An isogeometric finite element formulation for phase transitions on deforming surfaces

This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial differential equations (PDEs) that live on an evolving two-dimensional manifold. For the phase transitions, the PDE is the Cahn-Hilliard equation for curved surfaces, which can be derived from surface mass balance in the framework of irreversible thermodynamics. For the surface deformation, the PDE is the (vector-valued) Kirchhoff-Love thin shell equation. Both PDEs can be efficiently discretized using $C^1$-continuous interpolations without derivative degrees-of-freedom (dofs). Structured NURBS and unstructured spline spaces with pointwise $C^1$-continuity are utilized for these interpolations. The resulting finite element formulation is discretized in time by the generalized-$\alpha$ scheme with adaptive time-stepping, and it is fully linearized within a monolithic Newton-Raphson approach. A curvilinear surface parameterization is used throughout the formulation to admit general surface shapes and deformations. The behavior of the coupled system is illustrated by several numerical examples exhibiting phase transitions on deforming spheres, tori and double-tori.Comment: fixed typos, extended literature review, added clarifying notes to the text, added supplementary movie file

Aerodynamic shape optimization of a HSCT type configuration with improved surface definition

Two distinct parametrization procedures of generating free-form surfaces to represent aerospace vehicles are presented. The first procedure is the representation using spline functions such as nonuniform rational b-splines (NURBS) and the second is a novel (geometrical) parametrization using solutions to a suitably chosen partial differential equation. The main idea is to develop a surface which is more versatile and can be used in an optimization process. Unstructured volume grid is generated by an advancing front algorithm and solutions obtained using an Euler solver. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an automatic differentiator precompiler software tool. Aerodynamic shape optimization of a complete aircraft with twenty four design variables is performed. High speed civil transport aircraft (HSCT) configurations are targeted to demonstrate the process

Integration between Creativity and Engineering in Industrial Design

The objective of the paper is to illustrate which are the key issues today in the industrial design workflow, paying particular attention to the most creative part of the workflow, highlighting those nodes which still make hard the styling activities and giving a brief survey of the researches aimed at smoothing the transfer of the design intent along the whole design cycle and at providing tools even more adhering at the mentality of creative people. Based on the experience gained working in two different European projects, through the collaboration with industrial designers in the automotive and the household supplies fields, a general industrial design workflow will be depicted, highlighting the main differences between the automotive and non-automotive sectors; the problems still present in the design activity will be also illustrated. The paper includes short surveys, in relation to the aesthetic design, in matter of research activities aimed at - identifying the links between shape characteristics of a product and the transmitted emotions - better supporting, in a digital way, the 2D sketching phase and the automatic interpretation and transfer of the 2D sketches into a 3D surface model - improving the 3D Modeling phase