Structural Optimisation for 3D Printing Bespoke Geometries

STRUCTURAL OPTIMISATION FOR 3D PRINTING BESPOKE GEOMETRIES MARYAM HOUDA1 and DAGMAR REINHARDT2 University of Sydney, Australia 1,2 {maryam.houda|dagmar.reinhardt}@sydney.edu.au 1,2 Abstract. Current advances in 3D printing technology enable novel design explorations with the potential to inform printing deposition through generative scripting and structural performance analysis. This paper presents ongoing research that involves three scales of operation; a global geometry for multi-skin cellular mesh densities; localised skin-porosity detailing, and material structural optimisation. Centering on a chair as a test case scenario, the research explores the affordances of a serialised, multi-material 3D printing process in the context of digital instruction, customisation, and material efficiency. The paper discusses two case studies with consecutive optimisation, and outlines the benefits and limitations of 3D printing for structural optimisation and multi-material grading in the additive process. Keywords. 3D Printing; Bespoke Complexity; Digital Instruction; Mass Customisation; Multi-Material Grading; Robotic Deposition; Structural Optimisation. 1. Introduction: Additive Fabrication Introduced with the First Industrial Revolution, factory mass production favoured subtractive processes that require basic tooling and an easy teaching of skills. Constraints in material and assembly processes led to the perfection and permanency of the 20th century assembly line (Pye, 2013), where standardisation tied to productivity boosted economic growth. Ultimately, this adopted form of production resulted in standard part-to-part orthogonal elements, manufactured with readily available stock in factories (Castaneda et al. 2015). On the other hand, 3D printing engages in an economy of a single-production model to produce cost-effective, highly customised forms, directly buildable from a digital model without translation. It is constantly advancing in manufacturing criteria including material advancements (plastics, timber, metals, composites); deposition technologies, ranging from Stereolithography-to-PolyJett methods (Castaneda et al. 2015) and fabrication mechanics (single to multi-extruder nozzles). In the current context of Industry 4.0, 3D printing operates on a localised production scale with a uniform procedure of digital design, structural engineering and manufacturing. Material testing allows for an innovative exploration of design and structural possibilities, specifically printing thermoplastics and composite T. Fukuda, W. Huang, P. Janssen, K. Crolla, S. Alhadidi (eds.), Learning, Adapting and Prototyping, Proceedings of the 23rd International Conference of the Association for Computer-Aided Architectural Design Research in Asia (CAADRIA) 2018, Volume 1, 235-244. © 2018 and published by the Association for Computer-Aided Architectural Design Research in Asia (CAADRIA) in Hong Kong. 236 M. HOUDA AND D. REINHARDT polymers. A continuous application of design-to-production can support designers/manufacturers with a workflow that radically changes manufacturing of bespoke and industrial designs. Figure 1. Varying densities of porosity. 2. Methodology The research explores the advancements and potentials of 3D printing in two iterative case studies for single and multi-material/density extrusion of a full-scaled multi-cellular chair. This works as a prototype for larger architectural implications as the chair investigates internal and external stimuli, such as stress loads, applicable to building design. Inspired by the Panton Chair, the form is explicitly and ergonomically designed from a spline-curve profile to accommodate the human reclining body. It integrates form-finding processes via a digital framework and optimises material through porosity distribution for structural performance. The first case study focuses on generating parametric form and surface detailing where a 3mm thick seamless geometry is localised with a Voronoi pattern in the visual programming environment of Grasshopper. Cellular variables of size and agglomeration of perforating cells are initially coordinated by a primitive stress test using Scan-and-Solve (SNS) for Rhino3D, simulating displacement and indicating areas that require denser cell perforations for structural performance. Rapid prototyping of the mono-material chair is printed with glow-in-the-dark blue PLA using a desktop FlashForge Guider with a single-head extruder, allowing for full fidelity of the digital model. A second case study ratifies the physical prototype and part-to-part challenges of the original form, achieving structural optimisation with multi-material/multi-grade 3D printing, using a dual-head FlashForge Dreamer. It expands from the previous study by integrating structural performance workflows, tested with an empirical study of structurally optimised branch-like geometries inspired by nature, where biomimicry can be seen as a driver for functional performance. STRUCTURAL OPTIMISATION FOR 3D PRINTING BESPOKE GEOMETRIES 237 3. Case Study One: Cellular Strategies for Serialised Modules The first case study focuses on development of a digital framework across three scale of operation: global shape, localised materiality and cellular definition and modelling. The global shape of the chair is defined by three principal parametric-driver-curves, a central distinct curve profile and two symmetrical outer curves. These are subsequently ‘lofted’ to produce a generic surface for the optimisation and surface detailing processes that follow. Figure 2. Digital and Material framework. 