Experimental and numerical approaches for structural assessment in new footbridge designs (SFRSCC–GFPR hybrid structure)

Within the civil engineering field, the use of the Finite Element Method has acquired a significant importance, since numerical simulations have been employed in a broad field, which encloses the design, analysis and prediction of the structural behaviour of constructions and infrastructures. Nevertheless, these mathematical simulations can only be useful if all the mechanical properties of the materials, boundary conditions and damages are properly modelled. Therefore, it is required not only experimental data (static and/or dynamic tests) to provide references parameters, but also robust calibration methods able to model damage or other special structural conditions. The present paper addresses the model calibration of a footbridge bridge tested with static loads and ambient vibrations. Damage assessment was also carried out based on a hybrid numerical procedure, which combines discrete damage functions with sets of piecewise linear damage functions. Results from the model calibration shows that the model reproduces with good accuracy the experimental behaviour of the bridge.

A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation

A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for one- dimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.

Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field

We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the ‘pseudofermion dynamical theory’ (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents ζτ(k) controlling the singularities for both the longitudinal  and transverse (τ = t) dynamical structure factors for the whole momentum range  , in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.

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.

Development of procedures for the design, optimization and manufacturing of customized orthopaedic and trauma implants: Geometrical/anatomical modelling from 3D medical imaging

Tese de Doutoramento (Programa Doutoral em Engenharia Biomédica)

Factoriality and the pin-reutenauer procedure

We consider implicit signatures over finite semigroups determined by sets of pseudonatural numbers. We prove that, under relatively simple hypotheses on a pseudovariety V of semigroups, the finitely generated free algebra for the largest such signature is closed under taking factors within the free pro-V semigroup on the same set of generators. Furthermore, we show that the natural analogue of the Pin-Reutenauer descriptive procedure for the closure of a rational language in the free group with respect to the profinite topology holds for the pseudovariety of all finite semigroups. As an application, we establish that a pseudovariety enjoys this property if and only if it is full.

Blow-up and finite time extinction for p(x, t)-curl systems arising in electromagnetism

"Available online 22 March 2016"

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

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

Lösbarkeit und Finite-Elemente-Approximation eines mathematischen Modells für die Strömung in Magnetfluiddichtungen

Navier-Stokes-Gleichungen, Gleitrandbedingung, Konvektions-Diffusions-Gleichung, Finite-Elemente-Methode, Mehrgitterverfahren, Fehlerabschätzung, Iterative Entkopplung

Stabilized finite element methods applied to transient convection-diffusion-reaction and population balance equations

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

Representations of lattice point sets : theory, algorithms, applications

Magdeburg, Univ., Fak. für Mathematik, Habil.-Schr., 2006

Finite element analysis for flows in chemical reactors

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

Numerical analysis of finite volume schemes for population balance equations

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

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

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

Difference sets from projective planes

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013