Search results for "Galerkin method"
showing 10 items of 71 documents
A symmetric Galerkin boundary/domain element method for finite elastic deformations
2000
Abstract The Symmetric Galerkin Boundary Element Method (SGBEM) is reformulated for problems of finite elasticity with hyperelastic material and incompressibility, using fundamental solutions related to a (fictitious) homogeneous isotropic and compressible linear elastic material. The proposed formulation contains, besides the standard boundary integrals, domain integrals which account for the problem's nonlinearities through some (fictitious) initial strain and stress fields required to satisfy appropriate “consistency” equations. The boundary/domain integral equation problem so obtained is shown to admit a stationarity principle (a consequence of the Hu-Washizu one), which covers a number…
Electromagnetic Scattering by a Strip Grating with Plane-Wave Three-Dimensional Oblique Incidence by Means of Decomposition into E-Type and H-Type Mo…
1993
A numerical algorithm to analyze the plane-wave three-dimensional oblique incidence on a strip grating is presented. Electromagnetic field is decomposed into vector Floquet harmonics of the E-type and H-type modes. To impose boundary conditions on the incident, reflected and transmitted waves, two integral equations of Fredholm of first kind are obtained. These equations are solved numerically with the standard Galerkin procedure, and the convergence of the algorithm is examined numerically. Since the superficial current near the edges of a conducting strip have been taken into account, the computational algorithm shows a fast convergence. Results are compared with other numerical results a…
Convergence of Boobnov-Galerkin Method Exemplified
2004
In this Note, Boobnov–Galerkin’s method is proved to converge to an exact solution for an applied mechanics problem. We address in detail the interrelation of Boobnov–Galerkin method and the exact solution in the beam deflection problems. Namely, we show the coincidence of these two methods for clamped–clamped boundary conditions, using an alternative set of functions proposed by Filonenko-Borodich.12 Received 25 February 2003; accepted for publication 13 March 2004. Copyright c 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to th…
Finite-Element Modeling of Floodplain Flow
2000
A new methodology for a robust solution of the diffusive shallow water equations is proposed. The methodology splits the unknowns of the momentum and continuity equations into one kinematic and one parabolic component. The kinematic component is solved using the slope of the water level surface computed in the previous time-step and a zero-order approximation of the water head inside the mass-balance area around each node of the mesh. The parabolic component is found by applying a standard finite-element Galerkin procedure, where the source terms can be computed from the solution of the previous kinematic problem. A simple 1D case, with a known analytical solution, is used to test the accur…
Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods
2022
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the governing equations of elastodynamics, written using a first-order hyperbolic momentum-strain formulation…
Frictionless contact-detachment analysis: iterative linear complementarity and quadratic programming approaches.
2012
The object of the paper concerns a consistent formulation of the classical Signorini’s theory regarding the frictionless contact problem between two elastic bodies in the hypothesis of small displacements and strains. The employment of the symmetric Galerkin boundary element method, based on boundary discrete quantities, makes it possible to distinguish two different boundary types, one in contact as the zone of potential detachment, called the real boundary, the other detached as the zone of potential contact, called the virtual boundary. The contact-detachment problem is decomposed into two sub-problems: one is purely elastic, the other regards the contact condition. Following this method…
A robust and efficient method for obtaining the complex modes in inhomogeneously filled waveguides
2003
In this paper, we present a computational simulation of the complex wave propagation in inhomogeneously filled waveguides with lossless and lossy dielectrics. We use a biorthonormal-basis method as a numerical technique. The behavior of complex modes in different waveguides whose characterization with other methods involves some difficulties is analyzed. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 218–222, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10875
Shear-Thinning in Oligomer Melts—Molecular Origins and Applications
2021
We investigate the molecular origin of shear-thinning in melts of flexible, semiflexible and rigid oligomers with coarse-grained simulations of a sheared melt. Entanglements, alignment, stretching and tumbling modes or suppression of the latter all contribute to understanding how macroscopic flow properties emerge from the molecular level. In particular, we identify the rise and decline of entanglements with increasing chain stiffness as the major cause for the non-monotonic behaviour of the viscosity in equilibrium and at low shear rates, even for rather small oligomeric systems. At higher shear rates, chains align and disentangle, contributing to shear-thinning. By performing simulations …
Elastoplastic analysis by active macro-zones with linear kinematic hardening and von Mises materials.
2014
In this paper a strategy to perform elastoplastic analysis with linear kinematic hardening for von Mises materials under plane strain conditions is shown. The proposed approach works with the Symmetric Galerkin Boundary Element Method applied to multidomain problems using a mixed variables approach, to obtain a more stringent solution. The elastoplastic analysis is carried out as the response to the loads and the plastic strains, the latter evaluated through the self-equilibrium stress matrix. This matrix is used both, in the predictor phase, for trial stress evaluation and, in the corrector phase, for solving a nonlinear global system which provides the elastoplastic solution of the active…
Approximate survival probability determination of hysteretic systems with fractional derivative elements
2018
Abstract A Galerkin scheme-based approach is developed for determining the survival probability and first-passage probability of a randomly excited hysteretic systems endowed with fractional derivative elements. Specifically, by employing a combination of statistical linearization and of stochastic averaging, the amplitude of the system response is modeled as one-dimensional Markovian Process. In this manner the corresponding backward Kolmogorov equation which governs the evolution of the survival probability of the system is determined. An approximate solution of this equation is sought by employing a Galerkin scheme in which a convenient set of confluent hypergeometric functions is used a…