Optimizing Additive Manufacturable Structures with Computer Vision to Enhance Material Efficiency and Structural Stability

Abstract

This study introduces an innovative technique that merges computer vision with topology optimization to advance additive manufacturing. Employing advanced photogrammetry software, we obtain high-resolution images of the design domain, which are then used to develop accurate 3D models through meticulous scanning procedures. These models are transformed into an STL file format and remeshed using an adaptive algorithm within COMSOL 5.3 Multiphysics, facilitated by a custom MATLAB 2023 application. This integration achieves the optimal mesh resolution and precision in analytical assessments. We applied this technique to the design of a concrete pillar for 3D printing, targeting a 75% reduction in volume to improve the material efficiency and structural stability—critical factors for extraterrestrial applications. The design, captured with a 360-degree camera array, guided the MATLAB-based topology optimization process. By combining MATLAB’s optimization algorithms with COMSOL’s meshing and finite element analysis tools, we investigated various material-efficient configurations. The findings reveal a substantial volume reduction, especially in the central region of the design, effectively optimizing material utilization while preserving structural integrity. The optimization algorithm exhibited a swift and stable convergence, reaching near-optimal solutions within approximately 20 iterations.

1. Introduction

The trajectory of human progress and scientific development is inextricably linked to the exploration of space and the exploitation of extraterrestrial resources. As Earth’s finite reserves of critical materials and energy sources face depletion due to escalating global demands driven by population growth and industrial expansion, the necessity to extend resource acquisition beyond the terrestrial boundaries becomes increasingly apparent. The prospect of identifying and utilizing extraterrestrial resources presents a compelling solution to several of humanity’s most critical challenges. Among these, ensuring the sustainability of energy supply systems and providing the essential materials for advanced technologies are paramount. Furthermore, the extraction of off-world resources could play a vital role in supporting the human colonization and long-term habitability of extraterrestrial environments, and particularly in facilitating the construction of self-sustaining space habitats. This paradigm shift from a terrestrial to a space-based resource exploitation could enable the sustained advancement of technological civilization, mitigating the limitations imposed by Earth’s resource scarcity. Consequently, the scientific exploration and technological feasibility of extraterrestrial resource acquisition must be prioritized as a cornerstone of future space missions, laying the foundations for a new era in both space exploration and global resource management [1,2].

Advancements in space exploration technologies have dramatically enhanced our understanding of the cosmos and expanded the range of accessible space resources. For instance, asteroids rich in precious metals and rare earth elements present untapped opportunities for material acquisition that could revolutionize terrestrial industries. Furthermore, the utilization of lunar regolith for in situ construction and resource extraction exemplifies the potential for self-sustaining operations on other celestial bodies. These developments underscore the transformative potential of extraterrestrial resource exploitation in fostering sustainable development on Earth and laying the groundwork for human expansion into the broader solar system [3].

For example, Baumgart et al. [4] conduct an analysis of space-based projects and their alignment with the 2030 Agenda for Sustainable Development, focusing on the technological advancements and their implications for sustainability. Maiwald et al. [5] extend this discussion by examining how spaceflight technologies can be leveraged to support sustainable development on Earth, providing specific examples and practical applications. In a related vein, Iliopoulos and Esteban [6] explore the implications of privatization in sustainable space exploration, offering a critical evaluation of the benefits and challenges associated with this trend.

In space exploration, the integration of autonomous structural design and construction is critical due to the significant communication delays caused by vast distances. These delays render Earth-based directives impractical for real-time decision making during missions. Autonomous systems enable spacecraft and habitats to adapt in real time to the changing conditions and unexpected challenges without relying on continuous input from Earth. Utilizing artificial intelligence and advanced robotics, these systems can autonomously generate and implement optimized designs, enhancing the efficiency and resilience of space missions while mitigating the limitations imposed by delayed communications.

In this research, we aim to advance topology optimization as a pivotal methodology within the domain of non-parametric structural design. Our focus is on the development of an autonomous design tool underpinned by rigorous mathematical optimization, specifically designed for the simulation and analysis of structures via the finite element method (FEM). This approach seeks to fundamentally transform the structural design process by providing a systematic and robust framework that operates independently of predefined geometric parameters or traditional design constraints. By leveraging the flexibility of non-parametric techniques, the proposed tool facilitates the creation of optimized structural configurations that are purely driven by mathematical principles and performance criteria. This paradigm enables a more efficient exploration of the design space, ensuring that the resulting structures exhibit superior performance in terms of mechanical properties, such as strength, stiffness, and material distribution. Furthermore, this optimization framework is capable of accommodating complex loading conditions and material behaviors, ultimately contributing to more innovative, high-performance structural solutions. By advancing these methodologies, this research seeks to establish a foundation for autonomous, optimization-driven design systems that can enhance structural integrity and efficiency in various engineering applications [7,8,9]. The advent of topology optimization, originated by Michell [10] based on solving Maxwell’s lemma [11], has propelled computer-aided design to unprecedented heights, facilitating the comprehensive development of designs rooted in mathematical optimization principles. Although the realization of fully computer-based evaluation and design remains an aspirational objective, it stands as a pivotal imperative for propelling the frontiers of future transportation endeavors, particularly within the domain of deep space missions [12,13,14].

