Chapter 1. Introduction Chapter 2. Stress and Strain: Important Relationships Chapter 3. The Behavior of Bodies Under Stress Chapter 4. Principles and Analytical Methods Chapter 5. Numerical Methods Chapter 6. Experimental Methods Chapter 7. Tension, Compression, Shear, and Combined Stress Chapter 8. Beams Flexure of Straight Bars Chapter 9. Curved Beams Chapter 10. Torsion Chapter 11. Flat Plates Chapter 12. Columns and Other Compression Members Chapter 13. Shells of Revolution Pressure Vessels Pipes Chapter 14. Bodies under Direct Bearing and Shear Stress Chapter 15. Elastic Stability Chapter 16. Dynamic and Temperature Stresses Chapter 17. Stress Concentration Chapter 18. Fatigue and Fracture Chapter 19. Stresses in Fasteners and Joints Chapter 20. Composite Materials Chapter 21. Solid Biomechanics Appendix A. Properties of a Plane Area Appendix B. Mathematical Formulas and Matrices Appendix C. Glossary Index

Roark's Formulas for Stress and Strain

From the Publisher:
Introduction to Numerical Continuation Methods continues to be useful for researchers and graduate students in mathematics, sciences, engineering, economics, and business looking for an introduction to computational methods for solving a large variety of nonlinear systems of equations. A background in elementary analysis and linear algebra is adequate preparation for reading this book; some knowledge from a first course in numerical analysis may also be helpful.

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Introduction to Numerical Continuation Methods

Models of neural networks are developed from a biological point of view. Small networks are analysed using techniques from dynamical systems. The behaviour of spatially and temporally organized neural fields is then discussed from the point of view of pattern formation. Bifurcation methods, analytic solutions and perturbation methods are applied to these models.

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Neural networks as spatio-temporal pattern-forming systems

The investigation deals with questions relating to the existence of multiple solutions to hydrodynamic problems, especially questions about bifurcations of solutions and about stability. Although the aim is to resolve some of these questions generally, particular reference is made to events observed in the Taylor experiment on Couette flow between rotating cylinders, for which a new rationale is developed. In § 2 certain results for the abstract nonlinear problem of steady motion in a bounded fluid are summarized, including a set of generic properties that can be associated with real flows. In § 3 these results are applied to the interpretation of observable phenomena, and several predictions are made which are open to experimental checks. It is shown that new insights into the Taylor experiment are gained by considering its dependence on two parameters, one the Reynolds number R and the other the length l of the flow domain. Attention is paid to the initial development of cells as R is gradually increased from small values (§3.3), to a hysteresis phenomenon accompanying morphogenesis of the cellular structure at critical values of l (§3.4), and to properties of secondary modes possible above respective critical values of R (§ 3.5). In the appendix some corresponding interpretations are noted for the Benard problem of incipient convective motion.

Bifurcation Phenomena in Steady Flows of a Viscous Fluid. I. Theory

The eigenvalue problem for the Laplace operator in two dimensions is classical in mathematics and physics. Nevertheless, computational methods for estimating the eigenvalues are still of much current interest, particularly in applications to acoustic and electromagnetic waveguides. Although our primary interest is with the computational methods, there are a number of theoretical results on the behavior of the eigenvalues and eigenfunctions that are useful for understanding the methods and, in addition, are of interest in themselves. These results are discussed first and then the various computational methods that have been used to estimate the eigenvalues are reviewed with particular emphasis on methods that give error bounds. Some of the more powerful techniques available are illustrated by applying them to a model problem.

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Eigenvalues of the Laplacian in Two Dimensions

Bifurcation problems are considered where the primary bifurcation points are functions of a parameter $\tau $. It is shown that a multiple bifurcation point, which occurs for $\tau = \tau _0 $, may “split” into two (or more) simple primary bifurcation points and several secondary bifurcation points as $\tau $ varies from $\tau _0 $. These secondary points move along one or more of the primary branches as $\tau $ varies. This is shown to occur for a simple two-degrees-of-freedom system, which is a model for plate and rod buckling. This analysis shows that the splitting occurs in several different and physically significant ways. A new perturbation method is presented for analyzing problems which cannot be explicitly solved. The method is applied to study secondary bifurcations in the axisymmetric buckling of spherical shells. The paper concludes with a brief discussion of some physical problems where this new phenomenon may occur and where the perturbation method may be applicable.

Multiple Eigenvalues Lead to Secondary Bifurcation

A factoring and block elimination method for the fast numerical solution of block five diagonal linear algebraic equations is described. Applications of the method are given for the numerical solution of several boundary-value problems involving the bi- harmonic operator. In particular, 22 eigenvalues and eigenfunctions of the clamped square plate are computed and sketched.

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Block five diagonal matrices and the fast numerical solution of the biharmonic equation

The nonlinear deflections of a thin elastic simply-supported rectangular plate are studied. The plate is deformed by a compressive thrust applied along the short edges. For the boundary value problem considered we prove that the platecannot buckle for thrusts less than or equal to the lowest eigenvalue of the linearized buckling problem. For larger thrusts approximate solutions of the von Karman equations are obtained by an accelerated iteration method. Each iterate is numerically evaluated by a finite difference procedure. Using this method approximate solutions are obtained for thrusts considerably larger than the lowest eigenvalue. These solutions bifurcate from the eigenvalues of the linearized problem. In addition, an asymmetric solution is found which appears to branch from a previously bifurcated solution.The extensive numerical results are used to study the formation of boundary layers and the related problem of the plate’s ultimate load. On the basis of the numerical results, an energy mechanism ...

https://www.jstor.org/stable/pdfplus/2946454.pdf

Nonlinear buckling of rectangular plates

Natural frequencies and modes for the simply supported and the clamped 60° rhombic plate have been obtained numerically.

Free vibrations of rhombic plates and membranes

The first 21 normal modes and corresponding cutoff frequencies are obtained for the E modes of waveguides with regular hexagonal cross-sections. A previously developed numerical method, using inverse iterations, finite differences, and Richardson’s mesh extrapolation procedure, is employed. The inverse iteration method is modified by an orthogonalization procedure to obtain the higher modes. A block factoring method is used to solve the finite difference equations. This combination of numerical techniques yields excellent accuracy and speed of computation.

Louis Bauer

Papers

Multiple Eigenvalues Lead to Secondary Bifurcation

Block five diagonal matrices and the fast numerical solution of the biharmonic equation

Nonlinear buckling of rectangular plates

Free vibrations of rhombic plates and membranes

Cutoff Wavenumbers and Modes of Hexagonal Waveguides