Browsing by Author "Kamat, Manohar P."

Now showing 1 - 7 of 7
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    An Assessment Of Quasi-Newton Sparse Update Techniques For Nonlinear Structural Analysis
    Kamat, Manohar P.; Watson, Layne T.; Vanden Brink, D. J. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1980)
    In this paper an attempt is made to evaluate the performance of a few algorithms for unconstrained minimization of nonlinear functions that exploit sparsity of the Hessians of such functions. The evaluation is centered around large scale, geometrically nonlinear problems of structural analysis in general. In particular, the snap-through response of finite element models of a shallow elastic arch under a concentrated load at the crown is considered. The sensitivity of these algorithms to varying degrees of refinement of these finite element models as well as to the sparsity pattern of the Hessian of the potential surface in question are examined. The paper concludes by making recommendations on the choice of an algorithm based on the scale of the problem and the degree and type of nonlinearity.
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    Experiments with Conjugate Gradient Algorithms for Homotopy Curve Tracking
    Irani, Kashmira M.; Kamat, Manohar P.; Ribbens, Calvin J.; Walker, Homer F.; Watson, Layne T. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1990)
    There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernal of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.
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    Natural frequencies of curved elastic arcs
    Kudva, Jayanth N.; Nayfeh, Ali H.; Kamat, Manohar P. (Acoustical Society of America, 1978-12-01)
    A perturbation analysis is presented for calculating the inextensional natural frequencies of curved elastic arcs. Variation of the radius of curvature along the arc length is accounted for by considering the curvature to be a perturbation from a constant curvature, and utilizing the method of strained parameters. Frequencies thus derived for hinged parabolic arcs demonstrate good agreement with finite element solutions. The analysis could easily be extended to determine the natural frequencies of noncircular curved plates and shells.
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    Numerical-perturbation technique for the transverse vibrations of highly prestressed plates
    Nayfeh, Ali H.; Kamat, Manohar P. (Acoustical Society of America, 1977-01-01)
    Under the usual assumptions of small strains with moderately large rotations, the problem of the transverse vibrations of highly prestressed, nonuniform annular plates is reduced to the solution of the differential equation governing the transverse vibration of the corresponding prestressed membrane subject to modific boundary conditions that account for the effects of bending. The methods of matched asymptotic and/or composite expansions are used to determine these modified boundary conditions. The agreement of the results of both methods with known exact solutions for simple geometries demonstrates the efficiency of this technique when compared with other well-known numerical techniques.
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    Numerical-perturbation technique for the transverse vibrations of highly prestressed plates
    Nayfeh, Ali H.; Kamat, Manohar P. (Acoustical Society of America, 1975)
    Under the usual assumptions of small strains with moderately large rotations, the problem of the transverse vibrations of highly prestressed nonuniform annular plates is reduced to the solution of the differential equation governing the transverse vibration of the corresponding prestressed membrane subject to modified boundary conditions that account for the effects of bending. The method of composite expansions is used to determine these modified boundary conditions. The agreement of the present solution or results with known exact solutions for simple geometries demonstrates the efficiency of this method when compared with other well-known numerical techniques.
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    Preconditioned Conjugate Gradient Algorithms for Homotopy CurveTracking
    Irani, Kashmira M.; Ribbens, Calvin J.; Walker, Homer F.; Watson, Layne T.; Kamat, Manohar P. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1989)
    These are alogorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian Matrices. The HOMPACK alogorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here variants of the conjugate gradient algorithms are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.
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    A Robust Hybrid Algorithm for Computing Multiple Equilibrium Solutions
    Watson, Layne T.; Kamat, Manohar P.; Reaser, Michael H. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1984)
    This paper describes a hybrid method that seeks to combine the efficiency of a quasi-Newton method capable of locating stable and unstable equilibrium configurations with a robust homotopy method that is capable of tracking equilibrium paths with turning points while exploiting symmetry and sparsity of the Jacobian matrices. Numerical results are presented for a shallow arch problem.