This paper focuses on the design of a dedicated P1 function space to model elliptic boundary value problem on a manifold embedded in a space of higher dimension. Using the traces of the linear P1 shape functions, it introduces an algorithm to reduce the function space into an equivalent space having the same properties than a P1 Lagrange approximation. Convergence

This paper focuses on the design of a stable Lagrange multiplier space dedicated to enforce Dirichlet boundary conditions on embedded boundaries of any dimension. It follows a previous paper in a series of two, on the topic of embedded solids of any dimension within the context of the extended finite element method. While the first paper is devoted to the design of a dedicated P1 function space to solve elliptic equations defined on manifolds of codimension one or two (curves in 2D and surfaces in 3D, or curves in 3D), the general treatment of Dirichlet boundary conditions, in such a setting, remains to be addressed. This is the aim of this second paper. A new algorithm is introduced to build a stable Lagrange multiplier space from the traces of the shape functions defined on the background mesh. It is general enough to cover: (i) boundary value problems investigated in the first paper (with, for instance, Dirichlet boundary conditions defined along a line in a 3D mismatching mesh); but also (

Identified in the European strategy as a key enabling technology, Additive Manufacturing (AM) has a great potential for industries to reshape, improve and optimize product life cycle, with reduced environmental footprint such as material waste in production. Allowing to meet structural and multi-disciplinary requirements with complex freeform design at a much lower weight than high constrained conventional manufacturing, AM can benefit to numerous space applications. Beside manufacturing process development, software and process control are becoming absolutely necessary to support digitalization of industrial workflow. Dedicated tools such as Computer Aided Design (CAD), Computer Aided Engineering (CAE) and Computer Aided Manufacturing (CAM) were introduced in the digital manufacturing chain; however, their development was driven by standard manufacturing processes. Therefore, appropriate design methods for AM must emerge in a fully integrated end-to-end solution to foster and support the growth and competitiveness of AM. In order to support industrialization of AM, the European Space Agency has selected the Design4AM project, based on a strong partnership between Siemens and Sonaca, for “Development of Design Methods for AM including CAD Design, Optimization, FEM Analysis and Manufacturing features”. On one hand, the project aims at combining within a comprehensive end-to-end process, topology optimization, seamless CAD data flows and predictive process simulation in the Siemens’ NX™ and Simcenter™ environments. On the other hand, the integration of dedicated industrial design workflow within the enhanced Siemens Digital Innovation Platform is validated on a relevant ESA space application provided by Sonaca.