Search results for "Galerkin Method"
showing 10 items of 71 documents
Strain gradient elasticity within the symmetric BEM formulation
2014
The symmetric Galerkin Boundary Element Method is used to address a class of strain gradient elastic materials featured by a free energy function of the (classical) strain and of its (first) gradient. With respect to the classical elasticity, additional response variables intervene, such as the normal derivative of the displacements on the boundary, and the work-coniugate double tractions. The fundamental solutions - featuring a fourth order partial differential equations (PDEs) system - exhibit singularities which in 2D may be of the order 1/ r 4 . New techniques are developed, which allow the elimination of most of the latter singularities. The present paper has to be intended as a resear…
Equivalent-Single-Layer discontinuous Galerkin methods for static analysis of multilayered shells
2021
Abstract An original formulation for the elastic analysis of multilayered shells is presented in this work. The key features of the formulation are: the representation of the shell mean surface via a generic system of curvilinear coordinates; the unified treatment of general shell theories via an Equivalent-Single-Layer approach based on the through-the-thickness expansion of the covariant components of the displacement field; and an Interior Penalty discontinuous Galerkin scheme for the solution of the set of governing equations. The combined use of these features enables a high-order solution of the multilayered shell problem. Several numerical tests are presented for isotropic, orthotrop…
High-order simulation scheme for active particles driven by stress boundary conditions
2020
Abstract We study the dynamics and interactions of elliptic active particles in a two dimensional solvent. The particles are self-propelled through prescribing a fluid stress at one half of the fluid-particle boundary. The fluid is treated explicitly solving the Stokes equation through a discontinuous Galerkin scheme, which allows to simulate strictly incompressible fluids. We present numerical results for a single particle and give an outlook on how to treat suspensions of interacting active particles.
Statistical Modeling for the Flow of Short Fibers Composites
1994
Numerical results are given for the flow of fiber composites modelled as suspensions of non spherical particles. In this framework, because the many particles rotate, their state of orientation is described with a statistical approach. We used these methods to compute coupled solutions in which the orientation of the particles is affected by the flow and the flow itself depends on the orientation of the particles. The computation methods involve an augmented lagrangian approach and a streamline upwind petrov galerkin formulation to solve the convective orientation equation.
CAD of complex passive devices composed of arbitrarily shaped waveguides using Nyström and BI-RME methods
2004
In this paper, a novel computer-aided design (CAD) tool of complex passive microwave devices in waveguide technology is proposed. Such a tool is based on a very efficient integral-equation analysis technique that provides a full-wave characterization of discontinuities between arbitrarily shaped waveguides defined by linear, circular, and/or elliptical arcs. For solving the modal analysis of such arbitrary waveguides, a modified version of the well-known boundary integral-resonant-mode expansion (BI-RME) method using the Nyström approach, instead of the traditional Galerkin version of the method of moments, is proposed, thus providing significant savings on computational costs and implement…
Internal spring distribution for quasi brittle fracture via Symmetric Boundary Element Method
2009
Abstract In this paper the symmetric boundary element formulation is applied to the fracture mechanics problems for quasi brittle materials . The basic aim of the present work is the development and implementation of two discrete cohesive zone models using Symmetric Galerkin multi-zone Boundary Elements Method . The non-linearity at the process zone of the crack will be simulated through a discrete distribution of nodal springs whose generalized (or weighted) stiffnesses are obtainable by the cohesive forces and relative displacements modelling. This goal is reached coherently with the constitutive relation σ − Δ u that describes the interaction between mechanical and kinematical quantities…
Accurate Multilayered Shell Buckling Analysis via the Implicit-Mesh Discontinuous Galerkin Method
2022
A novel formulation for the linear buckling analysis of multilayered shells is presented. High-order equivalent-single-layer shell theories based on the through-the-thickness expansion of the covariant components of the displacement field are employed. The novelty of the formulation regards the governing equations solution via implicit-mesh discontinuous Galerkin method. It is a high-order accurate numerical technique based on a discontinuous representation of the solution among the mesh elements and on the use of suitably defined boundary integrals to enforce the continuity of the solution at the inter-element interfaces as well as the boundary conditions. Owing to its discontinuous natur…
Dynamics analysis of distributed parameter system subjected to a moving oscillator with random mass, velocity and acceleration
2002
Abstract The problem of calculating the response of a distributed parameter system excited by a moving oscillator with random mass, velocity and acceleration is investigated. The system response is a stochastic process although its characteristics are assumed to be deterministic. In this paper, the distributed parameter system is assumed as a beam with Bernoulli–Euler type analytical behaviour. By adopting the Galerkin's method, a set of approximate governing equations of motion possessing time-dependent uncertain coefficients and forcing function is obtained. The statistical characteristics of the deflection of the beam are computed by using an improved perturbation approach with respect t…
A symmetric Galerkin BEM for plate bending analysis
2009
Abstract The Symmetric Galerkin Boundary Element Method is employed in thin plate bending analysis in accordance with the Love–Kirchhoff kinematical assumption. The equations are obtained through the stationary conditions of the total potential energy, written for a plate whose boundary is discretized in boundary elements. Since the matrix coefficients are made up as double integrals with high order singularities, a strategy is shown to compute these coefficients in closed form. Furthermore, in order to model the kinematical discontinuities and to weight the mechanical quantities along the boundary elements, the Lagrangian quadratic shape functions, rather than C 1 type (spline, Hermitian),…
Discontinuous Galerkin semi-Lagrangian method for Vlasov-Poisson
2011
We present a discontinuous Galerkin scheme for the numerical approximation of the one-dimensional periodic Vlasov-Poisson equation. The scheme is based on a Galerkin-characteristics method in which the distribution function is projected onto a space of discontinuous functions. We present comparisons with a semi-Lagrangian method to emphasize the good behavior of this scheme when applied to Vlasov-Poisson test cases. Une méthode de Galerkin discontinu est proposée pour l’approximation numérique de l’équation de Vlasov-Poisson 1D. L’approche est basée sur une méthode Galerkin-caractéristiques où la fonction de distribution est projetée sur un espace de fonctions discontinues. En particulier, …