Amidst such missions, characterized by extensive distances from the central control center and potential communication disruptions stemming from orbital dynamics (excluding quantum communication and informatics), spacecraft may encounter hazardous events necessitating on-site repairs, such as the damage induced by asteroid impacts or mechanical fatigue. In scenarios involving manned missions, where crew members are theoretically in a state of deep hibernation, the execution of repairs by human personnel becomes unviable. Moreover, future deep space missions, encompassing endeavors such as mining, may prioritize unmanned operations for economic reasons, mandating the incorporation of artificial intelligence to orchestrate the design process and execute repairs autonomously.

Topology optimization, an advanced discipline encompassing both layout and generalized shape optimization, involves discretizing a design domain into finite components with well-defined spatial relationships—such as finite differences, discrete boxes, elements, or volumes. Initially conceived as a layout optimization problem, topology optimization is fundamentally concerned with the strategic design and distribution of material within a predefined spatial domain, where the positions of the traction and support points are fixed. Through this discretization, the design space can be systematically explored, allowing for the identification of the optimal structural configurations that meet performance criteria such as stiffness, strength, or material efficiency. By iteratively adjusting the material distribution across the design domain, topology optimization facilitates the creation of structures that balance competing objectives, such as minimizing weight while maximizing mechanical performance. This method, grounded in the principles of mathematical optimization and finite element analysis, enables engineers to transcend traditional design constraints, opening pathways for the development of novel, high-performance structural systems across a broad spectrum of engineering applications. The capacity to optimize layouts and shapes at the foundational level of structural design marks topology optimization as a transformative tool in the pursuit of more efficient, resilient, and sustainable structures.

Topology optimization has advanced significantly, driven by various methodologies. A key development was the use of numerical discretization by Dorn et al. [15], enabling precise structural representation and enhancing the optimization accuracy. Bartel [16] minimized the structure weight using sequential unconstrained minimization and Constrained Steepest Descent techniques. Charrett and Rozvany [17] applied the Prager–Shield method for optimal design in rigid-perfectly plastic systems under varied loads, while Rozvany and Prager [18] optimized a grillage-like continua. Rossow and Taylor [19] employed the FEM to optimize variable thickness sheets, introducing shape optimization with holes in the plates. Cheng and Olhoff [20] refined the FEM for optimizing annular plates, incorporating homogenization. Bendsoe’s discretized continuous optimality criterion (DCOC) led to the Solid Isotropic Material with Penalization (SIMP) method, crucial for reducing stress concentrations and utilizing image processing in design transformations [21,22,23]. Other notable methods include Evolutionary Structural Optimization (ESO), the Metaheuristic Structure Binary-Distribution (MSB) method [24], and shape optimization methods, particularly the level-set [25,26].

The early application of computer vision in computer-aided design has been explored extensively in scientific research. Initial studies systematically examined the advancements in computer vision techniques, focusing on the recognition and classification of 3D objects [27]. These investigations categorized the different types of object representations and detailed the steps involved in object recognition, emphasizing the importance of 3D sensors and databases in enhancing recognition capabilities [28]. Additionally, the integration of deep learning into the CAD systems has been proposed, with frameworks developed to automatically generate and evaluate 3D CAD designs, demonstrating significant potential to improve design efficiency and accuracy. Further research into the synergy between CAD and computer vision has aimed to automate the generation of recognition strategies based on geometric properties, advancing the automation of CAD data generation using computer vision techniques [29].

The task of design remains predominantly within the domain of engineers, which presents significant challenges under extreme conditions, such as in space exploration. These challenges are exacerbated by the complex, multidisciplinary nature of such problems [30], often requiring collaboration across multiple teams. In contrast, topology optimization has demonstrated progress in addressing multiphysics design challenges by directly integrating mathematical modeling with optimization techniques [31,32]. This approach holds promise for enabling the autonomous execution of design tasks by computational systems. However, the identification and definition of the design domain continue to rely on engineers, who must manually input this data into the design software. This dependency motivates the present work, which aims to bridge this gap by exploring methodologies for automating the entire design process—from the recognition of the design problem domain to the generation of the final optimized design.

As such, the present study delves into the innovative integration of camera technology within spacefaring vehicles to facilitate the comprehensive design and construction of habitable structures through advanced 3D printing methodologies [33,34,35,36]. Leveraging the concept of camera vision, the computational system discerns the parameters of the design domain, subsequently employing topology optimization techniques for streamlined design execution. The impetus driving this investigation stems from four primary considerations. Firstly, the inherent payload sensitivity of space missions necessitates stringent weight management, thereby advocating for the minimization of additional measurement devices, such as laser scanners, to mitigate the associated costs. Secondly, mindful of energy consumption, the adoption of computationally intensive methodologies like machine learning, while efficacious in expert system emulation, imposes significant computational burdens, contrasting with more resource-efficient optimization approaches such as the Method of Moving Asymptotes or the optimality criteria [37]. Thirdly, the logistical challenges posed by vast astronomical distances mandate expeditious communication between Earth and extraterrestrial habitats, underscoring the need for locally executable design processes. Finally, topology optimization emerges as a matured technique for 3D printing applications, further affirming its suitability for the envisaged spaceborne construction endeavors. The paper unfolds in a structured manner: elucidating computer vision in Section 2, expounding on topology optimization in Section 3, detailing the numerical investigation in Section 4, and concluding with Section 5.

