Isogeometric analysis and form finding

Abstract

Recent developments within the design of shells have seen an increased interest in utilizing active bending as form giving procedure [1]. This enables complex structures to be built from simple off-the-shelf materials. However, forming bending-active structures is highly dependent on the material properties, which makes the design process reliant on either physical testing or digital simulations. An associated problem with the simulation of this behavior is the lack of integration between modeling and analysis in conventional simulation techniques, a crucial concern since the final design is always an equilibrium shape with requirements on both structural and spatial integrity. IsoGeometric Analysis (IGA) is a method that aims to bridge precisely that gap between analysis and design, making it a suitable method for bending active structural design. This thesis explores an approach to the modeling and digital design of actively bent shells using the implementation of nonlinear IGA. Further on, two different ways of controlling the geometry, either by following the process forward and predicting the outcome or tracing it backwards during the construction procedure are proposed. Following the process forwards returns an implicitly controlled shell geometry through stepwise displacement of the boundaries of a flat sheet. However, as a design approach, one appealing strategy is to explicitly control the final geometry by a backwards tracing. This allows the designer to start from a desired outcome and instead tailor the stiffness to approximate this desired form. The procedure is tested in a case study where a combination of both forward prediction and backwards tracing is included. Both processes apply the Kirchhoff-Love shell theory [27] and uses the total Lagrangian formulation for the nonlinear computations