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When addressing problems with wicked tendencies in higher professional education, students experience complexity, uncertainty, and value divergence. Furthermore, they are confronted with disciplinary, organisational, and sector boundaries. Prior research has revealed variability in students’ experiences and boundary-crossing behaviour when dealing with problems with wicked tendencies. In this study we explore these differences by identifying student profiles based on the attributes that comprise the competence for dealing with problems with wicked tendencies, and by identifying their relations with students’ boundary-crossing behaviour and relevant work experience. Person-centred cluster analysis in a sample of first-year students (N = 264) from a bachelor’s programme in social work identified four student profiles, based on students’ self-assessed degree of creativity, critical thinking, initiative, proactivity, risk tolerance, and work efficacy. Meaningful relations with students’ prior work experiences and their boundary-crossing behaviour were found. These profiles could serve to better understand students’ boundary-crossing behaviour when confronted with problems with wicked tendencies, and help teachers foster the development of all students., Science Education and Communication

Integrated language, science and technology (ILS&T) instruction is a complex task for primary school teachers that requires professional development. Task-centered educational approaches such as the four-component instructional design (4C/ID) model are well suited for the development of complex professional skills. This article describes the application of the Ten Steps approach to the 4C/ID model in the domain of teacher education. The findings describe a blueprint for a 4C/ID-based teacher professional development program aimed at equipping in-service primary school teachers with the competences for ILS&T instruction, which can support instructional designers, teacher educators and researchers in making informed instructional design decisions., Science Education and Communication

Background and aims: Adopting healthier diets can drastically improve societal health. Our environment plays a crucial role in daily dietary choices and hospitals in particular can stimulate patients to adopt healthier eating habits. Unfortunately, no robust clinically applicable cuing tools exist to help guide in-hospital dietary interventions. The purpose of this study was to identify patient-related barriers and facilitators to adopting healthier dietary choices. Methods and results: This cross-sectional observational study was conducted on the cardiology ward of a university medical center between June 2020 and January 2021. Of the 594 patients asked and the 312 completed surveys on healthy eating intentions, 285 responses were considered for analysis. Notably, the majority of respondents were male (68.8%), with an average hospital stay of 3.3 days. The results indicate that cardiac patients attribute significantly greater influence on their dietary behavior to doctors compared to other caregivers, including dieticians (X2 = 37.09, df = 9, p < 0.001). Also, younger patients (below 70 years of age) were more inclined to plan changing dietary behavior than older patients. Most mentioned facilitators for adopting a healthier diet were more information/counseling, help in preparing food, support from family and friends, and more emphasis from a doctor. Conclusion: The study highlights the importance of involving doctors in formulating dietary policies and patient-directed interventions within hospital settings. It also sheds light on the barriers and facilitators for promoting healthier dietary behaviors among patients during their hospitalization., Methodologie en Organisatie van Design

Computational process modelling of metal additive manufacturing has gained significant research attention in recent past. The cornerstone of many process models is the transient thermal response during the AM process. Since deposition-scale modelling of the thermal conditions in AM is computationally expensive, spatial and temporal simplifications, such as simulating deposition of an entire layer or multiple layers, and extending the laser exposure times, are commonly employed in the literature. Although beneficial in reducing computational costs, the influence of these simplifications on the accuracy of temperature history is reported on a case-by-case basis. In this paper, the simplifications from the existing literature are first classified in a normalised simplification space based on assumptions made in spatial and temporal domains. Subsequently, all types of simplifications are investigated with numerical examples and compared with a high-fidelity reference model. The required numerical discretisation for each simplification is established, leading to a fair comparison of computational times. The holistic approach to the suitability of different modelling simplifications for capturing thermal history provides guidelines for the suitability of simplifications while setting up a thermal AM model., Computational Design and Mechanics, Mechanical, Maritime and Materials Engineering

Modeling of fluid flows in density-based topology optimization forms a longstanding challenge. Methods based on the Navier–Stokes equations with Darcy penalization (NSDP equations) are widely used in fluid topology optimization. These methods use porous materials with low permeability to represent the solid domain. Consequently, they suffer from flow leakage in certain areas. In this work, the governing equations for solid/fluid density-based topology optimization are reevaluated and reinterpreted. The governing equations are constructed using the volume averaged Navier–Stokes (VANS) equations, well known in the field of porous flow modeling. Subsequently, we simplify, interpret and discretize the VANS equations in the context of solid/fluid topology optimization, and analytically derive lower bounds on the Darcy penalization to sufficiently prevent flow leakage. Based on both the NSDP and VANS equations, two flow solvers are constructed using the Finite Volume method. Their precision and the lower bound on the Darcy penalization are investigated. Subsequently, the solvers are used to optimize flow channels for minimal pressure drop, and the resulting designs and convergence behavior are compared. The optimization procedure using the VANS equations is found to show less tendency to converge to inferior local optima for more precise flow solutions and is less sensitive to its parameter selection., Computational Design and Mechanics, Mechanical Engineering

