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Structural optimization
Development of 3D structural optimization algorithms for stiffness maximization
Material design
Design of architectured materials for reach an specific material response. The problem is solved via an inverse optimization problem with adjoint and level-set methods.
Addittive manufacturing
Optimal cells are designed considering additive manufacturing length-scale. Here an auxetic material is designed and then 3D-printed. Â
Lattice structures (Dehomogenization)
Lattice structures are designed via homogenization, optimization and dehomogenization. The optimization procedure is developed at the homogenized scale and dehomogenization is a postprocessing step obtaining then a fast and high resolution design.
Gripper design
Topology optimization is also useful when designing flexible structures. Here, an optimal gripping is obtained via maximizing the displacement of the tips with both density and level-set methods. The solution is then manufactured with 3D printing techniques.
Inverter design
Similar to the gripping, we design an inverter structure. The idea is to maximize the negative displacement of the tip when a vertical displacement is applied at the bottom. This may be understood as an apparent negative stiffness response.
Anisotropic perimeter
Thin bars may be optimal for stiffness, however the structure may be not manufacturable. Perimeter constraints may allow to globally penalize this thin bars. Similarly, anisotropic perimeter may penalize horizontal bars which may be not desired for overhang in 3D printing technologies.
Auxetics materials
Architectured materials may be designed to exhibit negative poisson ratio response. This is providing a positive vertical displacement when is horizontally pulled. This example is obtianed with density based methods.
Cantilever example
The classical benchmark in topology optimization in 2D and 3D when using level-set methods.
Bridge example
Another interesting example is the bridge design. Asking for maximum stiffness when a distributed vertical force is applied, the optimization provides recognizable bridge designs.
Perimeter (Total and relative)
Optimal design may also be applied to non-structural examples. Here the objective is to minimize the perimeter fulfilling a certain fraction volume. If the perimeter is the total (considering also the boundary) then a circle is obtained (left) if it is only the relative (boundary is not contributing to perimeter) an horizontal line appears as optimal solution.
3D Material design
Material may be also optimized in 3D applications. Here, some differents features (maximum bulk, minimum shear, etc) are required in the optimal design problem
Perimeter in 3D Topology Optimization
Perimeter may also be minimized in 3D examples. Interestingly, optimal solutions exhibit vertical surfaces. When penalizing the perimeter, the surfaces become thin bars.Â
3D lattice
Similarly, with topology optimization we may ask to have very small volumes values when maximizing the stiffness to obtain 3D lattice structures. Here some maximum bulk and shear lattice structures.
3D metamaterial
Materials may be designed to exhibit non-intuitive responses. Here, 3D metamaterials is obtained with level-set method and slerp algorithm.
Shape optimization
An interesting but different approach is to use shape derivative to optimize the shape of a domain. Here a circle, ellipse, hearth and flower example are solved
Chair example
Another exciting example is the optimal stool. Asking for maximal stiffness when applying a downwards-distributed vertical force in the top part of the domain and clamping the bottom part, we end up with an optimal stool.
Dehomogenization
Using dehomogenization technique and composing level-set methods with conformal maps, we are able to obtain structures with spatially varing holes. Here the parameters are randomly selected and the orientation is created sintetically.
Buckling design of a column
Another interesting structural optimization example is the design of the section along the length of the beam to maximize the first eigenvalue and then avoid buckling phenomena. Different optimal solutions are obtained.
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