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Galerkin Approach (galerkin + approach)

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Engineering	100%

Selected Abstracts

Computational aspects in 2D SBEM analysis with domain inelastic actions

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2010
T. Panzeca
Abstract The Symmetric Boundary Element Method, applied to structures subjected to temperature and inelastic actions, shows singular domain integrals. In the present paper the strong singularity involved in the domain integrals of the stresses and tractions is removed, and by means of a limiting operation, this traction is evaluated on the boundary. First the weakly singular domain integral in the Somigliana Identity (S.I.) of the displacements is regularized and the singular integral is transformed into a boundary one using the Radial Integration Method; subsequently, using the differential operator applied to the displacement field, the S.I. of the tractions inside the body is obtained and through a limit operation its expression is evaluated on the boundary. The latter operation makes it possible to substitute the strongly singular domain integral in a strongly singular boundary one, defined as a Cauchy Principal Value, with which the related free term is associated. The expressions thus obtained for the displacements and the tractions, in which domain integrals are substituted by boundary integrals, were utilized in the Galerkin approach, for the evaluation in closed form of the load coefficients connected to domain inelastic actions. This strategy makes it possible to evaluate the load coefficients avoiding considerable difficulties due to the geometry of the solid analyzed; the obtained coefficients were implemented in the Karnak.sGbem calculus code. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Meshfree simulation of failure modes in thin cylinders subjected to combined loads of internal pressure and localized heat

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2008
Dong Qian
Abstract This paper focuses on the non-linear responses in thin cylindrical structures subjected to combined mechanical and thermal loads. The coupling effects of mechanical deformation and temperature in the material are considered through the development of a thermo-elasto-viscoplastic constitutive model at finite strain. A meshfree Galerkin approach is used to discretize the weak forms of the energy and momentum equations. Due to the different time scales involved in thermal conduction and failure development, an explicit,implicit time integration scheme is developed to link the time scale differences between the two key mechanisms. We apply the developed approach to the analysis of the failure of cylindrical shell subjected to both heat sources and internal pressure. The numerical results show four different failure modes: dynamic fragmentation, single crack with branch, thermally induced cracks and cracks due to the combined effects of pressure and temperature. These results illustrate the important roles of thermal and mechanical loads with different time scales. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A new hybrid velocity integration method applied to elastic wave propagation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2008
Zhiyun Chen
Abstract We present a novel space,time Galerkin method for solutions of second-order time-dependent problems. By introducing the displacement,velocity relationship implicitly, the governing set of equations is reformulated into a first-order single field problem with the unknowns in the velocity field. The resulting equation is in turn solved by a time-discontinuous Galerkin approach (Int. J. Numer. Anal. Meth. Geomech. 2006; 30:1113,1134), in which the continuity between time intervals is weakly enforced by a special upwind flux treatment. After solving the equation for the unknown velocities, the displacement field quantities are computed a posteriori in a post-processing step. Various numerical examples demonstrate the efficiency and reliability of the proposed method. Convergence studies with respect to the h - and p -refinement and different discretization techniques are given. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Accuracy of Galerkin finite elements for groundwater flow simulations in two and three-dimensional triangulations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2001
Christian Cordes
Abstract In standard finite element simulations of groundwater flow the correspondence between hydraulic head gradients and groundwater fluxes is represented by the stiffness matrix. In two-dimensional problems the use of linear triangular elements on Delaunay triangulations guarantees a stiffness matrix of type M. This implies that the local numerical fluxes are physically consistent with Darcy's law. This condition is fundamental to avoid the occurrence of local maxima or minima, and is of crucial importance when the calculated flow field is used in contaminant transport simulations or pathline evaluation. In three spatial dimensions, the linear Galerkin approach on tetrahedra does not lead to M -matrices even on Delaunay meshes. By interpretation of the Galerkin approach as a subdomain collocation scheme, we develop a new approach (OSC, orthogonal subdomain collocation) that is shown to produce M -matrices in three-dimensional Delaunay triangulations. In case of heterogeneous and anisotropic coefficients, extra mesh properties required for M -stiffness matrices will also be discussed. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Design of nonlinear observers with approximately linear error dynamics using multivariable Legendre polynomials

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2006
Joachim Deutscher
Abstract This paper presents a numerical approach to the design of nonlinear observers by approximate error linearization. By using a Galerkin approach on the basis of multivariable Legendre polynomials an approximate solution to the singular PDE of the observer design technique proposed by Kazantzis and Krener (see (Syst. Control Lett. 1998; 34:241,247; SIAM J. Control Optim. 2002; 41:932,953)) is determined. It is shown that the L2 -norm of the remaining nonlinearity in the resulting error dynamics can be made small on a specified multivariable interval in the state space. Furthermore, a linear matrix equation is derived for determining the corresponding change of co-ordinates and output injection such that the proposed design procedure can easily be implemented in a numerical software package. A simple example demonstrates the properties of the new numerical observer design. Copyright © 2006 John Wiley & Sons, Ltd. [source]