High computational costs are encountered in topology optimization problems of geometrically nonlinear structures since intensive use has to be made of incremental-iterative finite element simulations. To alleviate this computational intensity, reduced-order models (ROMs) are explored in this paper. The proposed method targets ROM bases consisting of a relatively small set of base vectors while accuracy is still guaranteed. For this, several fully automated update and maintenance techniques for the ROM basis are investigated and combined. In order to remain effective for flexible structures, path derivatives are added to the ROM basis. The corresponding sensitivity analysis (SA) strategies are presented and the accuracy and efficiency are examined. Various geometrically nonlinear examples involving both solid as well as shell elements are studied to test the proposed ROM techniques. Test cases demonstrates that the set of degrees of freedom appearing in the nonlinear equilibrium equation typically reduces to several tenth. Test cases show a reduction of up to 6 times fewer full system updates., Computational Design and Mechanics, Mechanical Engineering

The published article contains a mistake in the notation of the strain–displacement matrix (Formula presented.) in Voigt notation concerning the isoparametric mapping and in the notation of the corresponding derivatives. As the mistakes relate only to the notation, and the implementation in the code was done correctly, they bear no consequences for the remainder of the manuscript and the results presented therein. The (Formula presented.) matrix defined inline after Eq. (11) on page 5 (repeated on pages 8 and 17) should be written as (Formula presented.) for an enriched element with n original shape functions and m enrichment functions. The differential operator (Formula presented.) in Eq. 12 should then have been defined in Voigt notation and in global coordinates as (Formula presented.) for elastostatics in 2-D and 3-D, respectively, and (Formula presented.) for heat conductivity in 2-D and 3-D, respectively. The derivatives in global coordinates are computed from the derivatives in local coordinates as (Formula presented.) for standard and enriched shape functions, respectively, where (Formula presented.) is the Jacobian of the intersected original element and (Formula presented.) is the Jacobian of the integration element. Furthermore, the derivative of (Formula presented.) with respect to the enriched node location (Formula presented.) in Equation 28 should be written as (Formula presented.) Note that the terms in (Formula presented.) corresponding to the standard shape functions are zero (this equation replaces Eq. 29 of the manuscript): (Formula presented.) as the Jacobian of the parent element is not influenced by the enriched node location, and the derivatives of the standard shape functions with respect to local coordinates of the parent element are constant. The components in (Formula presented.) corresponding to the enrichment functions are computed using (this equation replaces Eq. 30 in the manuscript) (Formula presented.) where the second term is z, Computational Design and Mechanics, Mechanical Engineering

The thixotropic properties of contemporary mortars allow the insertion of mortar in small vertical seams by using a mortar pump without the need for traditional formwork. In such a seam, a vertical mortar connection for the transfer of shear forces can be created by simply adding a profile to the mortar-to-concrete interfaces. In this way a constructible continious vertical shear connection can be constructed between storey-high precast concrete wall elements. In this investigation, narrow vertical mortar connections are developed for the transfer of shear forces in precast concrete shear walls with tying reinforcement in the slabs. The shear behaviour of five versions with differently shaped mortar-to-concrete interfaces is obtained from shear tests. All experimental results are presented and discussed, while the shear behaviour of the Staggered shear key connection is analysed in detail. Also, the shear behaviour of the five mortar connections are mutually compared and assessed on their performance for functioning as a vertical mortar connection. A diagonal bar model is proposed for simulating the shear behaviour of the Staggered shear key connection, which is called the “inclined compression strut model”. Also, an equation for predicting the shear capacity is proposed. The functioning of the model and equation are investigated by applying them in case studies with cantilever shear walls in versions with and without window openings., Concrete Structures

Phononic crystals can be designed to show band gaps—ranges of frequencies whose propagation is strongly attenuated in the material. In essence, their working principle is based on destructive interference of waves reflecting from the periodic arrangement of material interfaces (i.e., Bragg scattering). Consequently, capturing accurately the behavior at material interfaces requires appropriate numerical modeling and computational design techniques. However, the commonly used density-based representation in popular topology optimization methods results in a diffuse staircased boundary. The heavily refined finite element meshes required to compensate for this boundary description results in exceedingly large and expensive optimization problems. In this paper, we demonstrate the adverse effect of the density-based boundary description. Furthermore, we propose a level set-based topology optimization procedure with an enriched finite element method that shows improved performance when compared to the density-based approach., Computational Design and Mechanics, Mechanical, Maritime and Materials Engineering

