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Application of Topological Optimisation Technology to Bridge Design
Abstract
This paper presents the application of modern topology optimisation technology to bridge design. Topology optimisation aims to determine the best locations and shapes of cavities in the design domain and therefore is capable of effectively dealing with structural design of infrastructure such as bridges. Several methods of topology optimisation have been developed during the past three decades, among which the evolutionary structural optimisation (ESO) method is popular because of its simplicity in software implementation and effectiveness in solving a wide range of engineering problems. The development of ESO and its advanced version bi-directional evolutionary structural optimisation (BESO) has reached a level of maturity nowadays. Applications of this technique have emerged around the world especially in the past decade. In this paper, the implementation of this technique in structural design is presented, with a particular focus on the design of various bridges. The design applications involve the consideration of different constructional requirements such as support types and selections of the elevation/span. Geometric constraints are also taken into account in the design problem, such as the periodic constraint with which a variety of architecturally aesthetic yet structurally efficient designs are produced. This paper aims to present the application of this promising technology to bridge design and to reveal its potential in a wider range of applications.
... As the second example, we illustrate the performance of the developed framework on passive void and passive solid region within design domain to obtain bridge like shapes similar to [44]. Similar to previous example, we study two different cases. ...
... The output is an arch bridge whereas an easy guess could be that of a bench kind of shape. Compared to the output from [44], our Fig. 15 where the span of the design domain is 40 m. ...
... The optimized configuration obtained using the proposed approach is shown in Fig. 17b. We observe that the pattern is almost similar to an actual solution from literature [44]. Overall the proposed approach converges in 49 iterations and requires 3.924 GB GPU memory as detailed in Table 6. ...
We propose an efficient implementation of a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In addition to that, significant computational efficiency in memory requirement has been achieved using homogenization strategy. The algorithm has been integrated with versatile computing platform of MATLAB for ease of use and customization. The bottlenecking repetitive solution of the state equation has been solved using an optimized geometric multigrid approach along with CUDA parallelization enabling an order of magnitude faster in computational time than current state of the art implementations. The main novelty lies in the efficient implementation wherein on the fly computation of auxiliary matrices in the multigrid scheme and modification in interpolation schemes using homogenization strategy removes memory limitation of GPUs. Memory hierarchy of GPU has also been exploited for further optimized implementations. All these enable solution of structures involving hundred millions of three dimensional brick elements to be accomplished in a standard desktop computer or a workstation. Performance of the proposed algorithm is illustrated using several examples including design dependent loads. Results obtained indicate the excellent performance and scalability of the proposed approach.
... As the second example, we illustrate the performance of the developed framework on passive void and passive solid region within design domain to obtain bridge like shapes similar to [35]. Similar to previous example, we study two different cases. ...
... The output is an arch bridge whereas an easy guess could be that of a bench kind of shape. Compared to the output from [35], our result looks mostly similar; this validates the accuracy of the proposed approach for this problem. Fig. 14 where the span of the design domain is 40m. ...
... The optimized configuration obtained using the proposed approach is shown in Fig. 16(b). We observe that the pattern is almost similar to an actual solution from literature [35]. Overall the proposed approach converges in 49 iterations and requires 3.924 GB GPU memory as detailed in Table 5. ...
We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In addition to that significant computational efficiency in memory requirement has been achieved using homogenization strategy. The algorithm has been integrated with versitile computing platform of MATLAB for ease of use and customization. The bottlenecking repetitive solution of the state equation has been solved using an optimized geometric multigrid approach along with CUDA parallelization enabling an order of magnitude faster in computational time than current state of the art implementations. On-the-fly computation of auxiliary matrices in the multigrid scheme and modification in interpolation schemes using homogenization strategy removes memory limitation of GPUs. Memory hierarchy of GPU has also been exploited for further optimized implementations. All these enable solution of structures involving hundred millions of three dimensional brick elements to be accomplished in a standard desktop computer or a workstation. Performance of the proposed algorithm is illustrated using several examples including design dependent loads and multimaterial.Results obtained indicate the excellent performance and scalability of the proposed approach.
... Topology optimization is an effective strategy to generate lightweight, high-performance, and costefficient structures by determining cavities in continuous design domains [1,2]. These striking features have led to the adoption of optimal topologies for many novel engineering applications, such as civil structures [3], compliant mechanisms [4], energy absorption devices [5], fluidic devices [6], mechanical parts [7], and aerospace structures [8]. ...
... The bounds are updated according to the summation of current design variables, where λ is updated to be α lower or α upper , for the scenario of i y i < N * and i y i > N * , respectively. The bi-sectional iterative process is repeated until α upper − α lower < 10 −8 , which will satisfy the constraint stated in Equation 3. ...
Topology optimization techniques are typically performed on a design domain with predetermined support conditions to generate efficient structures. Allowing the optimizer to simultaneously design supports and to-pology offers new design possibilities to achieve improved structural performance and reduce the cost of supports. However, existing simultaneous optimization techniques are limited, with most methods requiring cumbersome procedures to pre-define support conditions, which may not be easy for the end-users. This study presents a new element-based simultaneous optimization method by introducing a layer of elements to the boundaries where supports are allowed, which can be simply implemented in finite element (FE) models. Computational algorithms are developed based on a combination of an optimality criteria (OC) method and the bi-directional evolutionary structural optimization (BESO) technique to determine support locations and the structural topology, respectively. A variety of examples are presented to demonstrate the effectiveness of the new method. It is found that the number, position, and stiffness of supports may significantly influence the structural topology. A support location analysis is used to validate the new method and confirms optimal designs. This study shows that treating element-based support locations as additional design variables can effectively obtain efficient and innovative structural designs. Two 3D examples are presented to demonstrate potential practical applications of the new method.