2. Computer Vision 3D Simulation Using Computer Vision

This study introduces the integration of photogrammetry into design engineering, utilizing camera-based techniques to enable 3D modeling of the design domain [38,39,40,41,42,43,44]. The foundational concepts of photogrammetry can be traced to the 1480s with the works of Leonardo da Vinci and his early research on perspective [45]. The first one to recognize the potential of using a camera for mapping was Aimé Laussedat, who is often credited as the “father of photogrammetry” [45]. Photogrammetry as a numerical technique began to be developed in the 1990s, through the works of the computer community vision [46]. The development of algorithms to realize the automatic matching between features also represents the beginning of actual photogrammetry. The different elements of the process involved in photogrammetry can be divided into two key steps: image processing and mathematical calculations. The beginning of the process of image processing consists of image alignment (also known as image registration). This step involves creating a coherent dataset by matching the corresponding points in overlapping images. This is achieved using algorithms to detect common features, such as edges and corners, and align the images accordingly. An image rectification corrector is applied to reduce the distortion caused by the camera lens, ensuring that the images accurately represent the geometry of the captured scene. Rectified images are essential for precise measurements and modeling. Image stitching involves combining multiple overlapping images into a single mosaic. This is a particularly important procedure for large-scale projects where multiple images are required to cover the entire area of interest. The resulting mosaic facilitates detailed analysis and measurements. The other key step in photogrammetry involves using mathematical calculations to derive accurate measurements and create detailed models from the processed images. The fundamental principle behind photogrammetry is triangulation. This involves determining the position of a point in the 3D space by measuring the distances and angles from two or more known positions. By using images of the same object or detail from different perspectives, photogrammetry software can precisely calculate the coordinates of each point. The basic formula for triangulation can be expressed as follows:

(1)$X={\displaystyle \frac{b·(x_1-x_2)}{x_1+x_2-2x_0}}$

(2)$Y={\displaystyle \frac{b·(y_1-y_2)}{y_1+y_2-2y_0}}$

(3)$Z={\displaystyle \frac{b·f}{x_1+x_2-2x_0}}$

where:

• -. $X$, $Y$, $Z$ are the coordinates of the point in 3D space.

• -. $b$ is the baseline distance between the two camera positions.

• -. $x_1$, $x_2$, $y_1$, $y_2$ are the coordinates of the point in the images.

• -. $x_0$, $y_0$ are the principal points of the images.

• -. $f$ is the focal length of the camera.

Bundle adjustment is a mathematical optimization technique employed to enhance the accuracy of the derived measurements in photogrammetry. It involves simultaneously refining the positions and orientations of cameras, along with the three-dimensional coordinates of the measured points, to minimize projection errors and ensure consistency across the dataset. By iteratively adjusting these parameters, bundle adjustment aims to achieve a globally optimal solution that reconciles the discrepancies between the observed and calculated image projections. This process is essential for improving the precision of the spatial reconstructions, particularly in applications requiring high-fidelity results, such as 3D modeling, mapping, and geospatial analysis. The effectiveness of bundle adjustment lies in its ability to account for and correct various sources of error, such as lens distortions and misalignments, thereby enabling the production of highly accurate geometric reconstructions. Consequently, it serves as a critical step in the photogrammetric workflow, ensuring the reliability and robustness of the final data output. The objective function for bundle adjustment can be expressed as:

(4)$\underset{X,P}{{\displaystyle \min }}{\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^n{\left|y_{ij}-f(P_i,X_j)\right|}^2}}$

where:

• -. Are the 3D coordinates of the points.

• -. $\mathbf{P}$ are the parameters of the camera poses.

• -. ${\mathbf{y}}_{\mathit{i}\mathit{j}}$ are the observed image coordinates.

• -. $f$ is the projection function mapping 3D points to 2D image coordinates.

Finally, using the dataset and algorithms, high-resolution 3D models can be generated for visualization, analysis, and further processing.

3. Topology Optimization

Topology optimization began as a deterministic discipline focused on physical models, evolving with advancements in mathematical methodologies. Initially, parametric optimization used heuristic methods to adjust the parameters within structural designs, like cross-sectional dimensions or material properties, to meet specific objectives such as minimizing stress. However, optimizing the material distribution within a structural domain proved complex, as it could not be easily defined by conventional quantities like mass or load. This led to the development of non-parametric methods, particularly topology optimization, which optimizes the structural layout and shape based on mathematical logic and objective criteria. Topology optimization represents a new design frontier, delivering the most efficient solutions within predefined constraints, driven purely by the requirements of the optimization process.

