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.

Influence of additives on the performance of a PVDF membrane

The field of use of membranes is wide and ranges from the automotive industry to biomedical uses. Many formulations and compositions find a niche where they are able to improve efficiency, running cost and quality of the product. The aim of this research is to expand GVS’s product portfolio introducing a new membrane formulation. A series of additives were researched and evaluated, adding them to the membrane solutions, which were then cast and characterised using techniques like Scanning Electron Microscopy (SEM), poroscopy, FT-IT ATR and measurements like Water Break Through (WBT), Air Flow (AF), thickness. This study ultimately focused on one additive, which effect on the membranes was studied in various compositions. Interesting insights were also collected on the stability of the polymer solutions over time, which was found to change the membrane properties significantly, mainly affecting airflow and water breakthrough. Properties of the membranes were studied to find possible correlations to the amount of additive. The additive seems however to change the membrane porometry considerably depending on the time of immersion in the water bath. A new procedure to yield uniform unsupported polymeric membranes for tensile tests was developed. The additive was found to reduce elongation at break and decrease tensile strength of the membranes, possibly hinting toward plasticization of the product.

Dynamic resolution of alpha-substituted dihydrocinnamic aldehydes. A new asymmetric synthesis of pharmaceutically important amine building blocks.

Crystallization-induced diastereoisomer transformation (CIDT) was successfully employed in the enantioselective synthesis of 2-alkyl-3-aryl-propan-1-amines. These products are seen as potentially useful building blocks in the field of asymmetric organic chemistry, notably for pharmaceutically relevant compounds. The procedure was based on a recently reported protocol for deracemization of dihydrocinnamic aldehydes in which enantiomerically enriched 1-(amino(phenyl)methyl)naphthalen-2-ol (Betti base) is employed as a resolving agent. Additionally, fenpropimorph, a biologically active substance which contains the 2-alkyl-3-aryl-propan-1-amine moiety was synthetized, as an attempt to assess the usefulness of the enantiomerically enriched amines.