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Public summary

In an effort to reduce the energy consumption in the built environment, considerable attention has been put on the renovation of existing Dutch residential buildings. In this regard, the IEBB (Integrated Approaches for the Energy Transition in Existing Buildings) has launched a major innovation program to offer innovative solutions that facilitate the industrialized retrofitting of buildings in The Netherlands. This report and the related project are part of IEBB, work package WP 3.3, which is concerned with a methodology to design optimized renovation panels for building façade replacements.

Within the scope of this project, the renovation strategy for existing buildings involves the replacing of existing façades with new optimized panels to improve their insulation quality. The goal of this project is to further develop a mathematical tool, Topology Optimization (TO), to design these new façade panels. The concurrent optimization of structural and thermal performance is desired since the panels must be structurally sound and should insulate thermally well. As such, concrete and insulation material properties are incorporated in the multi-material design as factors contributing either to stiffness or the thermal insulation level.

Summarized, practical engineering design projects may be formulated in terms of objectives and constraints. However, if Topology Optimization is used to propose solutions for these projects, often the practical objectives and constraints cannot be directly transferred to the mathematical objectives and constraints as used for TO (note that TO approaches in literature normally involve either (a) compliance as an objective with a volume constraint or (b) volume as an objective with stress constraints, and it is difficult to find explicit arguments why these specific approaches are used). If there are no practical objectives at all, a practical constraint should be reformulated as TO objective, for TO always needs at least one objective to steer the problem. Furthermore, to investigate trade-off solutions across several disciplines, consequently several practical constraints need to be reformulated as TO objectives. Finally, it is possible that constraints offer more room for optimizing objectives or satisfying other constraints if they are met near exactly, instead of conservatively. In that case, possibly the TO problem can be reformulated to meet the constraints more closely.

In the engineering design project here, three practical constraints were formulated (a minimum for thermal resistance, a maximum for structural displacement, and all stresses should be below a certain value), and no objective. As trade-off solutions across the structural and thermal disciplines needed to be studied, both the structural displacement and thermal resistance constraints were reformulated as TO objectives, by minimal structural compliance and maximal thermal compliance, respectively. Consequently, the stress constraints were kept as constraints. Using different weight factors for the two objectives, Pareto fronts were used to look up the situations for which one or both of the objectives met their related practical constraints. Specifically for the problem at hand, the structural displacement often showed conservative values compared to the constraint, whereas the thermal resistance constraint needed a certain thickness of the design space. Consequently, the maximum structural displacement could then only be met with unpractically thin outer faces. Finally, concrete stresses were often very conservatively meeting the constraints too, although locally stresses could be high. For better stress utilization, normally, it is expected that this can be resolved by a solution using the minimization of volume instead of the compliance as one of the objectives. However, preliminary research using this approach (via the MMA solver (Method of Moving Asymptotes)) has shown that the volume did not reduce and so stress utilization did not improve, and this would require further investigation. Furthermore, note that for a fixed volume, for stress levels to approach the yield strength limits, the size of the design domain and the magnitude of the applied load are critical factors. The stress levels must be elevated by using sufficiently large loads and smaller design domain dimensions.

This study presents two multi-objective optimization frameworks that are based on a weighted average scheme, allowing the user to control the emphasis on either structural or thermal objectives. Moreover, a modified Solid Isotropic Material with Penalization (SIMP) model is used to link concrete and insulation material properties to the optimization problem design variables. The material model contains the expressions for the Young's modulus and thermal conductivity of finite elements. The first framework is constrained by the volume of concrete material to limit the material usage, while the second framework employs concrete local stress constraints along with the concrete volume constraint. The Drucker-Prager yield criterion is used for the stress-based optimization framework, as it can handle asymmetric stress limits of concrete in tension and compression. Further, the density-based traditional TO method is used to solve the optimization problem. The gradient-based, iterative Method of Moving Asymptotes (MMA) is used as updating scheme for the design variables, which relies on the sensitivity information of objective and constraint functions.

The optimization frameworks are applied to three case studies, namely a façade panel, a double-faced concrete sandwich panel, and a part of a continuous wall-floor structure. Analysis of the optimized results demonstrated the ability of the algorithm to generate topological designs contributing to the objectives, as determined by a weight factor. In fact, the proposed design methods steered the problems to focus on being stiffer or more thermally insulative by controlling the materials’ distribution. The trade-offs between structural and thermal behavior have been illustrated by Pareto front curves, showing the conflicting nature of the two objective functions. In the case study of the sandwich panel, the analysis of the design properties suggests that the thermal resistance requirement governs the selection of an appropriate design, since both strength and stiffness requirements are met at all points of the developed Pareto front. Moreover, it is found that the two frameworks produce different topological designs. This is particularly noticeable around sharp corners of the design domains, where the stress-based framework avoids generating sharp corners by concrete material. However, considering the result properties such as maximum deflection and structural compliance, the volume-constraint framework provides stiffer designs. In addition, while the first framework offers a simple application and low computational cost, the second framework provides smoother designs at the cost of being computationally expensive.

The resulting optimized designs of this study can be used as a starting point for 3D printing technologies, in order to provide prefabricated 3D printed elements. As a demonstration, a 3D printed prototype is presented, based on one of the sandwich panel optimized designs. Moreover, as part of IEBB work package WP 4.3, for 3D concrete printed objects with insulation, two printing strategies are currently investigated by Arjen Deetman, a PhD at Eindhoven University of Technology. In the first strategy, two different motion manipulators are used that apply one of the materials, while the second strategy uses one motion manipulator that can apply both materials simultaneously.

For future work, it is recommended to investigate other possible approaches to address the multi-objective problem of this research. In addition, further research is required to determine if mathematical constraints can be implemented in a multi-objective TO problem as a way of addressing the manufacturing constraints associated with 3D printing.

Funded by: RVO-MMIP-TEUE919003 (Integrale Energietransitie Bestaande Bouw)