Non-parametric optimization methodologies, such as topology optimization, employ a hierarchical framework of cascade approximations initiated from the design variables. These methodologies, exemplified by techniques like the solid isotropic material with penalization (SIMP) method, involve a progressive series of refinements that guide the optimization process towards an optimal solution. The process begins with the discretization of the design domain into finite elements, which forms the foundation for representing material distribution across the structure. Objective criteria, such as stiffness maximization or weight minimization, are then formulated in terms of these design variables. As optimization proceeds, iterative updates are applied to the design variables based on the objective function and constraint evaluations, refining the material layout across the structure. The SIMP method, for instance, penalizes intermediate material densities to push the design towards clear binary material distribution, effectively enhancing the structural performance. Through this cascade of approximations, non-parametric optimization techniques ensure convergence to an optimized design that satisfies the prescribed performance criteria while maintaining computational efficiency and robustness in handling complex design spaces [25].

Topology optimization, guided by predefined objective criteria, typically revolves around compliance-based optimization objectives as presented in Equation (1). These criteria serve as fundamental pillars guiding the optimization process, ensuring that the resultant designs meet specified performance standards while adhering to structural integrity requirements.

In the context of the present study, MATLAB with COMSOL was employed to develop customized algorithms tailored to facilitate the topology optimization process [47].

(5)$\begin{array}{l}\min f(\rho )| E=E_{void}+{\rho }^q(E_{void}+E_{mat})\\ s.t. {\displaystyle {\int }_{{\mathsf{\Omega }}_d}\rho d\rho \le v, }\rho \in (0,1], \forall \rho \in {\mathsf{\Omega }}_d\end{array}$

where $f(\rho )$ is the objective function of the design variables, $\rho$. Here, $E$ represents the elemental penalized elastic tensor in terms of penalized design variable to power q. When the design variable is near zero, the elastic tensor of the discretization unit become $E_{void}$, while when the design variable reaches one, the elastic tensor become $E_{mat}$. Moreover, $v$ is the volume reduction condition within the design domain, ${\mathsf{\Omega }}_d$.

The significant strides made in advancing topology optimization also bring to light critical challenges that require careful consideration. Foremost among these challenges is the derivation of sensitivities in gradient-based optimization, particularly when dealing with complex, multi-layered functions. While numerical sensitivity analysis presents a viable approach, it is often accompanied by substantial costs in terms of time and computational resources. Achieving the desired outcomes typically necessitates high-resolution models, which, in turn, escalate the computational burden.

Moreover, the trade-offs inherent in discretization and simplification—although necessary and widely accepted—inevitably obscure certain physical phenomena, potentially compromising the accuracy of the solutions. The mathematical complexities present in intricate models further exacerbate these challenges, introducing a significant risk of computational instability and failure.

These challenges underscore the mathematical intricacies intrinsic to topology optimization. The design of the objective function stands out as a particularly critical aspect within the realm of mathematical optimization, necessitating meticulous attention and innovative strategies to effectively navigate these complexities.

A well-formulated objective function in optimization (such as the optimization algorithm addresses the anisotropy of material properties as the varying strengths of concrete in both tension and compression) can sometimes produce solutions that deviate significantly from the expectations established by the initial mathematical model [48]. A pertinent example is found in the topology optimization of heat conduction problems, where the resulting structures often resemble tree-like formations. This outcome challenges the intuitive expectation of achieving a uniform heat distribution through a solid medium, as the optimized structures display an uneven mass distribution. Yan et al. further corroborates these observations by presenting alternative models that question the validity of the traditional assumptions in topology optimization. Moreover, the discretization process itself poses substantial challenges, often resulting in infeasible design regions, particularly when higher-order degrees of freedom are involved. To mitigate these challenges, designers frequently apply supplementary filtering techniques, drawing upon their expertise and judgment to refine and enhance the optimization results.

Figure 1 illustrates the algorithm of the proposed method, detailing the approach to address these issues and improve the optimization process from the initial design phase to the final solution.

4. Results

This section presents a numerical study that investigates the integration of computer vision with topology optimization for designing structures tailored for additive manufacturing. We developed custom software for photogrammetry, employing camera systems to capture high-resolution, dynamic images within the designated design domain. These images enable the creation of detailed 3D models through comprehensive scanning protocols, ensuring the meticulous capture of intricate domain features (the model in Figure 2).

The design domain in this study is modeled as a square-based pillar, selected to address targeted challenges in structural optimization. The principal objective is to identify and autonomously assign the free upper edge of the pillar as the application site for top-loading forces. This design decision stems from the necessity to simulate realistic loading conditions, where the upper edge undergoes applied forces, thereby replicating operational scenarios such as vertical loading commonly encountered in structural engineering applications. The top-loading configuration is essential for evaluating the mechanical performance and load-bearing capacity of the structure under conditions mimicking real-world use. In contrast, the base of the pillar is rigidly fixed to simulate structural constraints, corresponding to scenarios where the foundation or support is permanently anchored to an immovable ground. This fixed-base configuration is critical for representing the stability and constraint conditions typical in practical applications, such as buildings or support columns, where the base serves as a static boundary, ensuring the fidelity of the structural simulation. Together, these boundary conditions form a representative framework for assessing the optimized design performance under realistic operational loads and constraints.