... There has been extensive research on the topology optimization of the single-material continuum based on the BESO method [8,9]. Apart from the applications to architectural design [10] and mechanical design [11], the BESO method has also been introduced to the fields of advanced materials [12], aircraft design [13] and biomechanics [14,15]. ...
... In each case, the mesh is set as 240×20×80, and the area of deck with a thickness of 1.5m is set as a non-design area shown as the darker area in Figure 3. The elements in these areas are kept as solid elements, but the material for each element is determined by Eq. (10). In this study, the non-designed domains are so designed to ensure that solid materials in this region will not be eliminated, and at the same time, reduce the use of steel as much as possible. ...
Topology optimization techniques based on finite element analysis have been widely used in many fields, but most of the research and applications are based on single-material structures. Extended from the bi-directional evolutionary structural optimization (BESO) method, a new topology optimization technique for 3D structures made of multiple materials is presented in this paper. According to the sum of each element's principal stresses in the design domain, a material more suitable for this element would be assigned. Numerical examples of a steel-concrete cantilever, two different bridges and four floor systems are provided to demonstrate the effectiveness and practical value of the proposed method for the conceptual design of composite structures made of steel and concrete.
... The bridge design, on the other hand, has had lesser attention from the TO point of view. Nevertheless, Zhang et al.'s work on bridge design accounting for construction constraints with ESO algorithms [103] and Xie et al.'s Bi-Directional Evolutionary Structural Optimisation (BESO) algorithms application to the bridge conceptual design (Figure 2b) [104] must be mentioned. [9], (b) structural design by Zalewski and Zabłocki [105], and (c) CITIC financial centre in Shenzhen by SOM [105]. ...
... 2021, 11, x FOR PEER REVIEW 5 of 66 (a) (b) Figure 2. (a) From cellular to topology optimised beam [106] (reproduced under the Creative Commons Attribution 4.0 International License, http://creativecommons.org/licenses/by/4.0/ accessed on 25 February 2021) and (b) bridge topology optimisation from problem statement to optimal solution [104]. ...
Topology Optimisation is a broad concept deemed to encapsulate different processes for computationally determining structural materials optimal layouts. Among such techniques, Discrete Optimisation has a consistent record in Civil and Structural Engineering. In contrast, the Optimisation of Continua recently emerged as a critical asset for fostering the employment of Additive Manufacturing, as one can observe in several other industrial fields. With the purpose of filling the need for a systematic review both on the Topology Optimisation recent applications in structural steel design and on its emerging advances that can be brought from other industrial fields, this article critically analyses scientific publications from the year 2015 to 2020. Over six hundred documents, including Research, Review and Conference articles, added to Research Projects and Patents, attained from different sources were found significant after eligibility verifications and therefore, herein depicted. The discussion focused on Topology Optimisation recent approaches, methods, and fields of application and deepened the analysis of structural steel design and design for Additive Manufacturing. Significant findings can be found in summarising the state-of-the-art in profuse tables, identifying the recent developments and research trends, as well as discussing the path for disseminating Topology Optimisation in steel construction.
... Addressing geometrical topology changes structural optimization approach deals with archiving best optimized structural performance of a predetermined form including the topology, contour and elementary sizes. As the practical finite elementary method, several general topology optimization approaches have been established and applied to many projects in different areas during past three decades, including aerospace industry, civil engineering and architecture design [8] [9] [10] [11]. Among them, the evolutionary structural optimization (ESO) approach developed as a popular method especially within structural engineers and architects due to its simplicity of implementation [12]. ...
... With the consistence of removing redundant material and adding demanding material at each iteration with the von Mises stress criterion and strain energy density criterion, the robust BESO approach would evolve a structure from an initial geometry with very crude shape into a completely different shape with better structural performance [15]. One kind of design strategy is to apply the modified result by BESO as the final design [8]. In this paper authors attempts to use BESO in a novel way to balance the design of the desired geometry and the design of the efficient structure. ...
Abstract With timber pieces to weave a large span, the Chinese rainbow bridge in the famous painting entitled “Scenery along the River During the Qingming Festival” shows a special structural type. According to its arch shape, joints and construction technology, the rainbow bridge is perhaps an optimized design in its historical context. This hypothesis motivates us to use topology optimization methods to evaluate the timber woven-arch system. This paper firstly overviews present studies on structural performance of the Chinese rainbow bridge and the bi-directional evolutionary structural optimization (BESO) method. Next, this study evaluates the rainbow bridge’s structural and architectural features using BESO. Then, this paper evaluates extant timber lounge bridges related to the Chinese rainbow bridge using the BESO method to reveal advantages and disadvantages. By matching woven patterns of the traditional Chinese rainbow bridge and force-flow patterns generated by BESO, a novel evaluation method for complex forms is introduced. Keywords: Chinese rainbow bridge, BESO, Structural optimization, Woven-arch, Ameba software
(15) (PDF) Structural and architectural evaluation of Chinese rainbow bridge and related bridge types using BESO method. Available from: https://www.researchgate.net/publication/348740810_Structural_and_architectural_evaluation_of_Chinese_rainbow_bridge_and_related_bridge_types_using_BESO_method [accessed Jan 25 2021].