3.1. MULTI-CELLULAR DISTRIBUTION Localised materialisation of the surface for both performance and aesthetics, is achieved via bespoke codes developed in Grasshopper. The generic ‘lofted’ form is populated with 1900 randomly-seeded points to allow for a point-cloud analysis of the geometry to be made. This analysis, in combination with more obvious structural prerequisites regarding areas of increased stress in specific load areas, required greater freedom to inform the redistribution of cell points, prior to their conversion to 3D Voronoi cells. Thus, the point distribution can be optimised into a multi-cellular material that varies in porosity and density for structural performance. In this case study, additional points are imported to strengthen the following priority load areas: top rest (25), back rest (280), chair spine (50), spine edges (50), seat edges (50), and foot (35), totalling to 2540 points. To achieve a multi-cellular distribution, a 3D Voronoi diagram is generated from the collection of the 2540 cell points that populate the generic form. Their 238 M. HOUDA AND D. REINHARDT cell openings are offset to create apertures that vary in porosity. Thus, the modelling of each cell is indexed to the overarching performance of the chair. Parametric variables, namely offset and thickness, ensure both viability for 3D printing (minimum thickness) and to achieve the stiffness and flexibility described previously. The techniques make full use of Weaverbird’s mesh subdivision and smoothening algorithms (Catmull Clark, Laplace) ensuring a watertight and stable mesh for printing purposes to allow for a low-to-high-polygon approach to the modelling of the final chair. This approach afforded a practical workflow that enabled a systematic reduction of geometric information during the analytical or form-finding design stage. Figure 3. Case Study One- 3D printed chair. 3.2. MATERIAL FRAMEWORK The chair is thickened evenly at 3mm and printed with a 1.75mm blue glow-in-the-dark PLA filament (Figure 3). The 3D model is made watertight ready for 3D printing. Using a commercially available 3D Printer, with a 250x250x200mm large print space, the FlashForge Guider prints the chair into eighteen separate pieces, using the maximum amount of working area. A raft and tree-structure supports are generated which are required in most 3D prints, as standard 3D extrusion is unable to deposit freestanding or cantilevered layers. Thus, the printing involves a layer-by-layer deposition of the CAD model brought to life from a virtual workspace and a set of digital instructions (2013, Strauss). 3D printing produces ‘raw’ objects which involve a post-production clean-up of rafts and supports, similar to the post-erection removal of a building’s scaffolding. All eighteen pieces are printed in a week and assembled and clamped with two-part epoxy glue for maximised bondage of the final product. In conclusion, what the engagement with digital instruction offers to designers is a direct deposition of a customised and material efficient form in a specific location. STRUCTURAL OPTIMISATION FOR 3D PRINTING BESPOKE GEOMETRIES 239 3D printing delivers the multiple complexities of the digitally designed chair from its seamless form, to the detailing of 2540 unique cells, dynamic scaling of cell openings, and cell smoothening. 4. Case Study Two: Structural Optimisation The second case study of this chair investigates form based on structural organisational strategies of specific materials that are able to perform at an optimal level as a response to a mechanical load (human-80 Kg). Rather than a primitive structural distribution of cell detailing, this case study investigates a data-informed material approach using branching mesh densities to produce a lightweight and structurally optimised chair. Similar to using analogue methods of form finding (Gaudi, Otto) the research here adopts a method of branching systems. This structurally optimised additive fabrication process is aided with computational design and finite element analysis (FEA) to generate a series of prototypical case studies of branch and node mesh densities. 