Refined shell elements for the analysis of functionally graded structures

The present paper considers the static analysis of plates and shells made of Functionally Graded Material (FGM), subjected to mechanical loads. Refined models based on the Carrera's Unified Formulation (CUF) are employed to account for grading material variation in the thickness direction. The governing equations are derived from the Principle of Virtual Displacement (PVD) in order to apply the Finite Element Method (FEM). A nine-nodes shell element with exact cylindrical geometry is considered. The shell can degenerate in the plate element by imposing an infinite radius of curvature. The Mixed Interpolation of Tensorial Components (MITC) technique is extended to the CUF in order to contrast the membrane and shear locking phenomenon. Different thickness ratios and orders of expansion for the displacement field are analyzed. The FEM results are compared with both benchmark solutions from literature and the results obtained using the Navier method that provides the analytical solution for simply-supported structures subjected to sinusoidal pressure loads. The shell element based on refined theories of the CUF turns out to be very efficient and its use is mandatory with respect to the classical models in the study of FGM structures

Pseudonymization risk analysis in distributed systems

In an era of big data, online services are becoming increasingly data-centric; they collect, process, analyze and anonymously disclose growing amounts of personal data in the form of pseudonymized data sets. It is crucial that such systems are engineered to both protect individual user (data subject) privacy and give back control of personal data to the user. In terms of pseudonymized data this means that unwanted individuals should not be able to deduce sensitive information about the user. However, the plethora of pseudonymization algorithms and tuneable parameters that currently exist make it difficult for a non expert developer (data controller) to understand and realise strong privacy guarantees. In this paper we propose a principled Model-Driven Engineering (MDE) framework to model data services in terms of their pseudonymization strategies and identify the risks to breaches of user privacy. A developer can explore alternative pseudonymization strategies to determine the effectiveness of their pseudonymization strategy in terms of quantifiable metrics: i) violations of privacy requirements for every user in the current data set; ii) the trade-off between conforming to these requirements and the usefulness of the data for its intended purposes. We demonstrate through an experimental evaluation that the information provided by the framework is useful, particularly in complex situations where privacy requirements are different for different users, and can inform decisions to optimize a chosen strategy in comparison to applying an off-the-shelf algorithm

A variable kinematic doubly-curved MITC9 shell element for the analysis of laminated composites

The present article considers the linear static analysis of composite shell structures with double-curvature geometry by means of a shell finite element with variable through-the-thickness kinematic. The refined models used are grouped in the Unified Formulation by Carrera (CUF) and they permit the distribution of displacements and stresses along the thickness of the multilayered shell to be accurately described. The shell element has nine nodes and the mixed interpolation of tensorial components (MITC) method is used to contrast the membrane and shear locking phenomenon. The governing equations are derived from the principle of virtual displacement (PVD) and the finite element method (FEM) is employed to solve them. Cross-ply spherical shells with simply-supported edges and subjected to bi-sinusoidal pressure are analyzed. Various laminations, thickness ratios, and curvature ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in the literature and the analytical solutions obtained using the CUF and the Navier's method. From the analysis, one can conclude that the shell element based on the CUF is very efficient and its use is mandatory with respect to the classical models in the study of composite structures. Finally, shells with different lamination, boundary conditions, and loads are also analyzed using high-order layer-wise theories in order to provide FEM benchmark solution

An isogeometric method for the Reissner-Mindlin plate bending problem

We present a new isogeometric method for the discretization of the Reissner-Mindlin plate bending problem. The proposed scheme follows a recent theoretical framework that makes possible to construct a space of smooth discrete deflections $W_h$ and a space of smooth discrete rotations \Rots_h such that the Kirchhoff contstraint is exactly satisfied at the limit. Therefore we obtain a formulation which is natural from the theoretical/mechanical viewpoint and locking free by construction

Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State Constraints

Finite element methods for a model elliptic distributed optimal control problem with pointwise state constraints are considered from the perspective of fourth order boundary value problems