... In recent years, topology optimization techniques based on finite element analysis (FEA) have assisted designers in finding elegant and efficient structures beyond their traditional experience [22][23][24]. By introducing the bi-directional evolutionary structural optimization (BESO) method into the design of bridges, lighter and more efficient structural forms can be obtained [25]. Recently, Li and Xie have developed the multimaterial bi-directional evolutionary structural optimization (MBESO) method [26,27], which can effectively solve multiple material topology optimizations, significantly improve structural performance and reduce material usage. ...
An innovative half-through network arch bridge with a main span of 470 m was proposed and designed using coarse aggregate ultra-high-performance concrete (CA-UHPC) and steel. To effectively resist the tremendous axial forces, we utilized circular hollow section arch ribs with a CA-UHPC outer layer and an inner steel tube in this proposal. To minimize the bending moment of the arch ribs, we arranged the inclined crossed hangers above the deck and similarly the columns below the deck, connecting the arch ribs with the main girder, and adopting a structural system of double-hinged arches. By incorporating the recently developed multi-material bi-directional evolutionary structural optimization method and through various parametric studies, we determined the best configuration for the bridge. We also used finite element analysis to investigate the corresponding structural responses. The numerical analysis demonstrates that the proposed bridge has excellent mechanical performance in terms of stability, overall structural stiffness, stress, and fatigue strength of each component. A comprehensive comparison between the proposed bridge and the more conventional concrete-filled steel tube (CFST) arch bridge under the same conditions reveals that: the construction-related CO2 emissions of the proposed bridge are significantly lower than those of the CFST bridge, while the economic indicators are slightly better. The proposed bridge is simpler, slenderer, and more elegant. Due to its innovative design, the proposed bridge can overcome a series of problems associated with conventional bridges such as the excessive self-weight of long-span concrete arch bridges, the challenges of welding thick steel plates on 2 / 38 all-steel arch bridges and the high cost of these structures, as well as the disadvantages of CFST arch bridges.
... Hong et al. (2003) applied the principal stress based evolutionary structural optimization (ESO) method to arch, cable-stayed and suspension bridges. Xie et al. (2018) optimized suspension, truss and shell bridges applying a bi-directional ESO technique. When the attention is focused on one particular bridge type, size optimization is a common area of research; some works consider also materials as design variables, while few works optimize the structural configuration. ...
... In a given domain and specified load cases and boundary conditions, topology optimization uses fewer materials to maximize structural performance (Kutylowski and Rasiak 2014). There are several optimization techniques in practical applications such as the homogenization method , the solid isotropic material with the penalization (SIMP) method (Bendsøe and Sigmund 1995), the level set method (Wang et al. 2003), the genetic algorithm and generalized pattern search algorithm (Tugrul 2012), sensitivity analysis (Lee and Bae 2008), harmony search algorithm (Saka 2007), firefly algorithm (FA) (Aydogdu and Akin 2014), enhanced colliding bodies optimization (ECBO) method (Kaveh and Rezaei 2015;Kaveh and Rezaei 2016), Jaya algorithm (Dede 2018;Artar and Daloglu 2019;Grzywinski et al. 2019;Dede et al. 2020), using teaching-learning based optimization (TLBO) method (Artar et al. 2017;Eirgash et al. 2019), charged system search(SCC) algorithm Kaveh and Talatahari 2011;Kaveh and Ilchi Ghazaan 2018) which can consider the nonlinear behavior of the structure and achieve optimum geometrical and topological design, ant colony methodology , Cuckoo Search algorithm , and the bidirectional evolutionary structural optimization (BESO) method (Huang and Xie 2007;Huang and Xie 2010;Xie et al. 2014;Li and Xie 2021;Picelli et al. 2021). Among them, the BESO method has been proved to be a simple, robust, efficient, and reliable algorithm applicable to many structural designs. ...
Shell bridges have attracted extensive interest in engineering research and practice. This paper aims to evaluate the effects of longitudinal and transverse curvatures on the optimal design of the shell bridge. For this purpose, a slant-legged steel shell footbridge with the same initial and target volumes of steel was chosen to build parametric geometric models with different curvature radii, and then topology optimization was carried out using the bi-directional evolutionary structural optimization (BESO) technique to obtain optimized designs with high structural stiffness. Furthermore, linear static analysis and eigenvalue analysis demonstrate that the displacement, von Mises effective stress, and the first-order vertical vibration frequency satisfied all the requirements of design regulations. Numerical results indicate that not only the longitudinal curvature but also the transverse curvature have a significant effect on the optimized designs of steel shell footbridge. While the mean compliance increased with the transverse curvature radius, it first decreased and then increased with the longitudinal curvature radius. Keywords: shell bridge; curvature radius; topology optimization; BESO method; optimal design; steel shell
(14) (PDF) Effects of Longitudinal and Transverse Curvatures on Optimal Design of Shell Footbridge. Available from: https://www.researchgate.net/publication/358221641_Effects_of_Longitudinal_and_Transverse_Curvatures_on_Optimal_Design_of_Shell_Footbridge [accessed Jan 30 2022].
