4,182 research outputs found
Modal interaction in postbuckled plates. Theory
Plates can have more than one buckled solution for a fixed set of boundary conditions. The theory for the identification and the computation of multiple solutions in buckled plates is examined. The theory predicts modal interaction (which is also called change in buckle pattern or secondary buckling) in experiments on certain plates with multiple theoretical solutions. A set of coordinate functions is defined for Galerkin's method so that the von Karman plate equations are reduced to a coupled set of cubic equations in generalized coordinates that are uncoupled in the linear terms. An iterative procedure for solving modal interaction problems is suggested based on this cubic form
A parallel solution for the symmetric Eigenproblem
A completely parallel algorithm for the symmetric eigenproblem AX = Lambda BX is outlined. The algorithm is parallel in the sense that the numerical operations do not occur in a fixed sequence. Therefore, a large number of operations can be programmed to be performed concurrently on a computer with multiple central processing units. The standard symmetric eigenvalue problem AX = Lambda X has the property that the n eigenvalues of the principal submatrix of A of order n are separated by the (n-1) eignvalues of the principal submatrix of order (n-1). The separation property delineated n intervals containing one eigenvalue. Each eigenvalue and corresponding eigenvector can be computed independently. The n eigenproblem calculations can be divided among multiple processing units
Numerical integration of asymptotic solutions of ordinary differential equations
Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration
Application of Newton's method to the postbuckling of rings under pressure loadings
The postbuckling response of circular rings (or long cylinders) is examined. The rings are subjected to four types of external pressure loadings; each type of pressure is defined by its magnitude and direction at points on the buckled ring. Newton's method is applied to the nonlinear differential equations of the exact inextensional theory for the ring problem. A zeroth approximation for the solution of the nonlinear equations, based on the mode shape corresponding to the first buckling pressure, is derived in closed form for each of the four types of pressure. The zeroth approximation is used to start the iteration cycle in Newton's method to compute numerical solutions of the nonlinear equations. The zeroth approximations for the postbuckling pressure-deflection curves are compared with the converged solutions from Newton's method and with similar results reported in the literature
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
Buckling of imperfect cylinders under axial compression
Donnell equations, Newton method, and numerical solution applied to buckling of imperfect cylinders under axial compressio
Buckling of cylindrical shell end closures by internal pressure
Buckling of cylindrical shell end closures by internal pressur
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
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
Tight contact structures and genus one fibered knots
We study contact structures compatible with genus one open book
decompositions with one boundary component. Any monodromy for such an open book
can be written as a product of Dehn twists around dual non-separating curves in
the once-punctured torus. Given such a product, we supply an algorithm to
determine whether the corresponding contact structure is tight or overtwisted.
We rely on Ozsv{\'a}th-Szab{\'o} Heegaard Floer homology in our construction
and, in particular, we completely identify the -spaces with genus one, one
boundary component, pseudo-Anosov open book decompositions. Lastly, we reveal a
new infinite family of hyperbolic three-manifolds with no co-orientable taut
foliations, extending the family discovered in \cite{RSS}.Comment: 30 pages, 10 figures. Added figures, extended result to all
monodromies, and added sections 5 and
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