Interactive design using peridynamics: Development of a design tool for the exploration of structurally efficient geometries

Examensarbete för masterexamen
Jonsson, Daniel
Edefors, Gabriel
With an ever-increasing demand on material efficiency, the use of optimization toolsin the design process is becoming a more common practice. Rather than optimizingstructures based on certain criteria, the authors propose an alternative approachwhere the designer interactively can change the geometry and get instant visualfeedback on how this affects the stress field. The particle method peridynamicsoffers a flexible mathematical formulation that allows for shape alterations duringruntime, making it a suitable theory to use for explorative design.The purpose of this thesis is to develop an interactive computational design tool thatcan support the designer in finding structurally efficient and aesthetically appealinggeometries in the early design stages. The tool is to be flexible to allow for a widevariety of solid mechanics problems, with the limitations of isotropic materials intwo dimensions. Furthermore, the designer is to have an active role and interact ina design feedback loop.The implementation is written in C#and exposed as a plugin to Grasshopper®,which runs within the CAD software Rhinoceros®. The theory used is a modifiedversion of peridynamics that allows for having varying particle sizes. This makes itpossible to have more densely packed particles at stress concentrations andboundaries. Furthermore, the underlying theory is tailored to quickly find thestatic solution after changes have been made to the geometry. For this purpose, astable time stepping scheme has been derived along with useful stress measures.The plugin has yielded results that agree well with benchmark solutions and thederived time step is conservative, yet close to the critical value. By using smallparticles on the boundaries and larger particles in the interior, maintainedaccuracy can be achieved for a significantly reduced computational cost.Furthermore, the plugin has been integrated in a parametric truss model to shapethe structural connections. In this setting the tool showed high interactivity as itresponded instantaneously to changes of shape and topology.In conclusion, the plugin effectively augments the skills of the designer and opensup for an alternative, more intuitive, design approach.
Particle Methods, Peridynamics, Smoothed Particle Hydrodynamics,Finite Element Method, Computational Design, Interactive Design, Grasshopper3d
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