Everyone of us has sat on a bench at some point of his/her life! However, it is probably rare to recall one that has attracted our interest.
Most of the times, the design of a bench is dictated by simplicity, while ensuring - using experience and intuition - stability for people sitting on top.
Now, suppose you find yourself sitting on the bench below. Would this be an experience you would remember for a lifetime?
Despite how simple an object can be in terms of usability, it may be subjected to loading scenarios that turn to be disproportionally difficult to handle with accuracy. Moreover, while some of these scenarios may be decisive for determining its shape based on structural performance, it may be difficult for people to recognize the loading scenario that shaped the result. In that case, the aesthetic appraisal deriving from the flow of forces is lost.
On the contrary, all people understand a bench as a structure that transmits the gravity forces of people sitting on it to the ground!
The results below are based on this simple loading scenario. We maximize the structural stiffness under some constraint on the total mass.
Based on "Gestalt" principles of human perception, we have imposed a double symmetry around the Y-Z and X-Z planes.
Moreover, both in order to ensure manufacturability for casting/milling, as well as to improve the visual result along certain directions, we have imposed corresponding design constraints.
Varying the mass limit, as well as the position of the fixed parts, we obtain different optimized shapes which may differ significantly in the way they transmit the loads from the loaded surface to the ground.
Figure: kinematic constraints and loading for the first load-case (LC1).
Figure: optimized shape for 25% of the total mass, imposing a milling constraint in the Y-direction (LC1).
Figure: optimized shape for 15% of the total mass, imposing a milling constraint in the Y-direction (LC1).
The definition of the LC1 turns unfavorable the placement of material at the central region. In fact, an arch-type structure is created to transfer the load in the most efficient manner. Instead, if we are interested to concentrate more material close to the central region, we dispose several ways.
A first choice consists to add in LC1 an additional load concentrated at the central region.
Figure: from top to bottom; increased percentage of material placed at the central region for increasing additional load in LC1.
A second choice consists in modifying the load-case, adding a fixation point in the middle. As expected, the algorithm will take advantage of this new fixation to transfer the loads in a more efficient manner.
Figure: kinematic constraints and loading for the second load-case (LC2).
Figure: optimized shape for the LC2.
Keeping only the central fixation (LC3), the algorithm results in a thoroughly different distribution of the material.
Figure: kinematic constraints and loading for the LC3.
Figure: optimized shape for the LC3, imposing a milling constraint in the Y-direction.
Figure: optimized shape for the LC3, imposing a milling constraint in the Z-direction.
At this point, we need to highlight again an important point.
The load-case used for the form-finding method may be an idealized scenario, used to achieve an aesthetically satisfying result. The fact that the structure has been optimized for a specific load-case does by no means indicate it is optimal for a different load-case.
For example, the bench above has been examined for static criteria, assuming fixed regions at the bottom surface. This may be a representative scenario if we extend the fixation regions inside the ground, as shown in the figure below. In addition, optimizing for stiffness does not imply other mechanical criteria are also optimized. In practice, any mechanical criterion (e.g. principal stress) shall be verified at the end of the optimization process, since the shape may require further modifications to be structurally sound.
Figure: detail for achieving fixation in practise (top); validation of principal stress in Discovery (ANSYS) (below).
Figure: validation of the optimized shape in contact using ANSYS-Mechanical.
Finally, concerning the realization of such complicated designs, contemporary manufacturing techniques provide the means to realize them, usually with moderate to high cost. More specifically:
3d-printing: the shape could be 3d-printed using plastic material for the legs, then joining these parts with a wooden top surface.
Milling: milling could be used for shapes derived under a corresponding milling constraint in some direction.
Molding: "artistic" molding could be used to create a thin shell of metal following the optimized form. Depending on the complexity of the form, the structure may be constructed in parts, then welded together. Moreover, the creation of the mold for complex form is usually based on a 3d-printed prototype.
There are furniture designs that retain their interest through time, serving as references for designers.
A variety of reasons may contribute to their attractiveness: simplicity, innovation in terms of material, pioneer shape, functionality, etc.
We found it interesting to re-visit some classical designs in order to examine the impact that CAE-based Computational MorphoGenesis could have on the fianl result, in terms of visual impact, total mass or aesthetical impact.
Dimensions: 110 cm width x 97 cm depth x 120 cm height.
Materials: fibreglass shell, aluminum foot, polyurethane foam cushions, upholstered with fabric.
Weight: 42.0 kg.
