Conceptual design of structural systems based on topology optimization and prefabricated components

Structural system design is the process of giving form to a set of interconnected components subjected to loads and design constraints while navigating a complex design space. While safe designs are relatively easy to develop, optimal designs are not. Modern computational optimization approaches employ population based metaheuristic algorithms to overcome challenges with the system design optimization landscape. However, the choice of the initial population, or ground structure, can have an outsized impact on the resulting optimization. This paper presents a new method of generating such ground structures, using a combination of topology optimization (TO) and a novel system extraction algorithm. Since TO generates monolithic structures, rather than systems, its use for structural system design and optimization has been limited. In this paper, truss systems are extracted from topologies through morphological analysis and artificial intelligence techniques. This algorithm, and its assessment, constitutes the key contribution of this paper. The structural systems obtained are compared with ground truth solutions to evaluate the performance of the algorithms. The generated structures are also compared against benchmark designs from the literature. The results indicate that the presented truss generation algorithm produces structures comparable to those generated through metaheuristic optimization, while mitigating the need for assumptions about initial ground structures.

SAP2000 is well-known commercial software for analysis and design of structural systems that is equipped with an open application programming interface (OAPI). In this work, a code written in C# able to solve three-dimensional topology optimization problems is presented, where a topology optimization framework was integrated into SAP2000 taking advantage of its OAPI feature. The code is partially based on the 99 and 88 line codes written by Sigmund (Struct Multidiscip Optim 21(2):120–127, 2001) and Andreassen et al. (Struct Multidiscip Optim 43(1):1–16, 2011). The code solves the problem of minimum compliance while through OAPI it takes advantage of all modelling capabilities of SAP2000. The paper covers the theoretical aspects of topology optimization incorporated in the code and provides detailed description of their numerical implementations. Special effort was made to the latter one, describing in detail all numerical aspects of the code, in order to facilitate the reader to understand the code, and therefore being able to further enhance its capabilities. The complete code can be downloaded from GitHub ( https://github.com/nikoslagaros/TOCP ).

This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself. Concerning the first topic, we investigate different means to improve the robustness of density-based numerical models including geometrical nonlinearities. The conventional approach (scaling the local material properties) can result in convergence problems due to excessive deformation in low-stiffness finite elements. To avoid excessive deformation, we combine the element connectivity parameterization method (adapting the connectivity between finite elements) with level-set-based topology optimization. Furthermore, we achieve greater robustness of analysis method using a second and improved approach called element deformation scaling. This approach eliminates the need for solving internal equilibrium equations (needed for the element connectivity parameterization method) via an explicit relation between the local internal and global external displacement field. The second focus of this thesis is on the optimization process of level-set-based topology optimization, and in particular its numerical consistency. We observe that signed-distance reinitialization of the level-set function affects the shape of a design in the optimization process. To minimize this effect, we propose a discrete level-set method that is based on an approximate Heaviside function and focusing on the implementation. Furthermore, we also propose a level-set-based topology optimization method using an exact Heaviside function and mathematical programming that effectively eliminates the need for reinitialization. We demonstrate that our density-based level-set method is closely related to conventional density-based topology optimization methods, while offering the advantage of more control over the geometrical complexity. On the other hand, we confirm that the dependence of the final result on the initial design which remains one of the big challenges for level-set-based topology optimization. The potential of the proposed level-set method is shown by applying it on problems with stress constraints and geometrical nonlinearities and performing manufacturing tolerant topology optimization. Finally, this thesis offers a review of level-set methods for structural topology optimization to identify and discuss the different approaches that are available in literature. We can distinguish between level-set methods by examination of their design parameterization, sensitivities, update procedures and regularization techniques. A level-set-based design parameterization offers the advantage of a crisp distinction between subdomains. For this reason, X-FEM approaches and conforming discretizations are an interesting option to retain the crisp nature of the level-set-based description of the design. Many level-set methods are combined with density-based numerical models and are, therefore, closely related to conventional density-based topology optimization methods. In particular, recently proposed projection methods have much in common with a level-set-based design description. The results of level-set-based TO methods often rely heavily on regularization techniques that introduce inconsistencies in the optimization process. Numerical consistency does not necessarily lead to the best search direction, but is essential to find a Karush-Kuhn-Tucker point of the discretized optimization problem.

