A new insight in stress recovery tecniques and hessian reconstruction methods

Stress recovery techniques have been an active research topic in the last few years since, in 1987, Zienkiewicz and Zhu proposed a procedure called Superconvergent Patch Recovery (SPR). This procedure is a last-squares fit of stresses at super-convergent points over patches of elements and it leads to enhanced stress fields that can be used for evaluating finite element discretization errors. In subsequent years, numerous improved forms of this procedure have been proposed attempting to add equilibrium constraints to improve its performances. Later, another superconvergent technique, called Recovery by Equilibrium in Patches (REP), has been proposed. In this case the idea is to impose equilibrium in a weak form over patches and solve the resultant equations by a last-square scheme. In recent years another procedure, based on minimization of complementary energy, called Recovery by Compatibility in Patches (RCP) has been proposed in. This procedure, in many ways, can be seen as the dual form of REP as it substantially imposes compatibility in a weak form among a set of self-equilibrated stress fields. In this thesis a new insight in RCP is presented and the procedure is improved aiming at obtaining convergent second order derivatives of the stress resultants. In order to achieve this result, two different strategies and their combination have been tested. The first one is to consider larger patches in the spirit of what proposed in [4] and the second one is to perform a second recovery on the recovered stresses. Some numerical tests in plane stress conditions are presented, showing the effectiveness of these procedures. Afterwards, a new recovery technique called Last Square Displacements (LSD) is introduced. This new procedure is based on last square interpolation of nodal displacements resulting from the finite element solution. In fact, it has been observed that the major part of the error affecting stress resultants is introduced when shape functions are derived in order to obtain strains components from displacements. This procedure shows to be ultraconvergent and is extremely cost effective, as it needs in input only nodal displacements directly coming from finite element solution, avoiding any other post-processing in order to obtain stress resultants using the traditional method. Numerical tests in plane stress conditions are than presented showing that the procedure is ultraconvergent and leads to convergent first and second order derivatives of stress resultants. In the end, transverse stress profiles reconstruction using First-order Shear Deformation Theory for laminated plates and three dimensional equilibrium equations is presented. It can be seen that accuracy of this reconstruction depends on accuracy of first and second derivatives of stress resultants, which is not guaranteed by most of available low order plate finite elements. RCP and LSD procedures are than used to compute convergent first and second order derivatives of stress resultants ensuring convergence of reconstructed transverse shear and normal stress profiles respectively. Numerical tests are presented and discussed showing the effectiveness of both procedures.

Attività enzimatica ed inibizione della tirosin-fosfatasi A (MptpA) di Mycobacterium tuberculosis in funzione del pH

La tubercolosi è una malattia infettiva causata dal batterio patogeno Mycobacterium tuberculosis. Tale micobatterio è in grado di secernere due importanti tirosin-fosfatasi, MptpA e MptpB, che esplicano un importante ruolo come fattori di virulenza permettendo la sopravvivenza del batterio all’interno dell’ospite mediante evasione della risposta immunitaria. In particolare, MptpA è un membro della famiglia delle tirosin-fosfatasi a basso peso molecolare ed è composta da 163 amminoacidi (17,9 kDa). L’enzima impedisce la normale maturazione del fagosoma e la fusione fagosoma-lisosoma, attraverso la defosforilazione della proteina VPS33B, inibendo così la risposta cellulare all’infezione. Obiettivo del seguente lavoro di tesi è stato analizzare il comportamento catalitico di MptpAW152F, variante caratterizzata dalla presenza di un solo triptofano, in funzione del pH. È stata inoltre valutata l’eventuale inibizione dell’attività enzimatica ad opera di alcuni composti naturali, i glucosinolati e di un inibitore di sintesi (L335-M34). Lo studio cinetico effettuato in presenza del substrato fosfotirosina ha evidenziato la presenza di un secondo sito allosterico, adiacente al sito attivo dell’enzima, che influenza l’attività di MptpAW152F. Questo risulta essere un promettente bersaglio per la progettazione di nuovi farmaci ed inibitori selettivi. La valutazione di alcuni tra questi, come l’inibitore sintetico L335-M34 ha riportato risultati promettenti. I saggi di attività in pre-steady-state in funzione del pH e le analisi SPR hanno permesso di indagare ulteriormente l’affinità di legame tra MptpAW152F e la fosfotirosina e di evidenziare il riarrangiamento strutturale dell’enzima da una forma aperta ad una forma chiusa, cataliticamente attiva.