This design approach is guided by the goal of accurately representing typical structural behaviors and constraints in a simplified yet effective manner. By assigning the free upper edge for loading and fixing the base, the model ensures that the optimization process can focus on refining the pillar’s structural efficiency under these defined conditions. This setup allows for a detailed exploration of how the pillar’s geometry influences its load-bearing performance, facilitating the identification of the optimal structural configurations that balance material usage and mechanical strength. Figure 2 illustrates these design choices, showcasing how the defined loading and constraint conditions are applied to the optimization problem, thus enhancing the relevance and applicability of the results to real-world engineering challenges.

Upon completing the 3D modeling, the model is converted into a stereolithography (STL) file, the standard format for additive manufacturing. This conversion, performed using an automated, precision-driven approach, ensures the accurate preservation of the details captured during the scanning phase. The STL file is subjected to remeshing through an adaptive meshing algorithm within the COMSOL Multiphysics environment, orchestrated by a MATLAB application. This integrated framework capitalizes on MATLAB’s computational capabilities and COMSOL’s robust simulation features to refine the mesh structure for subsequent computational analyses. The adaptive meshing process adjusts dynamically to geometric complexities, thereby enhancing the fidelity and accuracy of the simulations. Given the constraints of extraterrestrial environments, such as the Moon or Mars, this study emphasizes optimizing the printing time and minimizing the material consumption. By applying a volumetric reduction strategy, the objective is to reduce the volume of the original solid block by 50% while maintaining structural integrity and functionality. The design domain is imported into MATLAB for topology optimization, with COMSOL supplying high-quality finite element meshes and simulations to identify material-efficient design configurations suitable for advanced additive manufacturing.

The integration of MATLAB’s optimization capabilities with COMSOL’s simulation tools establishes a synergistic framework that significantly enhances both the fidelity and efficiency of the optimization process. This combined approach facilitates a comprehensive exploration of the design alternatives, enabling the identification of optimal structural configurations that achieve an effective balance between material efficiency and structural performance. In the context of autonomous topology optimization using photogrammetry, the process begins with capturing images of the physical object or environment, which are then processed through computer vision techniques to generate a 3D CAD model. This model represents the initial design domain. Following this, the topology optimization algorithms are applied to refine the design by eliminating superfluous material while preserving structural integrity. The performance of the optimized design is then assessed, and the final model is converted into an STL file format for 3D printing or further digital processing. This integration of photogrammetry with topology optimization streamlines and enhances the accuracy of the design process, thereby facilitating the creation of innovative and optimized structures.

Figure 3 illustrates the computer modeling for topology optimization, featuring a pillar subjected to vertical loading and securely anchored to the ground, thereby establishing fixed boundary conditions. The objective of the topology optimization is to minimize the design volume while simultaneously enhancing stiffness through the reduction in mechanical compliance. This method aligns with Tikhonov’s reciprocity principle, which addresses the non-convex nature of both stiffness and compliance optimization problems. In this study, the Young’s modulus of elasticity is normalized to unity, and the Poisson ratio is set at 0.3 to ensure consistency across all analyses. The results of this optimization process are presented in Figure 4.

Our study demonstrates a substantial reduction in the design domain’s volume, a primary goal of the optimization framework in comparation with parametric optimization methods [49]. This volume reduction follows a distinct spatial pattern, with the most significant reductions occurring centrally and tapering towards the peripheral areas near the structural constraints. This strategic material distribution enhances structural stability while optimizing material usage, analogous to civil engineering techniques where a weight reduction is achieved by incorporating hollow structures within solid frameworks. Such design strategies aim to maximize structural efficiency and performance while minimizing material consumption.

Figure 5 illustrates the convergence behavior of the optimization algorithm over successive iterations. The x-axis represents the number of iterations, while the y-axis depicts the normalized objective function value. Initially, the objective function value is near 1, indicating suboptimal conditions. However, as iterations advance, the objective function value significantly decreases, demonstrating the algorithm’s rapid convergence towards an optimal solution. By the 20th iteration, the curve begins to plateau near zero, indicating that the algorithm has effectively minimized the objective function and is approaching optimality. The initial steep decline followed by an asymptotic plateau highlights the algorithm’s efficiency and stability in the optimization process. This rapid reduction in the objective function value suggests that the method swiftly identifies a near-optimal solution, with subsequent iterations offering diminishing returns. The convergence graph underscores the algorithm’s ability to balance rapid convergence with stable minimization, ensuring the efficient achievement of an optimal or near-optimal solution.

