Finite integration methods for isospectral flows

In this paper we consider the approximate computation of isospectral flows based on finite integration methods( FIM) with radial basis functions( RBF) interpolation,a new algorithm is developed. Our method ensures the symmetry of the solutions. Numerical experiments demonstrate that the solutions have higher accuracy by our algorithm than by the second order Runge- Kutta( RK2) method.

Numerical simulations of Lamb waves in plates using a semi-analytical finite element method

Magdeburg, Univ., Fak. für Maschinenbau, Diss., 2011

Finite element analysis for flows in chemical reactors

Magdeburg, Univ., Fak. für Mathematik, Diss., 2010

Development of a new isogeometric finite element and its application for Lamb wave based structural health monitoring

Magdeburg, Univ., Fak. für Maschinenbau, Diss., 2012

Finite element simulation of an impinging liquid droplet on a hot solid substrate

Magdeburg, Univ., Fak. für Mathematik, Diss., 2014

Caracteritació de models funcionals d'àmfores romanes mitjançant Finite Element Analysis

Projecte de recerca elaborat a partir d’una estada al Laboratory of Archaeometry del National Centre of Scientific Research “Demokritos” d’Atenes, Grècia, entre juny i setembre 2006. Aquest estudi s’emmarca dins d’un context més ampli d’estudi del canvi tecnològic que es documenta en la producció d’àmfores de tipologia romana durant els segles I aC i I dC en els territoris costaners de Catalunya. Una part d’aquest estudi contempla el càlcul de les propietats mecàniques d’aquestes àmfores i la seva avaluació en funció de la tipologia amforal, a partir de l’Anàlisi d’Elements Finits (AEF). L’AEF és una aproximació numèrica que té el seu origen en les ciències d’enginyeria i que ha estat emprada per estimar el comportament mecànic d’un model en termes, per exemple, de deformació i estrès. Així, un objecte, o millor dit el seu model, es dividit en sub-dominis anomenats elements finits, als quals se’ls atribueixen les propietats mecàniques del material en estudi. Aquests elements finits estan connectats formant una xarxa amb constriccions que pot ser definida. En el cas d’aplicar una força determinada a un model, el comportament de l’objecte pot ser estimat mitjançant el conjunt d’equacions lineals que defineixen el rendiment dels elements finits, proporcionant una bona aproximació per a la descripció de la deformació estructural. Així, aquesta simulació per ordinador suposa una important eina per entendre la funcionalitat de ceràmiques arqueològiques. Aquest procediment representa un model quantitatiu per predir el trencament de l’objecte ceràmic quan aquest és sotmès a diferents condicions de pressió. Aquest model ha estat aplicat a diferents tipologies amforals. Els resultats preliminars mostren diferències significatives entre la tipologia pre-romana i les tipologies romanes, així com entre els mateixos dissenys amforals romans, d’importants implicacions arqueològiques.

Simulación de fluidos inmiscibles con el Particle Finite Element Method (PFEM)

Proyecto de investigación realizado a partir de una estancia en el Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC), Argentina, entre febrero y abril del 2007. La simulación numérica de problemas de mezclas mediante el Particle Finite Element Method (PFEM) es el marco de estudio de una futura tesis doctoral. Éste es un método desarrollado conjuntamente por el CIMEC y el Centre Internacional de Mètodos Numèrics en l'Enginyeria (CIMNE-UPC), basado en la resolución de las ecuaciones de Navier-Stokes en formulación Lagrangiana. El mallador ha sido implementado y desarrollado por Dr. Nestor Calvo, investigador del CIMEC. El desarrollo del módulo de cálculo corresponde al trabajo de tesis de la beneficiaria. La correcta interacción entre ambas partes es fundamental para obtener resultados válidos. En esta memoria se explican los principales aspectos del mallador que fueron modificados (criterios de refinamiento geométrico) y los cambios introducidos en el módulo de cálculo (librería PETSc, algoritmo predictor-corrector) durante la estancia en el CIMEC. Por último, se muestran los resultados obtenidos en un problema de dos fluidos inmiscibles con transferencia de calor.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Development and experimental validation of a finite element model of total ankle replacement.