... Hong et al. (2003) applied the principal stress based evolutionary structural optimization (ESO) method to arch, cable-stayed and suspension bridges. Xie et al. (2018) optimized suspension, truss and shell bridges applying a bi-directional ESO technique. When the attention is focused on one particular bridge type, size optimization is a common area of research; some works consider also materials as design variables, while few works optimize the structural configuration. ...
he most used design approach for civil engineering structures is a trial and error procedure; the designer chooses an initial configuration, tests it and changes it until all safety requirements are met with good material utilization. Such a procedure is time consuming and eventually leads to a feasible solution, while several better ones could be found. Indeed, together with safety, environmental impact and investment cost should be decisive factors for the selection of structural solutions. Thus, structural optimization with respect to environmental impact and cost has been the subject of many researches in the last decades. However, design techniques based on optimization haven’t replaced the traditional design procedure yet. One of the reasons might be the constructive feasibility of the optimal solution. Moreover, concerning reinforced concrete beam bridges, to the best of the author knowledge, no study in the literature has been published dealing with the optimization of the entire bridge including both the structural configuration and cross-section dimensions.
In this thesis, a two-steps automatic design and optimization procedure for reinforced concrete road beam bridges is presented. The optimization procedure finds the solution that minimizes the investment cost and the environmental impact of the bridge, while fulfilling all requirements of Eurocodes. In the first step, given the soil morphology and the two points to connect, it selects the optimal number of spans, type of piers-deck connections and piers location taking into account any obstacle the bridge has to cross. In the second and final step, it finds the optimal dimensions of the deck cross-section and produces the detailed reinforcement design. Constructability is considered and quantified within the investment cost to avoid a merely theoretical optimization. The wellknown Genetic Algorithm (GA) and Pattern Search optimization algorithms have been used. However, to reduce the computational effort and make the procedure more user-friendly, a memory system has been integrated and a modified version of GA has been developed. Moreover, the design and optimization procedure is used to study the relationship between the optimal solutions concerning investment cost and environmental impact.
One case study concerning the re-design of an existing road bridge is presented. Potential savings obtained using the proposed method instead of the classic design procedure are presented. Finally, parametric studies on the total bridge length have been carried out and guidelines for designers have been produced regarding the optimal number of spans.
... The evolutionary structural optimization (ESO) method proposed by Xie et al. (Xie and Steven 1994) takes the presence or absence of materials in a finite element grid as a design variable, and gradually removes invalid or inefficient materials to achieve the topology optimization of continuous structures. The ESO approach has been further developed in recent years (Munk 2019;Xie et al. 2018;Yin et al. 2019;Zuo et al. 2012;Zuo et al. 2016). ...
Even through the topology optimal truss-like structure based on the truss-like material model is very close to its analytical solution, further post-processing is required to form a truss or a homogeneous isotropic perforated plate. In this paper, an optimal truss-like material distribution field is expressed by a B-spline function. For the convenience of processing, the optimal material distribution domain of a truss-like structures is firstly extended into a curved quadrilateral extension domain. Then, the relationship between the B-spline curve clusters and the distribution of truss-like material members is established by a sample points array. Combined with the distribution of materials, a topology structure that meets the design requirements is formed. Numerical examples with three models show that the B-spline function can describe the distribution field of truss-like material members efficiently, and the number of the truss-like material members can be actively controlled to meet different design needs. Comparison between the optimal results and them of the traditional analytical solution is made and results show that the topological structure is close to the analytical solution.
... Topology optimization has been broadly accepted by the design community, and literature presents various civil engineering and architectural applications like designing bridges, e.g., [28,29]; designing high-rise buildings, e.g., [30]; and others e.g., [31]. The discussion regards various issues including, for example, different types of constraints [32] and the optimization of bi-material structures [33]. ...
Expectations and challenges of modern sustainable engineering and architecture stimulate intensive development of structural analysis and design techniques. Designing durable, light and eco-friendly constructions starts at the conceptual stage, where new efficient design and optimization tools need to be implemented. Innovative methods, like topology optimization, become more often a daily practice of engineers and architects in the process of solving more and more demanding up-to-date engineering problems efficiently. Topology optimization is a dynamically developing research area with numerous applications to many research and engineering fields, ranging from the mechanical industry, through civil engineering to architecture. The motivation behind the present study is to make an attempt to broaden the area of topology optimization applications by presenting an original approach regarding the implementation of the multi-domain and multi-material topology optimization to the design and the strengthening/retrofitting of structures. Moreover, the implementation of the design-dependent self-weight loading into the design model is taken into account as a significantly important issue, since it influences the final results of the topology optimization process, especially when considering massive engineering structures. As an optimization tool, the original efficient heuristic algorithm based on Cellular Automata concept is utilized.
... Throughout the history of architecture, the expression of building form has been limited by traditional building method, in which even slightly irregular forms can significantly change the time and cost needed for construction [2]. However, Since the introduction of computational aided design technology into the architectural design at the end of the 20th century, the topic of form-finding based on structural performance has gained new momentum [3]. The development of architectural technology is closely related to the evolution of structural morphology, from barrel arches and domes in the period of Greece and Rome to pendentives and flying buttresses in the period of Byzantium and Gothic; from physical models used by Antonio Gaudi and Frey Otto to the application of topological optimization technology to architectural designs, architectural morphology and structural optimization have always been reinforcing each other. ...