5. Conclusions

In conclusion, this numerical study introduces a novel integration of computer vision and topology optimization to enhance designs for additive manufacturing. Utilizing advanced photogrammetry software tailored for high-resolution camera systems, we capture dynamic images of the design domain to create highly accurate 3D models. These models are converted into an STL file format, preserving the detailed features from the scans. The subsequent remeshing process, performed using an adaptive meshing algorithm within the COMSOL Multiphysics environment and managed through a custom MATLAB application, ensures optimal mesh resolution and accuracy.

Our study specifically focused on designing a concrete pillar for 3D printing, targeting a 75% reduction in volume to improve material efficiency and structural stability—an essential consideration for resource-limited extraterrestrial environments. The pillar was scanned with a 360-degree camera array, and the resulting spatial data informed the MATLAB-based topology optimization process. By leveraging MATLAB’s optimization algorithms in conjunction with COMSOL’s meshing and finite element analysis (FEA) tools, we explored various material-efficient design configurations.

The optimization results, highlighting a substantial volume reduction primarily in the central region, demonstrate a strategic approach to enhancing material efficiency while maintaining structural integrity. This design strategy parallels civil engineering principles, aiming for optimal performance with minimal material usage. Additionally, the rapid and stable convergence of the optimization algorithm, achieving near-optimal solutions within approximately 20 iterations, underscores the method’s computational efficiency and robustness in managing complex design problems. This work advances the existing literature by demonstrating a practical application of integrated computational tools for optimizing additive manufacturing processes, contributing new insights into the optimization of complex structural designs.

Author Contributions

Conceptualization, M.A.A.; methodology, M.A.A. and M.S.; numerical simulations, M.A.A., M.S. and M.N.; writing—original draft preparation, M.A.A., M.S. and M.N. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data may be available from the correspondent author upon reasonable request.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures

Figure 1. Algorithm illustrating the proposed method for optimizing the design process.

Figure 2. The design domain for a pillar.

Figure 3. The computer vision-based design domain of the pillar.

Figure 4. Topology optimization designs.

Figure 5. Objective function history of the pillar design domain study case.

References

1. Dallas, J.A.; Raval, S.; Gaitan, J.P.A.; Saydam, S.; Dempster, A.G. Mining beyond earth for sustainable development: Will humanity benefit from resource extraction in outer space?. Acta Astronaut.; 2020; 167, pp. 181-188. [DOI: https://dx.doi.org/10.1016/j.actaastro.2019.11.006]

2. Xu, F. The approach to sustainable space mining: Issues, challenges, and solutions. IOP Conf. Ser. Mater. Sci. Eng.; 2020; 738, 12014. [DOI: https://dx.doi.org/10.1088/1757-899X/738/1/012014]

3. Steffen, O. Explore to exploit: A data-centred approach to space mining regulation. Space Policy; 2022; 59, 101459. [DOI: https://dx.doi.org/10.1016/j.spacepol.2021.101459]

4. Baumgart, A.; Vlachopoulou, E.I.; Vera, J.D.R.; Di Pippo, S. Space for the Sustainable Development Goals: Mapping the contributions of space-based projects and technologies to the achievement of the 2030 Agenda for Sustainable Development. Sustain. Earth; 2021; 4, 6. [DOI: https://dx.doi.org/10.1186/s42055-021-00045-6]

5. Maiwald, V.; Schubert, D.; Quantius, D.; Zabel, P. From space back to Earth: Supporting sustainable development with spaceflight technologies. Sustain. Earth; 2021; 4, 3. [DOI: https://dx.doi.org/10.1186/s42055-021-00042-9]

6. Iliopoulos, N.; Esteban, M. Sustainable space exploration and its relevance to the privatization of space ventures. Acta Astronaut.; 2020; 167, pp. 85-92. [DOI: https://dx.doi.org/10.1016/j.actaastro.2019.09.037]

7. Al Ali, M.; Shimoda, M. Hygrally activated displacement inverter using a multiphysics multiscale topology optimization with considering evaporation. Struct. Multidiscip. Optim.; 2023; 66, 224. [DOI: https://dx.doi.org/10.1007/s00158-023-03679-6]

8. Coffin, P.; Maute, K. Level set topology optimization of cooling and heating devices using a simplified convection model. Struct. Multidiscip. Optim.; 2016; 53, pp. 985-1003. [DOI: https://dx.doi.org/10.1007/s00158-015-1343-8]

9. Xia, Q.; Shi, T.; Wang, M.Y. A level set based shape and topology optimization method for maximizing the simple or repeated first eigenvalue of structure vibration. Struct. Multidiscip. Optim.; 2011; 43, pp. 473-485. [DOI: https://dx.doi.org/10.1007/s00158-010-0595-6]

10. Michell, A.G.M. LVIII. The limits of economy of material in frame-structures. Lond. Edinb. Dublin Philos. Mag. J. Sci.; 1904; 8, pp. 589-597. [DOI: https://dx.doi.org/10.1080/14786440409463229]

11. Maxwell, J.C. I.—On reciprocal figures, frames, and diagrams of forces. Earth Environ. Sci. Trans. R. Soc. Edinb.; 1870; 26, pp. 1-40. [DOI: https://dx.doi.org/10.1017/S0080456800026351]