Recently, a structural optimization design system linked with a FEM analysis system is going to be useful for a structural design, by a radical development of a computer environment. But, when structural engineers use this design system in practice, complicated operations are required to make an input-data. So this design system is not “a Practical Tool” for designers, we have to develop the structural optimization design system which is used easily for designers.Authors research the CIM for shipbuilding and develop a prototype CIM system. We call this system SODAS (System Of Design and Assembling for Shipbuilding). In the SODAS, designers can design a ship structure by design parameters and evaluate a designed structure by FEM directly.In this study, authors try to integrate a commercial structural optimization design system (GENESIS : which is developed in NASA) with the SODAS. We make relations clear between design parameters in the SODAS and design variables in the structural optimization design system. And we propose the method of system integration used by these relations. In the concrete, we develop the structural optimization design system based on the Product Model which supports designers powerfully by presenting optimal design-values.

A simplified method for reliability- and integrity-based design of engineering systems and its application to offshore mooring systems

The manifold microchannel (MMC) heat sink has been widely studied for liquid-cooling of power-dense electronic components. Conventionally, thermal-fluid performance of an MMC heat sink is analyzed via unit cell simulations and designed by varying the rectangular fin and channel geometries, namely size optimization. To further explore the performance potential of the MMC heat sink, this paper proposes topology optimization (TO) to design the optimal freeform fin/channel geometry to maximize heat transfer performance while minimizing the required pumping power. The heat transfer physics in an MMC heat sink is governed by conjugate heat transfer between an incompressible laminar fluid and a heated conductor. The MMC heat sink fin/channel geometry design is formulated as a material distribution problem in a periodic unit cell. Since TO describes the geometry non-parametrically, it facilitates innovative designs through the exploration of arbitrary shapes. The physics-governed design optimization problem is solved by mathematical programming using design sensitivities and an iterative gradient-based method. The thermal-fluid performance is presented for both conventional size optimization and the proposed TO approach, considering the heat transfer performance versus the required pumping power. It is demonstrated that the TO designed fin/channel geometries outperform those obtained through size optimization. Due to the shape complexity associated with the TO designed fin/channel geometries, they are not readily suitable for conventional manufacturing processes, e.g., machining and metal die-casting. However, such out-of-box designs fully exploit the flexibility offered by the latest advanced manufacturing processes, e.g., additive manufacturing and rapid investment casting.

The recent article by Burdisso and Fuller [‘‘Design of active structural acoustic control systems by eigenproperty assignment,’’ J. Acoust. Soc. Am. 96, 1582–1591 (1994)] does not fully illuminate the contributions of a number of prior authors for a crucial part of the work, that is, the development of weak radiator modes. This comment places the subject development of Burdisso and Fuller in context with the prior art. Further, it demonstrates the similarities of the subject development to prior work published by K. A. Cunefare [‘‘The minimum multimodal radiation efficiency of baffled finite beams,’’ J. Acoust. Soc. Am. 90, 2521–2529 (1991)]. The authors recognize and acknowledge that Burdisso and Fuller’s implementation of the concept, through eigenproperty assignment, is unique and valuable.

Combining topology optimization and additive manufacturing (AM) is a promising approach to breaking through the limitations of conventional design and developing innovative structures with high performance. However, the unique manufacturing constraints in AM should be considered when developing the topology optimization algorithms for AM. Material anisotropy is one of the common characteristics of AM materials due to the layer-by-layer manufacturing techniques. This work proposes a topology optimization approach for AM with strength constraints considering anisotropy. The Hoffman failure criterion is adopted to represent the anisotropic strength behaviors of AM materials. Based on the Hoffman failure criteria and the p-norm measure aggregation function, a global strength constraint formulation is established. Under the framework of solid isotropic material with penalization, we develop a topology optimization methodology to minimize the structural weight or volume fraction subject to structural stiffness and strength constraints. Several two-dimensional (2D) or 3D numerical test cases are performed to validate the effectiveness and performance of the developed method. The results indicated that the proposed method could make full use of material properties by considering anisotropic strength. Besides, the topological optimization considering strength anisotropy could be combined with build direction optimization to further reduce the structural weight.