This research explores innovations in structural design and construction through the generative design technique BESO (Bi-directional Evolutionary Structural Optimization)[1]and the application of robotic fabrication to produce efficient and elegant spatial structures. The innovative pavilion discussed in this paper demonstrates a design and fabrication process and thecollaborationbetween architecture and engineering research groups through a series of small-scale test models and a full-scale model of topologically optimized spatial structures. The focus of this work is the use of a modified BESO technique to optimize the structure which features branches of various sizes, inspired by Gaudi’s Sagrada Familia Bacilica, and the introduction of large-scalerobotic 3D printing developed at RMIT University.The advantages of the new design and construction process are efficient material usage and elegant structural forms.
... The academic world has been continuously active in the field of structural optimization of bridges from 1970 [4][5][6] until today. Topology optimization has been applied to identify the best material layout for several types of bridges [7][8]. When the attention is focused on one particular bridge type, size optimization is a common area of research; some works consider also materials as design variable, while few works optimize the structural configuration. ...
This work presents a procedure for the automated design and optimization of reinforced concrete beam bridges. The aim is to find solutions that minimize the investment cost and the environmental impact of the bridge. The complete structure is optimized including: number of spans, pier locations, pier-deck connections and deck dimensions. A detailed design of the deck reinforcement is included as well. Furthermore, constructability is considered and quantified within the investment cost to avoid a merely theoretical optimization. Genetic Algorithm (GA) and Pattern Search (PS) optimization algorithms are used. To reduce the computational time and make the procedure more user-friendly, a memory system is integrated and a modified version of GA is developed. In this paper, the proposed procedure is applied to re-design an existing bridge originally designed according to Eurocodes by an experienced engineer in 2013. Savings of 10-15% for both investment cost and environmental impact have been obtained. Finally, the proposed procedure has been applied to several alternatives with different total bridge lengths to suggest the optimal number of spans for a given total bridge length.
... In most of the works devoted to topology optimization of engineering structures, i.a. [16], the following main assumption is made: the structure is made of a homogenous material and must carry the specified load under the predefined constraints imposed on, among other things, its topology. But in the case of soil-steel structures, considered in this paper, this assumption should not be used since they are composite structures consisting of a relatively thin (usually steel) shell and backfill. ...
The paper proposes a procedure for shape optimization of flexible soil-steel structures. The mechanical behaviour of such structures is significantly different in comparison to other bridge construction technologies. The load bearing capacity of the backfill soil is of the key importance. This fact was taken into account. In particular, the energy optimality condition and simulated annealing algorithm were utilized. Due to the assumptions made, while originally formulating the condition, the optimal shapes should be regarded as the ones maximizing backfill mobilization. Thus, the method takes the advantage of the peculiar character of soil-steel structures and, therefore, should be regarded as specially dedicated to such type of engineering objects. A detailed formulation of the procedure is followed by a short review of the optimization results obtained by the author so far. In this regard two types of load were considered: dead-weight of the backfill and uniformly distributed load of the surface. However, the original contribution of the work is a proposal of the procedure modification allowing to identify the optimal shape of the shell of a soil-steel structure capable of carrying the moving load, i.e. without it being necessary to assume a priori the location of the vehicle. To achieve this the "worst case" logic was applied to modify optimality condition. The optimal shapes, obtained numerically for different types of loading including non-stationary truck load, and the relations between them suggest the potential for the practical use of the proposed optimization procedure.
... Chen et al. [22] obtained the optimal form of arch bridge using BESO and discussed the optimization results with different rise-to-span ratios. Felicetti et al. [23] applied BESO to bridge design in consideration of different requirements, for instance, support types, constraint types, and selections of span. However, this method has the numerical problem of checkerboard. ...
Topology optimization has developed rapidly in the past three decades; as a creative and efficient optimization technique, it has been applied in engineering fields of aerospace and mechanical. However, there are a few attempts in bridge form design. In this paper, the parametric level set method is utilized to solve the form finding of arch bridges. The optimization model for minimizing the structural compliance under the volume constraint is built. Three numerical examples of form finding of arch bridges are studied. Results show that the optimal structures which have well-distributed stress and smooth force transmission are almost identical with the actual forms of arch bridges. The optimal forms can be treated as alternatives in the preliminary design stage, and topology optimization has a bright prospect in form finding of arch bridges.
... Furthermore, some of the works do not apply optimization techniques to search the optimum solution, basing their results in practice experiences or treating as optimization the result of the comparison of two (or more) situations evaluated, like is the case of the works of Knight [4], Bhatti and Al-Gahtani [5] e Gocál and Dursová [6], for example. Other interesting works related to optimization of different bridges models are Ghasemi and Dizangian [7]; Mohammadzadeh and Nouri [8]; Xie et al. [9]; Kaveh, Bakhshpoori and Barkhori [10]; and Kutylowski and Rasiak [11]. ...