Total ankle replacement remains a less satisfactory solution compared to other joint replacements. The goal of this study was to develop and validate a finite element model of total ankle replacement, for future testing of hypotheses related to clinical issues. To validate the finite element model, an experimental setup was specifically developed and applied on 8 cadaveric tibias. A non-cemented press fit tibial component of a mobile bearing prosthesis was inserted into the tibias. Two extreme anterior and posterior positions of the mobile bearing insert were considered, as well as a centered one. An axial force of 2kN was applied for each insert position. Strains were measured on the bone surface using digital image correlation. Tibias were CT scanned before implantation, after implantation, and after mechanical tests and removal of the prosthesis. The finite element model replicated the experimental setup. The first CT was used to build the geometry and evaluate the mechanical properties of the tibias. The second CT was used to set the implant position. The third CT was used to assess the bone-implant interface conditions. The coefficient of determination (R-squared) between the measured and predicted strains was 0.91. Predicted bone strains were maximal around the implant keel, especially at the anterior and posterior ends. The finite element model presented here is validated for future tests using more physiological loading conditions.

Nonlinear Finite Element Study of Piles in Integral Abutment Bridges, HR-227, Part 2, 1982

The highway departments of the states which use integral abutments in bridge design were contacted in order to study the extent of integral abutment use in skewed bridges and to survey the different guidelines used for analysis and design of integral abutments in skewed bridges. The variation in design assumptions and pile orientations among the various states in their approach to the use of integral abutments on skewed bridges is discussed. The problems associated with the treatment of the approach slab, backfill, and pile cap, and the reason for using different pile orientations are summarized in the report. An algorithm based on a state-of-the-art nonlinear finite element procedure previously developed by the authors was modified and used to study the influence of different factors on behavior of piles in integral abutment bridges. An idealized integral abutment was introduced by assuming that the pile is rigidly cast into the pile cap and that the approach slab offers no resistance to lateral thermal expansion. Passive soil and shear resistance of the cap are neglected in design. A 40-foot H pile (HP 10 X 42) in six typical Iowa soils was analyzed for fully restrained pile head and pinned pile head. According to numerical results, the maximum safe length for fully restrained pile head is one-half the maximum safe length for pinned pile head. If the pile head is partially restrained, the maximum safe length will lie between the two limits. The numerical results from an investigation of the effect of predrilled oversized holes indicate that if the length of the predrilled oversized hole is at least 4 feet below the ground, the vertical load-carrying capacity of the H pile is only reduced by 10 percent for 4 inches of lateral displacement in very stiff clay. With no predrilled oversized hole, the pile failed before the 4-inch lateral displacement was reached. Thus, the maximum safe lengths for integral abutment bridges may be increased by predrilling. Four different typical Iowa layered soils were selected and used in this investigation. In certain situations, compacted soil (> 50 blow count in standard penetration tests) is used as fill on top of natural soil. The numerical results showed that the critical conditions will depend on the length of the compacted soil. If the length of the compacted soil exceeds 4 feet, the failure mechanism for the pile is similar to one in a layer of very stiff clay. That is, the vertical load-carrying capacity of the H pile will be greatly reduced as the specified lateral displacement increases.

Finite Element Analysis of Electrically Excited Quartz Tuning Fork Devices

Quartz Tuning Fork (QTF)-based Scanning Probe Microscopy (SPM) is an important field of research. A suitable model for the QTF is important to obtain quantitative measurements with these devices. Analytical models have the limitation of being based on the double cantilever configuration. In this paper, we present an electromechanical finite element model of the QTF electrically excited with two free prongs. The model goes beyond the state-of-the-art of numerical simulations currently found in the literature for this QTF configuration. We present the first numerical analysis of both the electrical and mechanical behavior of QTF devices. Experimental measurements obtained with 10 units of the same model of QTF validate the finite element model with a good agreement.

An alternative finite element formulation for determination of streamlines in two-dimensional problems

It is well known that the numerical solutions of incompressible viscous flows are of great importance in Fluid Dynamics. The graphics output capabilities of their computational codes have revolutionized the communication of ideas to the non-specialist public. In general those codes include, in their hydrodynamic features, the visualization of flow streamlines - essentially a form of contour plot showing the line patterns of the flow - and the magnitudes and orientations of their velocity vectors. However, the standard finite element formulation to compute streamlines suffers from the disadvantage of requiring the determination of boundary integrals, leading to cumbersome implementations at the construction of the finite element code. In this article, we introduce an efficient way - via an alternative variational formulation - to determine the streamlines for fluid flows, which does not need the computation of contour integrals. In order to illustrate the good performance of the alternative formulation proposed, we capture the streamlines of three viscous models: Stokes, Navier-Stokes and Viscoelastic flows.