Overview

The engineering community generally accepts that there exists only a small set of closed-form solutions for simple cases of bars, beams, columns, and plates. Despite the advances in powerful computing and advanced numerical techniques, closed-form solutions remain important for engineering; these include uses for preliminary design, for evaluation of the accuracy of approximate and numerical solutions, and for evaluating the role played by various geometric and loading parameters. Eigenvalues of Inhomogeneous Structures: Unusual Closed-Form Solutions offers the first new treatment of closed-form solutions since the works of Leonhard Euler over two centuries ago. It presents simple solutions for vibrating bars, beams, and plates, as well as solutions that can be used to verify finite element solutions. The closed solutions in this book not only have applications that allow for the design of tailored structures, but also transcend mechanical engineering to generalize into other fields of engineering. Also included are polynomial solutions, non-polynomial solutions, and discussions on axial variability of stiffness that offer the possibility of incorporating axial grading into functionally graded materials. This single-package treatment of inhomogeneous structures presents the tools for optimization in many applications. Mechanical, aerospace, civil, and marine engineers will find this to be the most comprehensive book on the subject. In addition, senior undergraduate and graduate students and professors will find this to be a good supplement to other structural design texts, as it can be easily incorporated into the classroom.

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9780849328923

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It is generally believed that closed-form solutions exist for only a relatively few, very simple cases of bars, beams, columns, and plates. This monograph is living proof that there are, in fact, not just a few such solutions. Even in the current age of powerful numerical techniques and high-speed, large-capacity computers, there are a number of important uses for closed-form solutions:

""This is a most remarkable and thorough review of the efforts that have been made to find closed-form solutions in the vibration and buckling of all manner of elastic rods, beams, columns and plates. The author is particularly, but not exclusively, concerned with variations in the stiffness of structural members. The resulting volume is the culmination of his studies over many years. ""What more can be said about this monumental work, other than to express admiration? The author's solutions to particular problems will be very valuable for testing the validity and accuracy of various numerical techniques. Moreover, the study is of great academic interest, and is clearly a labor of love. The author is to be congratulated on this work, which is bound to be of considerable value to all interested in research in this area."" -- Dr. H.D. Conway, Professor Emeritus, Department of Theoretical and Applied Mechanics, Cornell University ""It is generally believed that closed-form solutions exist for only a relatively few, very simple cases of bars, beams, columns, and plates. This monograph is living proof that there are, in fact, not just a few such solutions. Even in the current age of powerful numerical techniques and high-speed, large-capacity computers, there are a number of important uses for closed-form solutions: for preliminary design (often optimal) as bench-mark solutions for evaluating the accuracy of approximate and numerical solutions to gain more physical insight into the roles played by the various geometric and/or loading parameters ""This book is fantastic. Professor Elishakoff is to be congratulated not only for pulling together a number of solutions from the international literature, but also for contributing a large number of solutions himself. Finally, he has explained in a very interesting fashion the history behind many of the solutions."" -- Dr. Charles W. Bert, Benjamin H. Perkinson Professor Emeritus, Aerospace and Mechanical Engineering, The University of Oklahoma

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Elishakoff, Isaac

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