# Innovative Method for Automatic Shape Generation and 3D Printing of Reduced-Scale Models of Ultra-Thin Concrete Shells

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## Abstract

**:**

## 1. Introduction

## 2. Shape Generation Method and Project Assumptions

^{2}) using different combinations aiming at reaching the diversity of uses. Thus, prefabrication of the shell and space-functional flexibility converge in the genesis of the pilot-shell. Its configuration (an equilateral triangle in plan view) motivated the combinations shown in Figure 2. The shape of the shell, named H800N3, was conditioned by the design options previously mentioned.

## 3. Scale Model: Requirements, Constraints and Technologies

#### 3.1. Scale

#### 3.2. Thickness

#### 3.3. Shape Control

#### 3.4. 3D Printing

#### 3.5. Costs

## 4. Scale Models: Guidelines

^{®}produced by Robert McNeel & Associates [27] was selected. This software is based on the non-uniform rational basis spline (NURBS) geometry, a mathematical model currently used in graphic computation software to represent both curves and surfaces with accuracy and flexibility. It allows the description of any type of shape, from the most simple (2D curves) to the most organic and complex, such as three-dimensional free shapes [28].

#### 4.1. Step 1: Input of the Point Cloud to the CAD Environment

^{®}environment allows the visualization of the point cloud that represents the object (Figure 4(1)). Using the plug-in Resurf (function ‘PointCloudToMesh’), a regular mesh is generated, i.e., a surface discretized in triangular faces, creating a surface of curves, which is smoother the higher the number of points (Figure 4(2)). The solid is generated from this mesh. The Rhinoceros

^{®}software operates with mesh objects. A solid is interpreted as a closed volume, made of meshes, and is called a ‘solid mesh’. The mesh is generated starting from the mid-plan mesh by adding 2 mm layers each time (Figure 4(3)).

#### 4.2. Step 2: Preparation of the Three-Dimensional Model for Printing

#### 4.3. Step 3: Model Printing

#### 4.4. Step 4: Preparation of Moulds

#### 4.5. Step 5: Assembly of Pieces

#### 4.6. Step 6: Model Strengthening, Connections and Pre-Finishing

^{2}) providing the object with the required robustness (Figure 9(1)). The pre-accelerated polyester resin, used to apply the fibreglass fabric, also filled in and definitely consolidated the joints. The average drying time was circa half an hour with an average ambient temperature of approximately 22 °C.

#### 4.7. Step 7: Identification of Coordinates of Pressure Sensors

^{®}; and (iii) superimposing it on the virtual point cloud, also in plan view (Figure 10(2,3)). The coincident points were identified and marked on the virtual point cloud. The sub-cloud of points is shown in Figure 10(4) (red points isolated in a single layer). The script RhinoToExcel.rvb, available online, and imported to the Rhinoceros

^{®}environment, allowed the obtaining of the list of their coordinates.

#### 4.8. Step 8: Drilling, (Model) Painting, Installation of Pressure Sensors

## 5. Validation of the Printed Geometry

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Iterations of the shape and three-dimensional meshes in the AutoCAD (Autodesk Inc.) environment.

**Figure 2.**Combinations of the shell and three-dimensional meshes in the AutoCAD (Autodesk Inc.) environment.

**Figure 3.**Flow chart of the process with transition key-moments: (1) from conceptual to virtual; (2) from virtual to physical reality.

**Figure 5.**Preparation of 3D model for printing: (

**1**) solid mesh subdivision; (

**2**) modules; (

**3**,

**4**) printing volume of Replicator 2X (MakerBot Industries) for validation.

**Figure 6.**3D printing: (

**1**) printing on a Replicator 2X (MakerBot Industries); (

**2**) piece printed on a Dimension SST760 (Stratasys); (

**3**) final piece corresponding to one third of the shell with 2 mm thickness.

**Figure 7.**Preparation of moulds: (

**1**) cardboard mould to serve as test; (

**2**) MDF laser cut pieces with 3 mm; (

**3**) sub-mould in MDF with 3 mm to help building one third of the shell; and (

**4**) complete mould in MDF with 3 mm.

**Figure 8.**Assembling process: (

**1**) linking (third part) through glue points; (

**2**) speed dry using Ultraviolet Light-emitting diode (UV LED); (

**3**) linking all parts; (

**4**) stabilized shell.

**Figure 9.**Building the model: (

**1**) strengthening with fibreglass fabric; (

**2**) surface regularization and pre-finishing with coating; (

**3**) supports; and (

**4**) final (robust) model.

**Figure 10.**Points for location of pressure sensors: (

**1**) marking points on the scale model; (

**2**) image superimposed to the virtual points cloud; (

**3**) marking points on the virtual model; (

**4**) sub-cloud of points—red points.

**Figure 11.**Installation of pressure sensors: (

**1**) drilling; (

**2**) painting with coating; (

**3**) installation of pressure sensors; and (

**4**) final instrumented model.

**Figure 12.**Final scale model: (

**1**–

**3**) different views of the final scale model; (

**4**) preliminary tests at the closed circuit aerodynamic tunnel at LNEC.

**Figure 13.**The free shape shell ‘H800N3’ under natural light (22 of August 2014, 38°38′28.61″ N–9°12′44.64″ O, altitude: 95 m, time: 5:00 p.m.).

**Figure 14.**Free-form shell generated using a geometrically nonlinear analysis [10].

**Figure 16.**Plan view of the shell: reference point G (geometric centre), and the diagonal cross-sections defined by the planes MGH, JGL and IGK.

**Figure 17.**Diagonal cross-section defined by the plane MGH: Finite Element Method (FEM) vs. Photogrammetry curves.

**Figure 18.**Diagonal cross-section defined by the plane JGL: Finite Element Method (FEM) vs. Photogrammetry curves.

**Figure 19.**Diagonal cross-section defined by the plane IGK: Finite Element Method (FEM) vs. Photogrammetry curves.

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**MDPI and ACS Style**

Tomé, A.; Vizotto, I.; Valença, J.; Júlio, E.
Innovative Method for Automatic Shape Generation and 3D Printing of Reduced-Scale Models of Ultra-Thin Concrete Shells. *Infrastructures* **2018**, *3*, 5.
https://doi.org/10.3390/infrastructures3010005

**AMA Style**

Tomé A, Vizotto I, Valença J, Júlio E.
Innovative Method for Automatic Shape Generation and 3D Printing of Reduced-Scale Models of Ultra-Thin Concrete Shells. *Infrastructures*. 2018; 3(1):5.
https://doi.org/10.3390/infrastructures3010005

**Chicago/Turabian Style**

Tomé, Ana, Isaías Vizotto, Jónatas Valença, and Eduardo Júlio.
2018. "Innovative Method for Automatic Shape Generation and 3D Printing of Reduced-Scale Models of Ultra-Thin Concrete Shells" *Infrastructures* 3, no. 1: 5.
https://doi.org/10.3390/infrastructures3010005