High-impact dynamic-response analysis of nonlinear structures

Program predicts expected deformations and stresses in nonlinear simple geometric structures subjected to high-impact loading. Technique is based on node-wise predictor-corrector approach and requires moderate computer storage and run time for most problems. Program extends to include physical and geometrical nonlinearities

Geometric optics and boundary layers for Nonlinear Schrodinger equations

We justify supercritical geometric optics in small time for the defocusing semiclassical Nonlinear Schrodinger Equation for a large class of non-necessarily homogeneous nonlinearities. The case of a half-space with Neumann boundary condition is also studied.Comment: 44 page

Nonlinear flap-lag-extensional vibrations of rotating, pretwisted, preconed beams including Coriolis effects

The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes

Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric scattering transform on manifolds. Similar to the Euclidean scattering transform, the geometric scattering transform is based on a cascade of wavelet filters and pointwise nonlinearities. It is invariant to local isometries and stable to certain types of diffeomorphisms. Empirical results demonstrate its utility on several geometric learning tasks. Our results generalize the deformation stability and local translation invariance of Euclidean scattering, and demonstrate the importance of linking the used filter structures to the underlying geometry of the data.Comment: 35 pages; 3 figures; 2 tables; v3: Revisions based on reviewer comment

A potential for Generalized Kahler Geometry

We show that, locally, all geometric objects of Generalized Kahler Geometry can be derived from a function K, the "generalized Kahler potential''. The metric g and two-form B are determined as nonlinear functions of second derivatives of K. These nonlinearities are shown to arise via a quotient construction from an auxiliary local product (ALP) space.Comment: 12 pages, contribution to "Handbook of pseudo-Riemannian Geometry and Supersymmetry

Program for analysis of nonlinear equilibrium and stability (PANES)

PANES utilizes improved techniques for analysis of structures with material and geometric nonlinearities, including limit point and bifurcations behavior which occurs in buckling and collapse problems. Incremental loading, Newton-Raphson iteration, and higher order methods are used in program

Efficient multi-scale modelling of path dependent problems – complas 2017

With growing capabilities of computers use of multi-scale methods for detailed analysis of response with respect to material and geometric nonlinearities is becoming more relevant. In this paper focus is on MIEL (mesh-in-element) multi-scale method and its implementation with AceGen and AceFEM based on analytical sensitivity analysis. Such implementation enables efficient multi-scale modelling, consistency and quadratic convergence also for two-level path following methods for the solution of path dependent problems

Nonlinear bending-torsional vibration and stability of rotating, pretwisted, preconed blades including Coriolis effects

The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by comparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined

Study of solution procedures for nonlinear structural equations

A method for the redution of the cost of solution of large nonlinear structural equations was developed. Verification was made using the MARC-STRUC structure finite element program with test cases involving single and multiple degrees of freedom for static geometric nonlinearities. The method developed was designed to exist within the envelope of accuracy and convergence characteristic of the particular finite element methodology used