4.1. MULTI-SCALAR PERFORMATIVE BRANCH AND NODE MESH DENSITY In nature, fractal-like branching structures also known as dendriform structures are found in plant and tree growth, fashioned according to functional requirements, where splitting and diverging occurs for maximum sun exposure for the most efficient method of photosynthesis (Rian et al. 2014). Dendriform structures can also operate in architectural engineering as a structural system that can work in tension and compression (von Buelow, 2017). This is evident in Gaudi’s six-sided branching columns in La Sagrada Familia which transition into six branches to hold a vaulted roof (Hernandez, 2006). The reverse rotations resolved the structural performance of a single rotated geometry (Burry, 2002). Drawing from formative processes in nature, the second case study explores a multi-material, structurally optimised, computational design-to-fabrication process whereby material is deposited based on specific performative global and local restraints. A primitive stress test was initially simulated using Scan-and-Solve (Intact Solutions, 2017) for a visual analysis of stress levels. Areas highlighted in red indicated that a stronger, more durable material to be considered. Karamba is then simultaneously employed to a matrix of structural possibilities, in case study two, indicating stress moments in the geometry and adopts multi-material/multi-grading for the structural optimisation of non-linear curved forms. The bespoke, cellular form merges the organic with the industrial, contrasting the geometrical-driven structure in the first case study with a structurally optimised design in this iteration. A multi-scalar performative branch and node mesh density is investigated in Figure 4, where a parametric strategy at a macro-scale is implemented for functional requirements of supporting a human sitting on the chair, and a micro-scale material distribution coupled with FEA for multi-material distribution and optimisation of PLA and PETG. 240 M. HOUDA AND D. REINHARDT Figure 4. Stress test simulation using Scan-and-Solve (SNS). 4.2. MACRO SCALE DEVELOPMENT Localised materiality and cellular definitions take on structural optimisation and innovation as the form’s key driver while carrying over from case study one, the concepts of porosity, cell detailing and material optimisation. Structural optimisation now becomes the generator of the form, as a 200(l) x100(w) x 100(h) mm portion of the chair’s lofted form from case study one in Figure 5, is extracted as a testing ground to examine how two surfaces speak to each other. Point-to-point and branching examples are tested comparing linear and curvilinear surface grids, thickened with the ‘exoskeleton’ component in Grasshopper at 3mm and 5mm diameters for a shell view analysis in Karamba. In the visual structural analysis, minimal displacement of the geometry as well as minimal stress of the overall model are desired. Figure 5. Process of generating form for structural optimisation. The matrix in Figure 6 algorithmically applies conventional truss, lattice, beam, and dendriform structural systems to linear and curvilinear surfaces. FEA indicates that curvilinear surfaces account for greater utilisation figures due to less defined support points in Karamba. A 5mm thickness displays better utilisation values, where anything less than 50% is a safe indicator that the geometry will not break in tension under the applied force of an 80kg mechanical human load. Dendriform and lattice branching systems are the most effective, indicative of a fractal-like structural performance. While curvilinear surfaces are the desired STRUCTURAL OPTIMISATION FOR 3D PRINTING BESPOKE GEOMETRIES 241 framework or ‘skeleton’ for this bespoke geometry, it is necessary for an effective structural optimisation. A Voronoi rather than a regular grid offers a more natural relationship to a curvilinear surface. Where a Voronoi cell polygon varies between four to six sides, corresponding cells between each surface are connected and iteratively tested for 1, 2, 3, and 4 branches. The ‘Topologiser’ component optimises the structural diagram to eliminate duplicate points and identify node relationships. Branching structures are intensified and are most effective in two cases, 3 branches per cell and those with alternating cells which generate more node-and-branch intersections. The same structural strategies matrix is also tested to perform under different material properties, in this case PLA, PETG and a PLA hybrid. Figure 6. Regular Matrix (left), and Voronoi Matrix (right). 4.3. MICRO SCALE Figure 7. (left): Cross-sections of Gaudi’s columns (Image Source: Lorenzi & Francaviglia, 2010). (right): Three structural components observed across selected iteration. 242 M. HOUDA AND D. REINHARDT Alongside a material hybrid for structural enhancement, the organic dendriform structures with intersecting grid Voronoi cells is the most structurally optimised form. Three structural components are employed across the entire parametric geometry: truss, lattice, and dendriform. When considering material properties, the maximum stress indicated in utilisation figures are ideal. Structural analysis requirements for each material include the ‘Young Modulus’ which evaluates the material’s elasticity and relation between its deformation and the power needed to deform it; the ‘Shear Modulus’ which indicates the material’s response to strain; as well as the material’s ‘Specific Weight’; and ‘Yield Strength’. Table 1. Material Properties for structural analysis inputs