12. Barta, J. On the minimum weight of certain redundant structures. Acta Tech. Acad. Sci. Hung.; 1957; 18, pp. 67-76.

13. Sved, G. The minimum weight of certain redundant structures. Aust. J. Appl. Sci.; 1954; 5, pp. 1-9.

14. Hemp, W.S. Notes on the problem of the optimum design of structures. Aust. J. Appl. Sci.; 1958; 5, pp. 1-9.

15. Dorn, W.C.; Gomory, R.E.; Greenberg, H. Automatic design of optimal structures. J. Mec.; 1964; 3, pp. 25-52.

16. Bartel, D.L. Optimum Design of Spatial Structures. Ph.D. Thesis; University of California: Davis, CA, USA, 1969.

17. Charrett, D.E.; Rozvany, G.I.N. Extensions of the Prager-Shield theory of optimal plastic design. Int. J. Non-Linear. Mech.; 1972; 7, pp. 51-64. [DOI: https://dx.doi.org/10.1016/0020-7462(72)90021-2]

18. Rozvany, G.I.N.; Prager, W. Optimal design of partially discretized grillages. J. Mech. Phys. Solids; 1976; 24, pp. 125-136. [DOI: https://dx.doi.org/10.1016/0022-5096(76)90022-3]

19. Rossow, M.P.; Taylor, J.E. A finite element method for the optimal design of variable thickness sheets. AIAA J.; 1973; 11, pp. 1566-1569. [DOI: https://dx.doi.org/10.2514/3.50631]

20. Cheng, K.T.; Olhoff, N. An investigation concerning optimal design of solid elastic plates. Int. J. Solids Struct.; 1981; 17, pp. 305-323. [DOI: https://dx.doi.org/10.1016/0020-7683(81)90065-2]

21. Bendsoe, M.P.; Sigmund, O. Topology Optimization: Theory, Methods, and Applications; Springer: Berlin/Heidelberg, Germany, 2003.

22. Bendsoe, M.P.; Guedes, J.M.; Haber, R.B.; Pedersen, P.; Taylor, J.E. An analytical model to predict optimal material properties in the context of optimal structural design. J. Appl. Mech. Dec.; 1994; 61, pp. 930-937. [DOI: https://dx.doi.org/10.1115/1.2901581]

23. Bendsøe, M.P. Optimal shape design as a material distribution problem. Struct. Optim.; 1989; 1, pp. 193-202. [DOI: https://dx.doi.org/10.1007/BF01650949]

24. Al Ali, M.; Shimoda, M.; Benaissa, B.; Kobayashi, M. Non-parametric optimization for lightweight and high heat conductive structures under convection using metaheuristic structure binary-distribution method. Appl. Therm. Eng.; 2023; 233, 121124. [DOI: https://dx.doi.org/10.1016/j.applthermaleng.2023.121124]

25. Al Ali, M.; Shimoda, M. Investigation of concurrent multiscale topology optimization for designing lightweight macrostructure with high thermal conductivity. Int. J. Therm. Sci.; 2022; 179, 107653. [DOI: https://dx.doi.org/10.1016/j.ijthermalsci.2022.107653]

26. Liu, Y.; Li, Z.; Wei, P.; Wang, W. Parameterized level-set based topology optimization method considering symmetry and pattern repetition constraints. Comput. Methods Appl. Mech. Eng.; 2018; 340, pp. 1079-1101. [DOI: https://dx.doi.org/10.1016/j.cma.2018.04.034]

27. Hansen, C.; Henderson, T. CAD-Based Computer Vision: The Automatic Generation of Recognition Strategies; Springer: Berlin/Heidelberg, Germany, 1988; pp. 275-298.

28. Yoo, S.; Lee, S.; Kim, S.; Hwang, K.H.; Park, J.H.; Kang, N. Integrating deep learning into CAD/CAE system: Generative design and evaluation of 3D conceptual wheel. Struct. Multidiscip. Optim.; 2021; 64, pp. 2725-2747. [DOI: https://dx.doi.org/10.1007/s00158-021-02953-9]

29. Carvalho, L.E.; von Wangenheim, A. 3D object recognition and classification: A systematic literature review. Pattern Anal. Appl.; 2019; 22, pp. 1243-1292. [DOI: https://dx.doi.org/10.1007/s10044-019-00804-4]

30. Abali, B.E.; Barchiesi, E. Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization. Contin. Mech. Thermodyn.; 2021; 33, pp. 993-1009. [DOI: https://dx.doi.org/10.1007/s00161-020-00941-w]

31. Al Ali, M.; Shimoda, M.; Benaissa, B.; Kobayashi, M.; Takeuchi, T.; Al-Shawk, A.; Ranjbar, S. Metaheuristic aided structural topology optimization method for heat sink design with low electromagnetic interference. Sci. Rep.; 2024; 14, 3431. [DOI: https://dx.doi.org/10.1038/s41598-024-54083-z]

