Vitor M.A. Leitão

Recovering the source term in a linear diffusion problem by the method of fundamental solutions

This work considers the detection of the spatial source term distribution in a multidimensional linear diffusion problem with constant (and known) thermal conductivity. This work can be physically associated with the detection of non-homogeneities in a material that are inclusion sources in a heat conduction problem. The uniqueness of the inverse problem is discussed in terms of classes of identifiable sources. Numerically, we propose to solve these inverse source problems using fundamental solution-based methods, namely an extension of the method of fundamental solutions to domain problems. Several examples are presented and the numerical reconstructions are discussed.

Applications of multi-region Trefftz-collocation to fracture mechanics

This paper describes the application of a multi-region indirect Trefftz method in the analysis of two-dimensional linear elastic fracture mechanics problems. The technique allows for the use of subregions with the necessary continuity conditions being appropriately enforced at the interfaces. The system of equations is assembled by collecting all the required terms from the collocation of the displacement and the traction equations at a number of boundary points. Numerical tests were carried out which included the stress intensity factor computation for cracked plates (centre and edge cracks) and for a notched plate.

Advances in meshfree techniques

Preface A Global-Local Approach for the Construction of Enrichment Functions for the Generalized HIM and Its Application to Three-Dimensional Cracks, by C. Armando Duarte, Dae-Jin Kim and Ivo Babusca Study of Some Optimal XFEM Type Methods, by Elie Chahine, Patrick Laborde, Julien Pommier Yves Renard and Michel Salaun, by Generalized Finite Element Method in Mixed Variational Formulation: A Study of Convergence and Solvability, by W. Gois and S.P.B. Proenca Stability in Lagrangian and Semi-Lagrangian Reproducing Kernel Discretizations Using Nodal Integration in Nonlinear Solid Mechanics, by Jiun-Shyan Chen and Youcai Wu Simulation of Forming Processes by the cr-Shapes-Based Natural Element Method, by I. Alfaro, E. Cueto, F Chinesta and M. Doblare New Advances in Meshless Methods: Coupling Natural Element and Moving Least Squares Techniques, by F Chinesta, J. Yvonnet, P. Villon, P Breitkopf P Joyot, I. Alfaro and E. Cueto Eliminating Shear-Locking in Meshless Methods: A Critical Overview and a New Framework for Structural Theories, by Carlos Tiago and Vitor MA. Leitao FEMJSPH Coupling Techniques for High Velocity Impact Simulations, by Levent Aktay and Alastair F Johnson On the Construction of Mass Conservative and Meshless Adaptive Particle Advection Methods, by Armin Iske Spectral-Like Accuracy in Space of a Meshless Vortex Method, by LA. Barba A Hybrid Meshless/Spectral-Element Method for the Shallow Water Equations on the Sphere, by Christopher D. Blakely Iterated Approximate Moving Least Squares Approximation,by Gregory E. Fasshauer and Jack G. Zhang A Kansa Type Method Using Fundamental Solutions Applied to Elliptic PDEs, by Carlos J.S. Alves and Svilen S. Valtchev From Global to Local Radial Basis Function Collocation Method for Transport Phenomena, by Bozidar Sarler Computation of Static Deformations and Natural Frequencies of Shear Deformable Plates by an RBF-Pseudospectral Method with an Optimal Shape Parameter, by A.J.M. Ferreira andG.E. Fasshauer Author Index Subject Index.

On the implementation of a multi-region Trefftz-collocation formulation for 2-D potential problems

Abstract In this paper a formulation based on the Indirect Trefftz Method for the analysis of two-dimensional potential problems is described. This technique allows for the use of subregions (the necessary conditions being appropriately enforced at the interfaces), thus improving the expected accuracy of then numerical solution for domains which are not appropriately modelled by a single-region. The system of equations is assembled by collecting all the required terms from the collocation of the potential and the flux equations at a number of boundary points. Alternative schemes for the position of these points are proposed. Numerical tests of two-dimensional potential problems are presented, together with a discussion on the use of different solvers.

Elastoplastic simulation of fatigue crack growth: Dual boundary element formulation

Abstract In this paper an algorithm is proposed for the analysis of cracks growin in a stable manner in ductile materials. This algorithm uses a recently presented formulation of the elastoplastic dual boundary element method (EPDBEM) by Leitao et al. , which allows for crack problems to be modelled within a single-region formulation. The elastoplastic behaviour is modelled through the use of an approximation for the plastic component of the strain tensor on the region expected to yield. This region is discretized with internal quadratic, quadrilateral and/or triangular cells. This new algorithm for stable crack growth is based on the release of pairs of elements, which are assumed to be in contact prior to the formation of the crack. Crack-face contact is simulated by directly enforcing compatibility and equilibrium conditions between the surfaces of the crack. Elastoplastic fracture parameters, namely J -type integrals, can be calculated at all stages of the fatigue crack growth process. An example of the application of this technique is presented.

Eliminating Shear-Locking in Meshless Methods: A Critical Overview and a New Framework for Structural Theories

Meshfree methods are recent additions to the family of numerical techniques for the solution of partial differential equations. Issues like shear locking are yet to be clarified. Earlier expectations that these methods would be free from locking problems, were not confirmed. In particular, it is shown that, for the case of moderately thick structural beam and plate theories, if the same approximation is used for both displacement and rotation(s), then shear locking occurs.

Trefftz collocation for frequency domain elastodynamic problems

A Trefftz collocation method is proposed for the analysis of two-dimensional elastodynamic problems subjected to steady-state time-harmonic loads. Trefftz methods are characterized by the use of a superposition of a number of actual solutions of the homogeneous part of governing equations, the so-called T(Trefftz)-functions. This leads to high quality approximations where the unknowns are the weights of each of the T-functions considered. The unknowns are found by matching the approximations to the boundary conditions by following a standard collocation approach. The numerical implementation of the method is briefly described and results are obtained for two anti-plane elastodynamic problems. The results compare quite favourably to other results available in the literature whereby Galerkin and collocation boundary element methods were used.

A simple and less-costly integration of meshless Galerkin weak form

Computational efficiency and reliability are the most important requirements for the success of a meshless numerical technique. The efficiency of these methods depends on the proper choice of the interpolation scheme, numerical integration procedures and techniques of imposing the boundary conditions. From all these difficulties, the integration is the most time-consuming part in meshless calculation due to the large number of integration points needed for a sufficiently accuracy of the integration of the weak form. Also, insufficiently accurate numerical integration may lead a deterioration and rank-defieciency in the numerical solution. The difficulty is due to the complexity of the MLS shape functions in an integration domain.