Search results for "Galerkin method"
showing 10 items of 71 documents
Finite deformation analysis of laminated shell via the discontinuous Galerkin method
2022
In this work, we propose a novel formulation for the large displacements and post-buckling response analysis of laminated composite shell structures. In order to accurately recover the solution in the case of multilayered shells, the covariant components of the displacement field are approximated through the thickness using high-order structural theories. The non-linear two-dimensional total Lagrangian formulation is obtained starting from the Principle of Virtual Displacements for the three-dimensional elasticity assuming a linear constitutive relationship between the second Piola–Kirchhoff stress tensor and the Green-Lagrange strain tensor. The discontinuous Galerkin method is used in com…
IMPLICIT MESH DISCONTINUOUS GALERKIN FOR VARIABLE ANGLE TOW MULTILAYERED PLATES
2018
This works presents a novel computational scheme for variable angle tow (VAT) multilayered plates [1]. The characteristic features of the proposed scheme are the combined use of a discontinuous Galerkin (dG) formulation and an implicitly defined mesh. The formulation is based on the principle of virtual displacements (PVD) and the Equivalent Single Layer (ESL) assumption for the mechanical behavior of the VAT plates [2]. The problem is first placed within the dG framework by suitably introducing an auxiliary variable and by rewriting the set of equations governing ESL VAT plates as a firstorder system of differential equations. Following Arnold et al.[3] and by introducing suitably defined …
TRANSIENT AND FREE-VIBRATION ANALYSIS OF LAMINATED SHELLS THROUGH THE DISCONTINUOUS GALERKIN METHOD
2022
This paper presents a novel formulation for linear transient and free-vibration analysis of laminated shell structures based on Interior Penalty discontinuous Galerkin (DG) methods and variable-order through-the-thickness kinematics, whose combined use allows solving the shell problem with high-order accuracy throughout both the shell thickness and the shell modelling domain. The shell geometry is described via a generic system of curvilinear coordinates using either an analytical or a NURBS-based parametrization of the shell mid surface; the formulation also allows for the presence of cut-outs, which are implicitly represented by means of a level set function. After deriving the governing …
Buckling analysis of multilayered structures using high-order theories and the implicit-mesh discontinuous Galerkin method
2022
This work presents a novel formulation for the linear buckling analysis of multilayered shells. The formulation employs high-order Equivalent-Single-Layer (ESL) shell theories based on the through-the-thickness expansion of the covariant components of the displacement field, whilst the corresponding buckling problem is derived using the Euler’s method. The novelty of the formulation regards the solution of the governing equations, which is obtained via implicit-mesh discontinuous Galerkin (DG) schemes. The DG method 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 integral…
Wavelet-based efficient simulation of electromagnetic transients in a lightning protection system
2003
In this paper, a wavelet-based efficient simulation of electromagnetic transients in a lightning protection systems (LPS) is presented. The analysis of electromagnetic transients is carried out by employing the thin-wire electric field integral equation in frequency domain. In order to easily handle the boundary conditions of the integral equation, semiorthogonal compactly supported spline wavelets, constructed for the bounded interval [0,1], have been taken into account in expanding the unknown longitudinal currents. The integral equation is then solved by means of the Galerkin method. As a preprocessing stage, a discrete wavelet transform is used in order to efficiently compress the Fouri…
BIEM-based variational principles for elastoplasticity with unilateral contact boundary conditions
1998
The structural step problem for elastic-plastic internal-variable materials is addressed in the presence of frictionless unilateral contact conditions. Basing on the BIEM (boundary integral equation method) and making use of deformation-theory plasticity (through the backward-difference method of computational plasticity), two variational principles are shown to characterize the solution to the step problem: one is a stationarity principle having as unknowns all the problem variables, the other is a saddle-point principle having as unknowns the increments of the boundary tractions and displacements, along with the plastic strain increments in the domain. The discretization by boundary and i…
Symmetric Galerkin Boundary Element Methods
1998
This review article concerns a methodology for solving numerically, for engineering purposes, boundary and initial-boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form. The discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager’s sense. As main con…
High-fidelity analysis of multilayered shells with cut-outs via the discontinuous Galerkin method
2021
Abstract A novel numerical method for the analysis of multilayered shells with cut-outs is presented. In the proposed approach, the shell geometry is represented via either analytical functions or NURBS parametrizations , while generally-shaped cut-outs are defined implicitly within the shell modelling domain via a level set function . The multilayered shell problem is addressed via the Equivalent-Single-Layer approach whereby high-order polynomial functions are employed to approximate the covariant components of the displacement field throughout the shell thickness. The shell governing equations are then derived from the Principle of Virtual Displacements of three-dimensional elasticity an…
An Advanced Numerical Model in Solving Thin-Wire Integral Equations by Using Semi-Orthogonal Compactly Supported Spline Wavelets
2003
Abstract—In this paper, the semi-orthogonal compactly sup- ported spline wavelets are used as basis functions for the efficient solution of the thin-wire electric field integral equation (EFIE) in frequency domain. The method of moments (MoM) is used via the Galerkin procedure. Conventional MoM directly applied to the EFIE, leads to dense matrix which often becomes computation- ally intractable when large-scale problems are approached. To overcome these difficulties, wavelets can be used as a basis set so obtaining the generation of a sparse matrix; this is due to the local supports and the vanishing moments properties of the wavelets. In the paper, this technique is applied to analyze elec…
Thresholding projection estimators in functional linear models
2008
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows to get consistency under broad assumptions as well as minimax rates of convergence under additional regularity hypotheses. We also consider the particular case of Sobolev spaces generated by the trigonometric basis which permits to get easily mean squared error of prediction as well as estimators of the derivatives of the regression function. We prove these estimators are minimax and rates of convergence are given for some particular cases.