Our research focuses on the extraordinary mechanics of slender large-span shells, membranes, and elastic rod networks under extreme loading and during construction. Our work concerns shape generation and analysis approaches for innovative lightweight structural systems that enable a resilient, and sustainable built environment. We focus on the advancement of theoretical and computational approaches to predict and design the overall properties, stability, and failure of these systems. Capturing the nonlinear behavior of these structures, especially those with complex geometries, spatially varying loading, and those undergoing large displacements or even large strains, can be challenging due to the inherent computational complexity of modeling these behaviors. Their design and associated loading conditions are also complex because of their spatial (1-1000m) and temporal (50-200 years) scales, and the challenge of materializing these systems over those scales. In terms of methodology development, we have been working on a comprehensive framework with advanced analytical formulations, numerical form finding and optimization approaches, fluid/structure interaction models, and machine-learning algorithms to open new avenues for accelerated discoveries and automated optimal designs. In terms of applications, we have used this framework to successfully innovate structural and architectural systems ranging from macro-scale adaptive shading devices to large-scale storm surge barriers. Large-span shells, membranes, and rod networks exhibit fascinating mechanical behaviors because geometric nonlinearities arise even when their material properties are linear. Their shape and topology give them properties beyond what is possible with conventional structural systems. In this paper, I outline how we discovered, studied, designed and even built large-scale structural surfaces that can efficiently carry extreme loading, self-assemble, adjust their stiffnesses, elastically shift from one shape to another, or amplify motion.

Mathematical optimization theories are employed for the design of structures in structural optimization. Structural optimization is being widely utilized for practical problems due to well-developed commercial software systems. Three representative structural optimization systems such as Genesis, MSC Nastran and OptiStruct are investigated and evaluated by solving various test examples in different scales. The design capabilities of three software systems are explored and the performances of the systems are compared. The performance of structural optimization depends on the quality of the optimum solution and the computational time, and these aspects are compared from an application viewpoint. For a fair comparison, the same formulations are utilized, and the same optimization methods are employed for each example. Also, the same system environment is prepared, and the same optimization parameters are used. Additionally, various design options of each software system are tested for the best performance. Linear static response size, shape, topology, topometry and topography optimizations are applied to the examples and the results are compared. No system seems to be the best in all cases and each system has advantages and disadvantages depending on the application. In general, Genesis is excellent in computational time while OptiStruct gives excellent optimum solutions, in size, topometry and topology optimizations. Meanwhile, MSC Nastran presents good solutions in shape and topography optimizations.

With the rapid advancement of computing technology, mathematical modeling and computer simulations have become common and standard methods for design of complex systems. To exercise these models intelligently and eliminate the burden of manual iteration, manipulating inputs and reviewing outputs, optimization strategies are applied in a simulation-based design environment. In reality, the knowledge that engineers have about the design problem is imperfect and incomplete, uncertainty always exists in simulation-based design. The conventional deterministic optimization techniques do not consider the impact of such uncertainties. If the system responses driving the design decisions are very sensitive to these uncertainties, serious problems might confront the designer. Performance of the actual system may differ greatly from expected optimum performance. Again, if the design solution is near one or more constraint boundaries, then even slight uncertainties or changes in the operating environment could produce failed, unsafe designs, and/or result in substantial performance degradation. In recent years, the concept of reliability and robust design has become very popular. Probabilistic design analysis and statistical modeling allow the identification of designs that qualify as not only feasible, but as consistently feasible in the face of uncertainty. Reliability based topology optimization (RBTO) extends the reliability notion to the area of structural topology optimization. Although reliability based design optimization (RBDO) is a well established research area, very few work has been presented in the area of RBTO. In this study, we give an overview of the various works done in the field of RBTO. Ever since Bendsoe and Kikuchi introduced the topology optimization using a homogenization method, many topology optimization methods have been developed for the both linear and nonlinear structures. Traditional topology optimization methods drive the topology of a structure to an optimum design based on the constraint on mass. Kharmanda et al. introduced reliability constraints in deterministic topology optimization problem. They proposed a heuristic strategy that aims to reduce mass while improving the reliability level of the structure without greatly increasing its weight. But the limit state function used by them was not based on failure criteria for the structure. Their formulation considered uncertainty with respect to ∗Design Automation Laboratory †Advisor geometrical dimension and applied load only. Also their reliability analysis seems to be independent of the boundary and loading condition, so their results showed similar values for the uncertain variables for different structures. Tovar et al. have developed the Hybrid Cellular Automaton (HCA) method for structural synthesis of continuum material where the state of each cell is defined by both density and strain energy. In Agarwal, a decoupled RBDO approach is employed such that the topology optimization is separate from the reliability analysis. Patel et al. showed the use of RBTO using the gradient free Hybrid Cellular Automata (HCA) method. Their formulation incorporates uncertainty with respect to material property also. They considered limit state function based on failure modes on the output displacements. This study aims at giving a comparative study on these methods. It points out the advantages and disadvantages of the methods, and their significance in the field of RBTO. As large numbers of design variables are associated with continuum topology optimization problems, RBTO methods are inherently computationally expensive because of additional required system analysis associate with RBDO. Based on the observations, this study presents an efficient method for incorporating reliability analysis in topology optimization.

