Discusses special techniques and new methods, including Fourier and Laplace transforms, extremum principles via weight functions, and singular surfaces and discontinuity waves.
This is a textbook written for use in a graduate-level course for students of mechanics and engineering science. It is designed to cover the essential features of modern variational methods and to demonstrate how a number of basic mathematical concepts can be used to produce a unified theory of variational mechanics. As prerequisite to using this text, we assume that the student is equipped with an introductory course in functional analysis at a level roughly equal to that covered, for example, in Kolmogorov and Fomin (Functional Analysis, Vol. I, Graylock, Rochester, 1957) and possibly a graduate-level course in continuum mechanics. Numerous references to supplementary material are listed throughout the book. We are indebted to Professor Jim Douglas of the University of Chicago, who read an earlier version of the manuscript and whose detailed suggestions were extremely helpful in preparing the final draft. We also gratefully acknowedge that much of our own research work on va ri at i ona 1 theory was supported by the U. S. Ai r Force Offi ce of Scientific Research. We are indebted to Mr. Ming-Goei Sheu for help in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gude for her excellent and painstaking job of typing the manuscript. This revised edition contains only minor revisions of the first. Some misprints and errors have been corrected, and some sections were deleted, which were felt to be out of date.
Prof. W. Z. Chien was born on 9 October, 1912 and 1982 saw the 70th anniversary of his birth. Some of his friends, colleagues, and former students prepared this special volume in honour of his outstanding contribution to the field of mechanics. The volume does not contain contributions from all of his students and friends and for this we apologize. Prof. Chien's family have lived. in Qufangquiao Village, Hongshengli, Wuxi County, Jiangsu Province for generations. Many members of his family have been teachers in this village. When he was 14 years old his father died and for a time it appeared necessary to terminate his education but, fortunately, an uncle, Chien Mu, who later became a very famous historian in China, came to his aid and he was able to continue his studies. In 1931 he took entrance exams and was simultaneously admitted to five prestigious Chinese universities. Of these, he chose to enter Tsing-hau University in Beijing, with major work in physics. He received his baccaulaurate in 1935 and taught at middle school for a time until he was awarded a Sino:'British scholarship to study abroad. In the competition for this award, three of the recipients were in the field of mechanics: Prof. C. C. Lin, Prof. Kuo Yung-huai, and Prof. Chien Wei-zang. All three arrived in Toronto in August, 1940 and entered the Depart ment of Applied Mathematics of the University of Toronto to study under Prof. J. L. Synge.
We three editors of this volume are former Ph. D. students of Professor Mircea Cohn at the University of Waterloo, Canada. Donald Grierson obtained his Ph. D. degree in 1968, Alberto Franchi in 1977, and Paolo Riva in 1988, and as such, we span almost the entire career of Professor Cohn at Waterloo. Even though we graduated during different decades in his life, we share similar views of Mircea Cohn as an educator, researcher and man. Together we recall that he was very firm in his resolve that we get the most out of the education he was facilitating for us. Together we agree that he was inspirational in his desire to have us carry out the very best research work we were capable of. Together we feel particularly fortunate to have had such a dedicated and distinguished individual as Professor Cohn as our Ph. D. research advisor. It is with great pleasure that we ack nowledge him as our mentor and friend. We began in 1989 to plan this volume as a tribute to Professor Cohn on the occasion of his 65th birthday in 1991. Upon contacting his many former students and research associates from around the world, we were not surprised to find that they too shared our feelings of respect and admiration for Mircea Cohn as an educator, researcher and man.
These proceedings contain the papers presented at the Fourth International Conference on Finite Elements in Water Resources, held in June, 1982, at the University of Hannover, Federal Re public of Germany. This Conference continued the successful series of previous conferences held at Princeton University in 1976, at Imperial College in 1978, and at the University of Mississippi in 1980. Since Finite Elements have proved to be a powerful means for analysing water resource problems, the principal objective of the Conference was to provide an exchange of experiences in practical applications of the finite element method and to establish a forum for discussion regarding accuracy, economy, limitations and improvements. Related discretization methods were included within the scope of the Conference. New develop ments in numerical and computational techniques, basic mathe matical formulations, and soft- and hardware aspects were considered to be equally important topics for an exchange of ideas between both theoretically and practically oriented re searchers. The Conference Organizing Committee is very grateful to the many distinguished scientists who attended the Conference, and for their contributions towards the proceedings. This collection of papers in being made available to a wider audience of en gineers and scientists by CML Publications in Southampton, U.K.
Mixing scientific, historic and socio-economic vision, this unique book complements two previously published volumes on the history of continuum mechanics from this distinguished author. In this volume, Gérard A. Maugin looks at the period from the renaissance to the twentieth century and he includes an appraisal of the ever enduring competition between molecular and continuum modelling views. Chapters trace early works in hydraulics and fluid mechanics not covered in the other volumes and the author investigates experimental approaches, essentially before the introduction of a true concept of stress tensor. The treatment of such topics as the viscoelasticity of solids and plasticity, fracture theory, and the role of geometry as a cornerstone of the field, are all explored. Readers will find a kind of socio-historical appraisal of the seminal contributions by our direct masters in the second half of the twentieth century. The analysis of the teaching and research texts by Duhem, Poincaré and Hilbert on continuum mechanics is key: these provide the most valuable documentary basis on which a revival of continuum mechanics and its formalization were offered in the late twentieth century. Altogether, the three volumes offer a generous conspectus of the developments of continuum mechanics between the sixteenth century and the dawn of the twenty-first century. Mechanical engineers, applied mathematicians and physicists alike will all be interested in this work which appeals to all curious scientists for whom continuum mechanics as a vividly evolving science still has its own mysteries.