32. Al Ali, M.; Shimoda, M. Toward multiphysics multiscale concurrent topology optimization for lightweight structures with high heat conductivity and high stiffness using MATLAB. Struct. Multidiscip. Optim.; 2022; 65, 207. [DOI: https://dx.doi.org/10.1007/s00158-022-03291-0]

33. Madhavan, B.B.; Wang, C.; Tanahashi, H.; Hirayu, H.; Niwa, Y.; Yamamoto, K.; Tachibana, K.; Sasagawa, T. A computer vision based approach for 3D building modelling of airborne laser scanner DSM data. Comput. Environ. Urban Syst.; 2006; 30, pp. 54-77. [DOI: https://dx.doi.org/10.1016/j.compenvurbsys.2005.01.001]

34. Brutto, M.L.; Meli, P. Computer vision tools for 3D modelling in archaeology. Int. J. Herit. Digit. Era; 2012; 1, pp. 1-6. [DOI: https://dx.doi.org/10.1260/2047-4970.1.0.1]

35. Aicardi, I.; Chiabrando, F.; Lingua, A.M.; Noardo, F. Recent trends in cultural heritage 3D survey: The photogrammetric computer vision approach. J. Cult. Herit.; 2018; 32, pp. 257-266. [DOI: https://dx.doi.org/10.1016/j.culher.2017.11.006]

36. Xu, S.; Wang, J.; Shou, W.; Ngo, T.; Sadick, A.-M.; Wang, X. Computer vision techniques in construction: A critical review. Arch. Comput. Methods Eng.; 2021; 28, pp. 3383-3397. [DOI: https://dx.doi.org/10.1007/s11831-020-09504-3]

37. Svanberg, K. The method of moving asymptotes—A new method for structural optimization. Int. J. Numer. Methods Eng.; 1987; 24, pp. 359-373. [DOI: https://dx.doi.org/10.1002/nme.1620240207]

38. Colomina, I.; Molina, P. Unmanned aerial systems for photogrammetry and remote sensing: A review. ISPRS J. Photogramm. Remote Sens.; 2014; 92, pp. 79-97. [DOI: https://dx.doi.org/10.1016/j.isprsjprs.2014.02.013]

39. Baqersad, J.; Poozesh, P.; Niezrecki, C.; Avitabile, P. Photogrammetry and optical methods in structural dynamics—A review. Mech. Syst. Signal Process.; 2017; 86, pp. 17-34. [DOI: https://dx.doi.org/10.1016/j.ymssp.2016.02.011]

40. Baltsavias, E.P. A comparison between photogrammetry and laser scanning. ISPRS J. Photogramm. Remote Sens.; 1999; 54, pp. 83-94. [DOI: https://dx.doi.org/10.1016/S0924-2716(99)00014-3]

41. Fraser, C.S.; Brown, D.C. Industrial photogrammetry: New developments and recent applications. Photogramm. Rec.; 1986; 12, pp. 197-217. [DOI: https://dx.doi.org/10.1111/j.1477-9730.1986.tb00557.x]

42. Hanke, K.; Grussenmeyer, P. Architectural Photogrammetry: Basic Theory, Procedures, Tools; Taylor & Francis: Abingdon, UK, 2002; pp. 1-2.

43. Valença, J.; Júlio, E.; Araújo, H.J. Applications of photogrammetry to structural assessment. Exp. Tech.; 2012; 36, pp. 71-81. [DOI: https://dx.doi.org/10.1111/j.1747-1567.2011.00731.x]

44. Sapirstein, P. Accurate measurement with photogrammetry at large sites. J. Archaeol. Sci.; 2016; 66, pp. 137-145. [DOI: https://dx.doi.org/10.1016/j.jas.2016.01.002]

45. Da Vinci, L. The Notebooks of Leonardo da Vinci; Courier Corporation: North Chelmsford, MA, USA, 2012.

46. Boufama, B.; Mohr, R.; Veillon, F. Euclidean constraints for uncalibrated reconstruction. Proceedings of the 1993 (4th) International Conference on Computer Vision; Berlin, Germany, 11–14 May 1993; pp. 466-470.

47. Al Ali, M. Optimization for Engineers. Fundamentals of Orthopedic Design with Non-Parametric Optimization; Springer: Singapore, 2024; pp. 53-89. [DOI: https://dx.doi.org/10.1007/978-981-97-1040-9_3]

48. Giorgio, I.; Ciallella, A.; Scerrato, D. A study about the impact of the topological arrangement of fibers on fiber-reinforced composites: Some guidelines aiming at the development of new ultra-stiff and ultra-soft metamaterials. Int. J. Solids Struct.; 2020; 203, pp. 73-83. [DOI: https://dx.doi.org/10.1016/j.ijsolstr.2020.07.016]

49. Khodzhaiev, M.; Reuter, U. Structural optimization of transmission towers using a novel Genetic Algorithm approach with a variable length genome. Eng. Struct.; 2021; 240, 112306. [DOI: https://dx.doi.org/10.1016/j.engstruct.2021.112306]