Newton's method: A link between continuous and discrete solutions of nonlinear problems

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions

Homotopy hyperbolic 3-manifolds are hyperbolic

This paper introduces a rigorous computer-assisted procedure for analyzing hyperbolic 3-manifolds. This procedure is used to complete the proof of several long-standing rigidity conjectures in 3-manifold theory as well as to provide a new lower bound for the volume of a closed orientable hyperbolic 3-manifold

Buckling of imperfect cylinders under axial compression

Donnell equations, Newton method, and numerical solution applied to buckling of imperfect cylinders under axial compressio

The stability of shallow spherical shells under concentrated load

Effect of load area on deformation of clamped spherical cap and behavior of transition from axisymmetric to asymmetric deflection shape

Buckling of cylindrical shell end closures by internal pressure

Buckling of cylindrical shell end closures by internal pressur

Solution of the symmetric eigenproblem AX=lambda BX by delayed division

Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity

Modal analysis of a computer disk drive

The normal (real) modes of a Winchester type hard disk drive were determined in the frequency range 0-2200hz. Two methods of analysis were used in order to allow cross-correlation of the results. Experimental modal analysis was performed using Structural Measurement Systems\u27 (SMS) Modal 3.0 analysis system and the requisite experimental hardware. A finite element analysis was also performed using MSC/NASTRAN; the NASTRAN model was created using the PATRAN pre-processing program. In order to alleviate the complications associated with matching the structural mounting conditions, a free-free analysis was performed using NASTRAN, and a light string was used to free mount the test specimen for the experimental work. The two analyses showed a one-to-one correspondence of modes; both showed 15 modes in the frequency range. Deviations of the NASTRAN natural frequencies from the experimentally determined natural frequencies ranged from -22 percent to +11.7 percent. Of the 15 modes, 10 showed deviation magnitudes of 10 percent or less, and 6 of the 15 were below 5 percent. Mode shape correlation was performed solely by observation. Errant DOFs in the experimental mode shapes made correlation difficult for several of the modes. In particular, the modes which showed higher frequency deviation (in excess of 10 percent) did not yield exact mode shape correlation although the primary deflection patterns were similar

Lenna Lowe Yost, temperance, and the ratification of the woman suffrage amendment by West Virginia

This thesis is a biography of West Virginia native Lenna Lowe Yost and her role in two important reform causes---temperance and woman suffrage. It explores Yost\u27s life and political accomplishments in both regional and national venues, progressing from her childhood, through her early activism, and culminating with the passage of the national woman suffrage amendment. During the Progressive Era, as Yost reached the apex of her career as an indispensable state leader, she had to navigate between divisions in the suffrage movement as well as local conflicts between prohibitionists and suffragists. In these movements Lenna Yost proved herself to be a skilled organizer and influential reformer, whose fight for the betterment of women\u27s and children\u27s lives opened the door for women nationally to become politically active. This study strives to place Yost\u27s work in West Virginia in a national context, similar to the efforts of women in more progressive states of the era