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Shape and topology optimization in conceptual architectural design: criteria, constraints and interpretation step
Recently architects have started recognizing Shape & Topology (S&T) optimization methods [1,2] as valuable tools in the conceptual design of shapes . Forms resulting from S&T optimization can be simultaneously characterized by some notion of mechanical and aesthetical optimality. Moreover, the fact that the designer is able to define his/her own criteria to optimize, makes it possible that the obtained shapes reflect his/her personal architectural identity. The main objective of this WP is to identify what kind of criteria and constraints are suitable to be used in S&T optimization for applications in conceptual architectural design. The collaboration of architects and applied mathematicians of the consortium is required in order to formulate, as mathematical functions, the criteria to optimize, as well as possible additional aesthetic constraints. We also aim to test different methods for interpreting the results into CAD designs or exporting directly the results to files suitable for rapid prototyping, such as 3D-printing of maquettes. The formulation of usual S&T optimization problems for structural mechanics makes use of the classical elasticity theory for continuous media . Therefore, such results may be directly exploitable for applications in mechanical engineering, but not in civil engineering, since structural members of interest are assumed to exhibit the mechanical behaviour of beams or shells and be connected in various ways. Thus, it is evident that an interpretation step is needed. In contrast, it is not evident what kind of load cases and constraints shall be used in order to drive the structural form towards an optimal shape, since the actual load cases and constraints will be imposed on the final shape, after the interpretation step. Some kind of compromise shall be established, in order neither to add severe difficulties in the optimization problem, nor to converge to a shape far from reality.
WP2 - Shape and topology optimization in conceptual architectural design: criteria, constraints and
interpretation step [Months: 4-24]
Among the different S&T optimization methods that exist in the literature, the level-set method is chosen as the most appropriate one [1,6]. The reason is that this method is purely geometric, in contrast to other well-known density methods [2,7], and thus suitable for architectural criteria of geometric nature. In order to test the developments of this Work Package, an optimization platform developed under the collaboration of several participants will be used. Here is a description of the various Tasks to undertake: Task 2.1: Bibliography search The first part is purely bibliographic and consist in identifying which previous developments that already appeared in the literature are meaningful for conceptual architectural design. The additional difficulty to the optimization problem and the impact on the optimal shape shall be identified for the different criteria and constraints, as well as for the mechanical frameworks of their application. Task 2.2: Particular criteria for architectural design During the second part, criteria specifically dedicated to architectural design will be developed. At a second step, their corresponding shape derivative needs to be calculated, which is a necessary component of S&T optimization. The shape derivative indicates how the shape shall change in order to improve the defined criterion and its calculation can be nontrivial . Task 2.3: Case studies definition During the third part, the collaborators shall define several case studies for testing their approach. Two different types of structures will be defined and several optimization problems will be posed on each of them. According to the obtained solutions, the team will possibly reject some of the proposed formulations. The first structure will resemble the entrance of Qatar National Conventional Center, designed by Arata Isozaki . The goal is to guide the design towards a freeform structure. The second test case will be a metal bridge, connecting two skyscrapers, similar to the one proposed by Prof. Paulino . In this example, we seek to interpret the result as a truss. Task 2.4: Interpretation step of optimized shapes The results of S&T optimization consist in massive continuous media and need to be interpreted into classical structural members used in civil engineering, such as beams or shells. Thus, a CAD design shall be provided to the structural engineer. For tube-like structures, the team will try to create automatically the 3D CAD design. For truss structures, a manual interference seems inevitable, since we need to verify that the produced truss is not a mechanism. Task 2.5: 3D printing of optimized forms In this last part of the WP, we are interested in producing automatically files formats for direct 3D printing of the results. This can be helpful for architects that wish to use the obtained forms in exhibitions by creating small-scale maquettes.