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.

Creep deflection of low-strength reinforced concrete flexural members strengthened with carbon fiber composite sheets

The low-strength concrete is defined as a concrete where the compressive cubic strength is less than 15 MPa. Since the beginning of the last century, many low-strength concrete buildings and bridges have been built all over the world. Being short of deeper study, composite sheets are prohibited in strengthening of low-strength reinforced concrete members (CECS 146; ACI 440). Moreover, there are few relevant information about the long-term behavior and durability of strengthened RC members. This fact undoubtedly limits the use of the composite materials in the strengthening applications, therefore, it is necessary to study the behaviours of low-strength concrete elements strengthened with composite materials (FRP) for the preservation of historic constructions and innovation in the strengthening technology. Deformability is one of criteria in the design of concrete structures, and this for functionality, durability and aesthetics reasons. Civil engineer possibly encounters more deflection problems in the structural design than any other type of problem. Many materials common in structural engineering such as wood, concrete and composite materials, suffer creep; if the creep phenomenon is taken into account, checks for serviceability limit state criteria can become onerous, because the creep deformation in these materials is in the same order of magnitude as the elastic deformation. The thesis presents the results of an experimental study on the long-term behavior of low-strength reinforced concrete beams strengthened with carbon fiber composite sheets (CFRP). The work has investigated the accuracy of the long-term deflection predictions made by some analytical procedures existing in literature, as well as by the most widely used design codes (Eurocode 2, ACI-318, ACI-435).

Characterization of a 3D-printed low-cost flexible dielectric material for the realization of innovative WPT wearable applications

The aim of this thesis is to demonstrate that 3D-printing technologies can be considered significantly attractive in the production of microwave devices and in the antenna design, with the intention of making them lightweight, cheaper, and easily integrable for the production of wireless, battery-free, and wearable devices for vital signals monitoring. In this work, a new 3D-printable, low-cost resin material, the Flexible80A, is proposed as RF substrate in the implementation of a rectifying antenna (rectenna) operating at 2.45 GHz for wireless power transfer. A careful and accurate electromagnetic characterization of the abovementioned material, revealing it to be a very lossy substrate, has paved the way for the investigation of innovative transmission line and antenna layouts, as well as etching techniques, possible thanks to the design freedom enabled by 3D-printing technologies with the aim of improving the wave propagation performance within lossy materials. This analysis is crucial in the design process of a patch antenna, meant to be successively connected to the rectifier. In fact, many different patch antenna layouts are explored varying the antenna dimensions, the substrate etchings shape and position, the feeding line technology, and the operating frequency. Before dealing with the rectification stage of the rectenna design, the hot and long-discussed topic of the equivalent receiving antenna circuit representation is addressed, providing an overview of the interpretation of different authors about the issue, and the position that has been adopted in this thesis. Furthermore, two rectenna designs are proposed and simulated with the aim of minimizing the dielectric losses. Finally, a prototype of a rectenna with the antenna conjugate matched to the rectifier, operating at 2.45 GHz, has been fabricated with adhesive copper on a substrate sample of Flexible80A and measured, in order to validate the simulated results.