The present study aimed to supply parameters that lead to optimized design in composite bridges. To achieve the proposed objectives has been formulated an optimization problem which aims to reduce the cost of bridge cross section by varying the dimensions of the steel girders. The implementation of the proposed formulation has been done by creating a design routine in MS Excel and using the Solver to find the optimized sections to the girders. The specification used in the analysis and design of the girders has been the AASHTO (2012), and the cases studied are of simple span bridges with different spans and a variable number of steel girders in its cross section. The results obtained enabled identification of parameters aimed at the optimized design of composite bridges, showing that the use of criteria based on optimization techniques can lead to a significant reduction in the cost of the structures.
... A considerable amount of literature has been published on size, shape and topology optimization of bridge structures in the last decades [1,2,3,4]. The researchers use a wide spectrum of optimization methods, inter alia, structural evolutionary optimization (ESO) [5,6], bi-directional ESO (BESO) [7], genetic algorithm (GA) [4], and others, e.g. ...
The paper presents results of shape optimization of underground structure. First, the objective function is proposed based on the energetic equivalence principle. The excavation is replaced, within the approach proposed, by an artificial very compliant material and the optimal shape of the excavation is postulated as the one that minimizes the energy of volumetric strain cumulated in it. The solution is looked for using the stochastic optimization approach, namely the simulated annealing (SA) procedure. A soil-steel bridge structure with different loads and boundary conditions is investigated. The results representing the optimized shapes of the structures examined are presented.
This paper proposes a novel bridge design approach based on multi-material topology optimization, which realizes the process from conceptual design to detailed design, and an innovative bridge form is obtained with the proposed approach. In the present study, the multi-material bi-directional evolutionary structural optimization (MBESO) method, which is developed from the bi-directional evolutionary structural optimization (BESO) method, is used as the algorithm which can effectively handle topology optimization problems involving multiple materials. Since the method assigns two different materials to the tension and compression members in a structure, it is particularly suitable for designing bridge structures composed of steel and concrete. A three-span bridge with a main span of 350 m is used as an example to apply the MBESO method for the topology optimization design, and a set of techniques are introduced, such as the variation of the design domain, the utilization of symmetry, the selection of the non-design domain and the consideration of multiple load cases, to obtain multiple optimization results. By 2 comprehensively studying the functionality, ease of construction, and aesthetic properties, a competitive result is selected as the proposed conceptual design for the bridge, and then a detailed design, including an implementable construction process, is achieved and verified by finite element analysis. The comparison between the proposed bridge and other typical bridge types based on technical and economic indicators clearly shows the obvious advantages of the new type of bridge design. This research work realizes the whole process to obtain the detailed design of a new bridge type from the form-finding with the MBESO method, revealing the considerable value of applying multi-material topology optimization to the design of practical long-span bridges.
In this paper, a deep learning-based model is proposed which is capable of automatically generating the structural topology configurations with the minimum structural compliance and deformation under various load conditions and volume fraction limitations. The deep-learning model combines the advanced algorithms of Convolutional Neural Network (CNN) with U-net architecture and Recurrent Neural Network (RNN) with Long-Short Term Memory (LSTM) architecture. The established data-driven framework learns the structural evolution process from training data samples, which are randomly generated in finite element simulations employing an element removal strategy. The well-trained model is successfully utilized for two types of cases: two-dimensional and three-dimensional cantilever-beam structural topology designs. The deep-learning model outperforms the traditional methods in terms of lower time cost and broader applicability, demonstrating the potential of such a data-driven approach to accelerate the process of preliminary structural design.
Topology optimization (TO) has rapidly evolved from an academic exercise into an exciting discipline with numerous industrial applications. Various TO algorithms have been established, and several commercial TO software packages are now available. However, a major challenge in TO is the post-processing of the optimized models for downstream applications. Typically, optimal topologies generated by TO are faceted (triangulated) models, extracted from an underlying finite element mesh. These triangulated models are dense, poor quality, and lack feature/parametric control. This poses serious challenges to downstream applications such as prototyping/testing, design validation, and design exploration. One strategy to address this issue is to directly impose downstream requirements as constraints in the TO algorithm. However, this not only restricts the design space, it may even lead to TO failure. Separation of post-processing from TO is more robust and flexible. The objective of this paper is to provide a critical review of various post-processing methods and categorize them based both on targeted applications and underlying strategies. The paper concludes with unresolved challenges and future work.
This article presents the results of a study of the efficiency of post-tensioned bridges. It is an initial step toward a broader goal of providing designers with a simple and rational basis for assessing the efficiency of bridge design concepts. The approach consisted first of establishing a set of parameters defining the primary characteristics of the bridge type considered, simply supported multiple-T systems. Within a defined range of parameter values, designs were generated and checked by computer against applicable safety and serviceability criteria. A subset of valid cases was extracted with the lowest value of reference depth, defined as the ratio of the cross-sectional area and deck width. Reference depth was used as the primary measure of efficiency because it measures concrete quantity, independent of span or width. The study shows that cross sections with three webs minimize reference depth. For each span length, the range of values for span-to-depth ratio for efficient cross sections is well defined and limited. Minimizing reference depth does not require large quantities of prestressing steel.
Deflections tend to have more significance in modern structures, especially those that are either taller, longer, or have wider spans than earlier designs. It is also necessary to provide desirable distributions of internal forces in order to achieve effective, efficient and elegant structures.
This book presents four structural concepts relating to deflections and internal forces in structures, and demonstrates a number of routes and physical measures together with their implementation for creating desirable distributions of internal forces and for designing structures against deflection. Hand calculation examples, with and without using the implementation measures, are provided to quantify the effectiveness and efficiency of the structural concepts. Practical examples, including several well-known structures, are considered qualitatively to illustrate the practical implementation of the structural concepts and show their structural rationale.