of each material. Where there are higher stress moments in the shell view analysis of the final iteration model in both the generic PLA and PETG models, a PLA composite is allocated for multi-material 3D printing to perform better in tension strength than PLA. Table 2. FEA results indicating PLA Hybrid performs the best for a multi-material application. The final mesh geometry is refined using Weaverbird’s Catmull Clark Subdivision for a smoothened material finish. The printing takes on average 55 hours for each iteration, with printing settings of 35% infill, 53mm/s extruder speeds and tree-structure supports using the FlashForge Dreamer. Initially, despite the use of an ooze wall (Figure 8) a multi-material deposition of PLA and PETG printed without success due to bondage issues of different thermoplastics in conventional desktop 3D printers. Ultimately, PLA and a PLA composite (Print 3: PLA Hybrid) results rather in a successful multi-grade additive process as they are from the same material category. FEA results in Karamba indicate that this print can carry the most stress capacity or ‘utilisation’. In this material-driven approach, the form is predominantly PLA, thereby producing a cheaper print for yet a structurally optimised output. STRUCTURAL OPTIMISATION FOR 3D PRINTING BESPOKE GEOMETRIES 243 Figure 8. Print 1(left). Print 2 (middle), and Print 3 (right). 5. Discussion The first case study demonstrated that 3D printing can afford multi-skin cellular mesh densities and localised skin-porosity detailing for bespoke form-finding. The second showed that an understanding of structural typologies resolve the structural integrity of the seamless chair design. Therefore digital feedback loops between material, geometry and fabrication allow for the efficient production of additive, multi-material bespoke geometries that vary in mesh density. The piece-to-piece production indicates the prototyping capabilities of a commercial 3D printer for a quick, cost-effective experimental analysis of additive fabrication. The development of an algorithmic process for a material and structural data-informed geometry extends the research towards generating the entire form and thus the application of large-scale 3D printing that entails multi-axis robotic fabrication. SLAM research is a relevant example that is interested in alternative methods to the layer -by- layer deposition of conventional 3D printers, essentially implementing the orientation flexibility of a 6-axis robotic arm to 3D extrude stress lines to achieve a structurally optimised pattern in relation to a geometry’s axial forces (Tam et al., 2016). New empirical studies arise when investigating varying load area profiles including different branch-structure parameters and cell densities for spanning longer distances between curvilinear surfaces, as well as new experiments for topographic 3D printing and multi-material grading. By shifting from thermoplastics to an appropriate construction material, ideally concrete, an industrial relevance could be realised, expanding the workspace and reachability of additive fabrication in construction (Ardiny et al., 2015). 6. Conclusion This research has discussed ongoing research into a novel, material efficient design to production framework for additive processes intended for architectural design where form-finding is informed at a micro and macro scale, by a structurally- performative material application. The merging fields of design to fabrication and computation to engineering seeks to create a materially informed architecture (Mostafavi & Bier, 2016) simultaneously allowing for bespoke design, 244 M. HOUDA AND D. REINHARDT cost-effective detailing and real-time structural performance. What this research informs is that when dealing with curvilinear surfaces and bespoke typologies, digital designers cannot fall back on standardised and repetitive structural formats but must appropriate a novel system such as fractal systems found in nature. In this mindset digital designers become both structural and material-aware innovators. We must learn what nature has already solved, adopting the lessons of these branch-like systems to maximise the performance of digital technologies. Three topics define future work: i. scalability, ii. material optimisation using multi-functional-graded materials, iii. and multiple extruder heads for new material blends for novel additive possibilities. While in both case studies fabrication was thus restricted to individual segmented pieces, opening up more degrees of freedom and reachability, larger products could be printed at full scale (Lipson, 2013). Future work will eliminate piece-to-piece production and propose a truer replication of digital design and efficient workflow, using a robotic arm equipped with a 3D extruder to print the chair as a whole. Acknowledgements The authors of this paper would like to acknowledge the support given for 3D printing from the Design, Modelling and Fabrication Lab (DMaF) at the University of Sydney School of Architecture, Design and Planning. 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