The Ball Chair was designed in 1963 and debuted at the Cologne Furniture Fair in 1966. The chair is one of the most famous and beloved classics of Finnish design and it was the international breakthrough of Eero Aarnio:
“My intention, once decided, was purely functional. To create the most practical form for this new material (fibreglass) I was working with.
A sphere seemed the right shape for a strong and malleable material.”
Our intention, for this example, was to re-examine the design of the shell in order to reduce the mass of the chair.
From a purely structural point of view, it is evident that a great percentage of the total mass does not contribute mechanically into transferring the loads from the shell to the foot.
Therefore, it is interesting to re-visit the design and create an optimized mechanism for the load transfer, which then may be covered again by a thin shell structure, aiming to create the same visual result as the original design.
We have used the Topology Optimization module of ANSYS Mechanical to maximize the structural stiffness using 50% of the initial mass.
Moreover, we impose a design-symmetry in the Y-Z plane.
For the structural analysis, we have fixed the lower part, where the shell joins the foot of the chair, while we have applied a uniform pressure load at a region that corresponds to the actual sitting surface.
Figure: kinematic constraints (in blue) and pressure load (in red).
As expected, the optimizer removes most of the mass from the upper part, which contributes less in the structural performance of the chair. Only a small part of the upper structure is kept, which functions as a tractor. In addition, some material has been removed from the two sides, forming a truss structure transferring axial loads.
This optimized shape may serve as an initial concept for the design of a more efficient chair in terms of mass/stiffness ratio.
Figure: optimized shape (top); optimization evolution (bottom).
Stools are multifunctional pieces of furniture.. Not only are they that extra seat, but they are also that nightstand, flower stand, or side table.
Their Nordic style follows a a minimal approach that tries to combine functionality and beauty.
Figure: Hübsch Stools.
An alternative way of thinking could be to adopt an organic style that allows to visualize the flow of forces from the sitting surface to the ground.
We have tried to achieve this goal using once more the Topology Optimization module of ANSYS Mechanical, searching to maximize the structural stiffness using some prescribed quantity of the material.
Figure: Kinematic constraints and vertical loading used for the Hübsch Stools (due to symmetry only 1/6-th is considered).
Figure: Optimized shape for a "short" Hübsch Stool.
Figure: Optimized shape for a "tall" Hübsch Stool.
From the optimized shapes above, one observes that the optimized shape differs radically between the two cases.
In the first case, denoted "short" Hübsch Stool, the loads are transferred via thin bars, spread over the top surface, to the three main legs.
Instead, the optimized shape for the "tall" Hübsch Stool disposes another mechanism, since the loads are first transferred to a central thick bar, then spread again towards four legs.
Varying the dimensions of the design domain, as well as other parameters of the optimization problem, one may create a whole collection of optimized shapes whose form may differ significantly.
The Guéridon table, which was produced in 1949 by the designer and engineer Jean Prouvé for the University of Paris, is a convincing demonstration of clear structural principles. This wooden table is a variation of Prouvé's architecturally informed design vocabulary in a natural material, proving that modern tables do not have to be made out of steel and glass.
Figure: Prouvé Guéridon.
More than 70 years after the inspiration of Jean Prouvé, we can try to emphasize even further on the structural principles of the Guéridon table, taking advantage of modern optimization techniques, as well as innovative manufacturing methods for the realization of variable infill structures.
Such structures, bear in mind the notion of meso-scale structures, often met in nature via biological processes. Beyond being optimized, the lattice structures exhibit an architecturally interesting behavior under different lighting conditions.
In this example, we have tried to optimize separately the upper part of the table and the legs. Both are assumed to be filled with lattice structures, whose density varies from 0.1 to 0.4. We search to optimize the density distribution, so as to maximize the structural rigidity, using 25% of the volume.
Figure: Mechanical set-up for the top-surface of the Prouvé Guéridon. Due to symmetry, only 1/6-th of the structure is used for the structural analysis.
Figure: Two load-cases used for the legs of the Prouvé Guéridon, corresponding to vertical and horizontal loading.
The optimized lattice density appears in the figure below. Then, SpaceClaim (ANSYS) provides the capability to reconstruct a lattice structure from the optimized density distribution. If one is interested in 3d-printing the lattice structure, the surrounding surfaces could be closed with glass or some kind of transparent material.
Figure: Optimized density distribution for the top-surface.
Figure: Optimized density distribution for the legs.
Figure: Lattice re-construction from the optimized density distribution of the top-surface.
Figure: Lattice re-construction from the optimized density distribution of the legs.