The book is especially suitable for advanced undergraduate and postgraduate students studying civil engineering or architecture, and should enhance the holistic comprehension of structural engineers and architects.
By observing naturally occurring structures such as shells, bones and trees it becomes obvious that the topology and shape of these structures achieve their optimum over a long evolutionary period and adapt to whatever environment they find themselves in. This paper is to demonstrate the possibility of achieving similar shape and layout optimization by using the finite element analysis and training the software to follow a particular evolutionary path.
Describes development work to combine the basic ESO with the additive evolutionary structural optimisation (AESO) to produce bidirectional ESO whereby material can be added and can be removed. It will be shown that this provides the same results as the traditional ESO. This has two benefits, it validates the whole ESO concept and there is a significant time saving since the structure grows from a small initial one rather than contracting from a sometimes huge initial one where 90 per cent of the material gets removed over many hundreds of finite element analysis (FEA) evolutionary cycles. Presents a brief background to the current state of Structural Optimisation research. This is followed by a discussion of the strategies for the bidirectional ESO (BESO) algorithm and two examples are presented.
The increasing complexity of engineering systems has sparked rising interest in multidisciplinary optimization (MDO). This paper surveys recent publications in the field of aerospace, in which the interest in MDO has been particularly intense. The primary c hallenges in MDO are computational expense and organizational complexity. Accordingly, this survey focuses on various methods used by different researchers to address these challenges. The survey is organized by a breakdown of MDO into its conceptual components, reflected in sections on mathematical modelling, approximation concepts, optimization procedures, system sensitivity, and human interface. Because the authors' primary area of expertise is in the structures discipline, the majority of the references focus on the interaction of this discipline with others. In particular, two sections at the end of this review focus on two interactions that have recently been pursued with vigour: the simultaneous optimization of structures and aerodynamics and the simultaneous optimization of structures with active control.
This paper presents a method for topology optimization of periodic structures using the bi-directional evolutionary structural
optimization (BESO) technique. To satisfy the periodic constraint, the designable domain is divided into a certain number
of identical unit cells. The optimal topology of the unit cell is determined by gradually removing and adding material based
on a sensitivity analysis. Sensitivity numbers that consider the periodic constraint for the repetitive elements are developed.
To demonstrate the capability and effectiveness of the proposed approach, topology design problems of 2D and 3D periodic structures
are investigated. The results indicate that the optimal topology depends, to a great extent, on the defined unit cells and
on the relative strength of other non-designable part, such as the skins of sandwich structures.
This paper presents an improved algorithm for the bi-directional evolutionary structural optimization (BESO) method for topology optimization problems. The elemental sensitivity numbers are calculated from finite element analysis and then converted to the nodal sensitivity numbers in the design domain. A mesh-independency filter using nodal variables is introduced to determine the addition of elements and eliminate unnecessary structural details below a certain length scale in the design. To further enhance the convergence of the optimization process, the accuracy of elemental sensitivity numbers is improved by its historical information. The new approach is demonstrated by solving several compliance minimization problems and compared with the solid isotropic material with penalization (SIMP) method. Results show the effectiveness of the new BESO method in obtaining convergent and mesh-independent solutions.
This paper proposes a method for topology optimization of periodic structures on dynamic problems by using an improved bidirectional evolutionary structural optimization (BESO) technique. Frequency optimization and frequency-stiffness optimization are formulated for periodic continuum structures at the macroscopic level under arbitrary loadings and boundaries. Numerical instabilities that occur in common topological frequency optimization are dealt with by eliminating singular and single-hinged elements and removing alternative
element groups in case of sudden drops of the relevant frequency. Layout periodicity of the optimal design is guaranteed by creating a representative unit cell (RUC) on the basis of a user-defined cell mode and averaging the sensitivities from all unit cells into the RUC. The capability and effectiveness of the proposed approach are demonstrated by numerical experiments with various cell modes.
In this paper, a new algorithm for bi-directional evolutionary structural optimization (BESO) is proposed. In the new BESO method, the adding and removing of material is controlled by a single parameter, i.e. the removal ratio of volume (or weight). The convergence of the iteration is determined by a performance index of the structure. It is found that the new BESO algorithm has many advantages over existing ESO and BESO methods in terms of efficiency and robustness. Several 2D and 3D examples of stiffness optimization problems are presented and discussed.
Two figures are reciprocal when the properties of the first relative to the second are the same as those of the second relative to the first. Several kinds of reciprocity are known to mathematicians, and the theories of Inverse Figures and of Polar Reciprocals have been developed at great length, and have led to remarkable results. I propose to investigate a different kind of geometrical reciprocity, which is also capable of considerable development, and can be applied to the solution of mechanical problems.
