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Over the past few years, there is growing interest within the architectural community in topology optimization as a means of generating aesthetic and efficient structural forms by computational means. This opens up many opportunities for achieving efficient design where optimization serves as a bridging link connecting architects and structural engineers in the conceptual design stage. The architect’s input is then inspired by optimal structural forms that often resemble structures in nature. At the same time, the engineer can restrict the design so that it makes optimal use of resources and is physically viable. Considering recent technological advancements, one can envision a strictly digital design process, beginning with finding the optimal structural form using computational methods and ending in robotic manufacturing.

Realization of the vision of digital design requires further development of topology optimization procedures to account for realistic mechanical models – including inelastic material response and high order effects such as buckling. For the computational tool to be attractive for practicing architects, it needs to deliver accurate results in short time, preferably with an interactive interface – an application for architects to “play” with. The main challenge this project faces is in achieving interactive abilities while considering rather complex mechanical models.

The research plan comprised of four building blocks. The first two parts focused on increasing the efficiency of 3-D topology optimization procedures that can be implemented in CAD software and can be executed on a standard PC. First, multigrid preconditioning was integrated into a PCG iterative solver (MGCG) for solving the state equations in 3-D topology optimization problems. Significant reduction in computing time was achieved, thanks to several advancements: utilizing MGCG instead of standard iterative solvers; relating the number of MGCG iterations to the geometric parameters of the problem – filter size and number of grid levels; and linking the required accuracy of the design sensitivities to the progress of optimization, so that relatively rough approximations can be acceptable thus reducing computational burden. In a second research effort, computational time was further reduced by switching from a minimum compliance formulation to a minimum volume formulation and by exploiting the benefits of “stiff preconditioning” in a reanalysis-based procedure. Reanalysis techniques that are typically employed based on matrix decomposition within a direct solve, were extended to iterative procedures in the form of recycled preconditioning. The two research sub-projects lead to the development of 3-D topology optimization procedures that can solve problems with hundreds of thousands of finite elements within minutes on a single processor. This paves the way for efficient implementations in plug-ins for CAD software, which is the overall target of the CIG project.

The following two segments of the project focused on incorporating realistic mechanical models. In third part of the project, an effective approach was formulated for topology optimization of skeletal structures (trusses and frames) that accounts for all buckling considerations. The use of geometric nonlinear models with various imperfections, enabled to capture buckling of single members, unstable configurations and global buckling. The fourth part of the project focused on optimization of reinforced and pre-stressed concrete. Continuum and truss topology optimization were combined with material nonlinearity to formulate a consistent framework for optimizing reinforced concrete members based on realistic simulation of the nonlinear response. Furthermore, a novel optimization procedure for prestressed concrete was suggested, combining topology optimization of the concrete phase with shape optimization of the embedded cable. Finally, a spin-off of the project aims to extend the earlier results on reanalysis-based procedures to the nonlinear regime – so that optimization based on the abovementioned nonlinear models can be performed efficiently.
These topics stem directly from the overall aim of the project – promoting the utilization of topology optimization for conceptual design of civil engineering structures. The results achieved in the various stages of the CIG project can provide architects and engineers a valuable suite of computational procedures. Adoption of the developed optimization-based approaches by practitioners can enable a reduction in material consumption in the construction industry and can enhance architect-engineer collaboration in early design stages.

The funding received for the Marie Curie CIG project had a tremendous impact on the PI’s integration into the host institution. The PI now leads a viable research group consisting of 12 members and is involved in several interdisciplinary collaborations, within the host institution and abroad.

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