ISOMAXENT · Development of a design-through-analysis methodology based on a coupled isogemetrcic-maximum entropy approach

Development of a design-through-analysis methodology based on a coupled isogemetrcic-maximumentropy approach

Although Computer Aided Design (CAD) and Numerical Analysis have usually been two detached disciplines, a lot of effort has been made over the last few years to seek a tighter integration. The recent development of Isogeometric Analysis (IGA) was one of the main achievement in this direction. The key idea of IGA is to use for the Analysis the same basis functions employed in CAD, which in most of the cases are non-uniform rational B-splines (NURBS). However, their tensor product nature poses some limitations in the trivariate volume parametrization of complex shapes and in local refinement, operations not needed for CAD but particularly important for Analysis. The project aimed at developing a coupled approach where IGA is blended with Maximum Entropy meshless approximants to overcome to such limitations, which prevents IGA to fully develop outside of the academic world into industry, and thus to create a design-through-analysis methodology with many potential industrial applications. On implementing the action, the blending theory previously developed by the Researcher and the Supervisor in 2D was extended to the 3D case. While the extension to watertight NURBS geometries with conforming patches was straightforward, the case of complex trimmed multi-patch geometries appeared significantly challenging. Therefore, a collocation approach based on high order Maxent approximants was developed, allowing the direct resolution of differential problems on a grid of points adapted to the boundary. The proposed framework was applied to the simulation of different types of problems and its applicability to industrial relevant cases was proved by solving high-scale problems with a computational time in the same order of that required by standard finite element methodologies. The Researcher considered also the use of smooth surface approximants for mechanobiology and focused on the specific case of the intestinal crypt mechanics, where important contributions to the state of the art were found.

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