The evolutionary structural optimisation (ESO) method has been under continuous development since 1992. Traditionally, the method was conceived from the engineering perspective that the topology and shape of structures were naturally conservative for safety reasons and therefore contained an excess of material. To move from the conservative design to a more optimum design would therefore involve the removal of material. Thus the ESO method started from a design space much bigger than the optimum and the final topology or shape emerged by a process of removal of unwanted/inefficient/lowly stresses material. The original algorithms allowed for two forms of evolution. One was there the understressed material could be removed from anywhere in the allowable design space, and with compensation for checker-boarding this produces an optimum topology under the prescribed environments. The second form only allows removal from the surface or parts of the surface (called nibbling in the ESO lexicon); this produces a Min–Max situation where the maximum surface stress is reduced to a minimum. It has been demonstrated that the ESO process produces a surface that is an iso-stress contour thus satisfying the Min–Max optimality criterion. The present paper addresses the opposite evolutionary process whereby the structure evolves from a base which is the minimum structural form required to carry the load regardless of the magnitude of the stress levels. Material is added in the proximity of high stress to ameliorate its effect and hence the final structural form emerges. Only singly connected regions are formed in the present analysis and thus the additive ESO process is the opposite of the nibbling SO, mentioned above, that produces optimum surface shapes. The paper presents a brief background to the current state of structural optimisation research. This is followed by a discussion of the strategies for the additive ESO (AESO) algorithm and two examples are presented.
A simple evolutionary procedure is proposed for shape and layout optimization of structures. During the evolution process low stressed material is progressively eliminated from the structure. Various examples are presented to illustrate the optimum structural shapes and layouts achieved by such a procedure.
Purpose
This paper surveys the current state and capabilities of three dimensional printing (3DP). A comprehensive review of 3D Printing applications is presented. The scope of the applications includes design, manufacturing, the medical field and architecture.
Design/methodology/approach
A large variety of manufacturing applications such as rapid pattern making and rapid tooling using the 3DP process directly or as core technology, as well as further implications in design and engineering analysis, medicine, and architecture are presented and evaluated.
Findings
Some research issues are also discussed. An attempt, based on the state of the art, to show weaknesses and opportunities, and to draw conclusions about the future of this important process rounds up this paper.
Research limitations/implications
The scope of this research survey is limited to evaluation and comparison of processes that may be characterised as 3D printing technologies.
Practical implications
The study is very useful as a basis for matching evaluated 3D printing machine and process capabilities to user requirements, and forms a framework on which future comparative studies can build.
Originality/value
A comprehensive overview of the capabilities of 3DP processes is presented and evaluated. It shows the application of 3D printing beyond concept modelling. The paper is valuable for researchers as well as individuals, who require adequate and relevant comparative information during decision making.
Two types of solutions may be considered in generalized shape optimization. Absolute minimum weight solutions, which are rather unpractical, consist of solid, empty and porous regions. In more practical solutions of shape optimization, porous regions are suppressed and only solid and empty regions remain. This note discusses this second class of problems and shows that a solid, isotropic microstructure with an adjustable penalty for intermediate densities is efficient in generating optimal topologies.
Although automation has advanced in manufacturing, the growth of automation in construction has been slow. Conventional methods of manufacturing automation do not lend themselves to construction of large structures with internal features. This may explain the slow rate of growth in construction automation. Contour crafting (CC) is a recent layered fabrication technology that has a great potential in automated construction of whole structures as well as subcomponents. Using this process, a single house or a colony of houses, each with possibly a different design, may be automatically constructed in a single run, imbedded in each house all the conduits for electrical, plumbing and air-conditioning. Our research also addresses the application of CC in building habitats on other planets. CC will most probably be one of the very few feasible approaches for building structures on other planets, such as Moon and Mars, which are being targeted for human colonization before the end of the new century.
Optimal shape design of structural elements based on boundary variations results in final designs that are topologically equivalent to the initial choice of design, and general, stable computational schemes for this approach often require some kind of remeshing of the finite element approximation of the analysis problem. This paper presents a methodology for optimal shape design where both these drawbacks can be avoided. The method is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, isotropic material, with the requirement that the resulting structure can carry the given loads as well as satisfy other design requirements. The computation of effective material properties for the anisotropic material is carried out using the method of homogenization. Computational results are presented and compared with results obtained by boundary variations.
Evolutionary Topology Optimization of Continuum Structures: Methods and Applications Application of computational morphogenesis to structural design
- X Huang
- Ym Xie
- H Ohmori
- H Futai
- T Iijima
- A Muto
- H Hasegawa
[10] Huang X, Xie YM. Evolutionary Topology
Optimization of Continuum Structures: Methods
and Applications, John Wiley and Sons, Ltd.:
Chichester, England, 2010.
[11] Ohmori H, Futai H, Iijima T, Muto A,
Hasegawa H. Application of computational morphogenesis to structural design. Proceedings of
Frontiers of Computational Sciences Symposium,
Nagoya, Japan, 11-13 October, 2005, 45-52.
Generalized shape optimization without homogenization
- Gin Ozvany
- M Zhou
- T Birker
[5] R ozvany GIN, Zhou M, Birker T. Generalized
shape optimization without homogenization.
Struct. Optim. 1992; 4: 250-254.
Application of computational morphogenesis to structural design
- H Ohmori
- H Futai
- T Iijima
- A Muto
- H Hasegawa
Ohmori H, Futai H, Iijima T, Muto A,
Hasegawa H. Application of computational morphogenesis to structural design. Proceedings of
Frontiers of Computational Sciences Symposium,
Nagoya, Japan, 11-13 October, 2005, 45-52.
- M Sasaki
Sasaki M. Flux Structure, Toto: Tokyo, 2005.