Optimally stiffened thin shell structures in 3D printing.

Thin shell structures have been widely applied in crafts, art, industry, architecture, aerospace, etc. The dilemma in printing thin shell structures is the balance between material efficiency and structural soundness. The use of more material will produce a more solid and sound structure but it takes more time and material to fabricate. On the contrary, a thinner structure is more economical but the object tends to be more fragile or deformable. Therefore the problem of finding an optimal supporting structure is crucial to save printing material consumption while maintaining mechanical performance. To solve the problem, some methods have been proposed such as inserting struts, local thickening, skin-frame structure, grid-shell structure and Voronoi structure. However, these techniques either use traditional finite elements or ignore shell contribution. The advantages of attaching stiffeners seamlessly to skin surface are: • Stiffeners can alleviate interior space compared to insertion of struts or Voronoi structure; • Stiffeners are less likely to cause stress concentration compared to skin- frame structure which connects frame to skin at nodes; • The stiffened plate theory takes stiffeners and surface as a coupled system by adding stiffness contribution of stiffener elements to corresponding plate elements which yields more accurate solution; • The strength or ability to resist bending can be further improved by improving shape of stiffeners. Inspired by these good properties of stiffeners, the research presents three computational methods to automatically generate optimized layout and size of stiffeners: First, the research discretizes the input geometry into a triangular mesh. The faces and edges of the mesh are taken as traditional plate and beam elements respectively. The contributions from stiffeners (beams) are assembled to corresponding plate elements and the coupled system is solved to obtain initial stress field. An optimization framework is proposed to use the initial stress field to guide the layout of stiffeners to follow the flow of stress, and to optimize the shape of stiffeners once the layout is fixed. The disadvantage of this approach is that stiffeners need to align with edges and in order to fulfil this requirement the input mesh has to update iteratively during flow process. To maintain the geometry, the second approach is to formulate the stiffeners using same shape functions from plate elements. This method assembles stiffness contribution from any stiffener within a plate element without re-meshing the triangular mesh. An optimization framework to generate uni- and bi-directional stiffeners using this stiffened element is proposed to reinforce thin shell structures. The intuitive way of distributing stiffeners equally in space is not the best way to create the supporting structure as it does not follow the stress field