Concurrent topology optimization of macrostructures and material microstructures for natural frequency

This paper deals with topology optimization seen from an industrial and a manufacturing point of view. What the industrial users see as key issues when implementing topology optimization are frequently not the topics that the academic environments consider when implementing topology optimization. One of the key issues is that topology optimization should be integrated into an existing CAD and CAE environment (example of FE-solvers: ABAQUS, ANSYS, CATOPO, NX Nastran, MSc Nastran, MSc Marc and Permas). Here, it is of importance to note that the models analyzed in the industrial CAE environments often consist of many finite elements (can be more than 2 million elements) and different types of elements (continuum, beam, membrane, shell, bar and rigid elements) which all can be employed in the same model. Furthermore, symmetry and manufacturing constraints are important for ensuring that the results of the topology optimized are manufacturable. Several examples will be given of how structural topology optimization can be used as an add-on module in existing CAE environments However, from an academic point of view an add-on module including topology optimization for commercial FE-solvers is also of interest because the latest finite element and solver technology can be applied in the modeling for the topology optimization. Furthermore, the aim is also to show where the industry is today and which demands exist for the future. The results reported here are based upon the work done by FE-Design and their industrial partners using the topology optimization module (TOSCA.topo) and smooth module (TOSCA.smooth) of the program TOSCA.

Optimal design of porous and periodic microstructures through topology identification of the associated periodic unit cell (PUC) constitutes the topic of this work. Here, the attention is confined to two-phase heterogeneous materials in which the topology identification of manufacturable 3D-PUC is conducted by means of a topology optimization technique. The associated objective function is coupled with 3D numerical homogenization approach that connects the elastic properties of the 3D-PUC to the target product. The topology optimization methodology that is adopted in this study is the combination of solid isotropic material with penalization (SIMP) method and optimality criteria algorithm (OCA), referred to as SIMP-OCA methodology. The fairly simple SIMP-OCA is then generalized to handle the topology design of 3D manufacturable microstructures of cubic and orthotropic symmetry. The performance of the presented methodology is experimentally validated by fabricating real prototypes of extremal elastic constants using additive manufacturing. Experimental evaluation is performed on two designed microstructures: an orthotropic sample with Young’s moduli ratios [Formula: see text], [Formula: see text] and a cubic sample with negative Poisson’s ratio of [Formula: see text]. In all practical examples studied, laboratory measurements are in reasonable agreement with the prescribed values; thus, corroborating the applicability of the proposed methodology.

Human activity-induced vibrations in slender structural systems become apparent in many different excitation modes and consequent action effects that cause discomfort to occupants, crowd panic and damage to public infrastructure. Resulting loss of public confidence in safety of structures, economic losses, cost of retrofit and repairs can be significant. Advanced computational and visualisation techniques enable engineers and architects to evolve bold and innovative structural forms, very often without precedence. New composite and hybrid materials that are making their presence in structural systems lack historical evidence of satisfactory performance over anticipated design life. These structural systems are susceptible to multi-modal and coupled excitation that are very complex and have inadequate design guidance in the present codes and good practice guides. Many incidents of amplified resonant response have been reported in buildings, footbridges, stadia and other crowded structures with adverse consequences. As a result, attenuation of human-induced vibration of innovative and slender structural systems very often requires special studies during the design process. Dynamic activities possess variable characteristics and thereby induce complex responses in structures that are sensitive to parametric variations. Rigorous analytical techniques are available for investigation of such complex actions and responses to produce acceptable performance in structural systems.This paper presents an overview and a critique of existing code provisions for human-induced vibration followed by studies on the performance of three contrasting structural systems that exhibit complex vibration. The dynamic responses of these systems under human-induced vibrations have been carried out using experimentally validated computer simulation techniques. The outcomes of these studies will have engineering applications for safe and sustainable structures and a basis for developing design guidance.