Isogeometric methods for simulation and optimization

Isogeometric analysis (IGA) is the concept of unifying CAD-like geometry descriptions and the numerical discretization of partial differential equations by using a common parameterization in terms of spline functions such as B-Splines, NURBS, T-Splines, etc. This close connection of geometry and discretization can eliminate the time-consuming mesh generation step of traditional finite element analysis, significantly increase the accuracy or reduce the computational effort due to the smoothness of spline functions, and facilitates a straight-forward integration of design, simulation and optimization through a consistent parameterization of shape and material design variables.

At CPS, we develop isogeometric finite element and collocation methods for applications in structural and continuum mechanics, as well as multiphysics problems. We integrate them into seamless workflows for design, simulation, optimization and fabrication for various applications.

Projects and research activities

Isogeometric design optimization of a cantilever beam and a lattice structure
Isogeometric design optimization of a cantilever beam and a lattice structure

Collocation methods approximate the solution of the strong form of a differential equation and thus require smooth shape functions for the discretization. This can be easily achieved by using splines in the framework of isogeometric analysis. Over recent years, we have developed an isogeometric collocation framework for geometrically exact 3D beams, which can be applied for the simulation of beams and beam structures subject to large deformations, including contacts and dynamics. Using mixed methods, locking phenomena are avoided and inelastic (elasto-visco-plastic) material behavior can be investigated. Furthermore, geometric and material design optimization as well as shape optimization can be applied to tailor the mechanical behavior of beam structures.

These methods are successfully integrated into design, simulation, optimization and fabrication workflows for the 3D printing of lattice structures, 4D printing of temperature-responsive structures with shape-memory-effect, as well as 3D knitted functional textiles. Furthermore, they are also at the core of multiscale simulation frameworks and used for the homogenization of the effective behaviors of lattice structures and textiles.

Contacts: Oliver Weeger

Virtual image correlation for the IGA-beam simulation of a foam
Virtual image correlation for the IGA-beam simulation of a foam

In collaboration with INSA Toulouse, we are developing virtual image correlation methods that enable the generation of spline-based beam representations with varying cross-sections directly from image data, e.g., from CT or MRI scans. Using these approaches, isogeometric twins of 3D printed lattices and foam-like structures can be obtained, which are directly suitable for computational analysis and optimization.

Contacts: Oliver Weeger

In collaboration with the Mechanics of Functional Materials group at TU Darmstadt, we are developing geometrically exact and continuum 3D beam formulations for the efficient modeling of the interaction of mechanical and chemical phenomena in battery microstructures. Using isogeometric finite element and collocation methods, these beam models will be used for the investigation and optimal design for harnessing of instabilities.

This work is funded by the DFG under the project “Microlattice structures for lithium-ion battery electrodes: Chemo-mechanical beam modeling of diffusion-induced instabilities and optimal design”.

Contacts: Juan Alzate

This work is funded by the Graduate School of Excellence Computational Engineering (GSC CE) at TU Darmstadt.

Contacts: Yusuf Elbadry

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