Een onderzoek naar het gebruik van sociale robotica in primair onderwijs ten behoeve van de ontwikkeling van technische en sociale vaardigheden voor leerlingen met een autismespectrumstoornis (ASS) RoboWise: An investigation into the use of social robotics in primary education for developing technological and social skills in children with an autism spectrum disorder (ASD), Science Education and Communication

Additive manufacturing of metal parts involves phase transformations and high temperature gradients which lead to uneven thermal expansion and contraction, and, consequently, distortion of the fabricated components. The distortion has a great influence on the structural performance and dimensional accuracy, e.g., for assembly. It is therefore of critical importance to model, predict and, ultimately, reduce distortion. In this paper, we present a computational framework for fabrication sequence optimization to minimize distortion in multi-axis additive manufacturing (e.g., robotic wire arc additive manufacturing), in which the fabrication sequence is not limited to planar layers only. We encode the fabrication sequence by a continuous pseudo-time field, and optimize it using gradient-based numerical optimization. To demonstrate this framework, we adopt a computationally tractable yet reasonably accurate model to mimic the material shrinkage in metal additive manufacturing and thus to predict the distortion of the fabricated components. Numerical studies show that optimized curved layers can reduce distortion by orders of magnitude as compared to their planar counterparts., Mechanical Engineering, Materials and Manufacturing

In recent years, the Q-factor of Si 3 N 4 nanomechanical resonators has significantly been increased by soft-clamping techniques using large and complex support structures. To date, however, obtaining similar performance with smaller supports has remained a challenge. Here, we make use of torsion beam supports to tune the Q-factor of Si 3 N 4 string resonators. By design optimization of the supports, we obtain a 50% Q-factor enhancement compared to the standard clamped-clamped string resonators. By performing experimental and numerical studies, we show that further improvement of the Q-factor is limited by a trade-off between maximizing stress and minimizing torsional support stiffness. Thus, our study also provides insight into dissipation limits of high-stress string resonators and outlines how advanced designs can be realized for reaching ultimate f 0 × Q product while maintaining a small footprint., Dynamics of Micro and Nano Systems, QN/Groeblacher Lab, Computational Design and Mechanics, Mechanical Engineering, QN/Steeneken Lab

The design of high-performance mechatronic systems is very challenging, as it requires delicate balancing of system dynamics, the controller, and their closed-loop interaction. Topology optimization provides an automated way to obtain systems with superior performance, although extension to simultaneous optimization of both topology and controller has been limited. To allow for topology optimization of mechatronic systems for closed-loop performance, stability, and disturbance rejection (i.e. modulus margin), we introduce local approximations of the Nyquist curve using circles. These circular approximations enable simple geometrical constraints on the shape of the Nyquist curve, which is used to characterize the closed-loop performance. Additionally, a computationally efficient robust formulation is proposed for topology optimization of dynamic systems. Based on approximation of eigenmodes for perturbed designs, their dynamics can be described with sufficient accuracy for optimization, while preventing the usual threefold increase of additional computational effort. The designs optimized using the integrated approach have significantly better performance (up to 350% in terms of bandwidth) than sequentially optimized systems, where eigenfrequencies are first maximized and then the controller is tuned. The proposed approach enables new directions of integrated (topology) optimization, with effective control over the Nyquist curve and efficient implementation of the robust formulation., Computational Design and Mechanics, Mechanical, Maritime and Materials Engineering

Overheating is a major issue especially in metal Additive Manufacturing (AM) processes, leading to poor surface quality, lack of dimensional precision, inferior performance and/or build failures. A 3D density-based topology optimization (TO) method is presented which addresses the issue of local overheating during metal AM. This is achieved by integrating a simplified AM thermal model and a thermal constraint within the optimization loop. The simplified model, recently presented in literature, offers significant computational gains while preserving the ability of overheating detection. The novel thermal constraint ensures that the overheating risk of optimized designs is reduced. This is fundamentally different from commonly used geometry-based TO methods which impose a geometric constraint on overhangs. Instead, the proposed approach takes the process physics into account. The proposed method is validated via an experimental comparative study. Optical tomography (OT) is used for in-situ monitoring of process conditions during fabrication and obtained data is used for evaluation of overheating tendencies. The novel TO method is compared with two other methods: standard TO and TO with geometric overhang control. The experimental data reveals that the novel physics-based TO design experienced less overheating during the build as compared to the two classical designs. A study further investigated the correlation between overheating observed by high OT values and the defect of porosity. It shows that overheated regions indeed show higher defect of porosity. This suggests that geometry-based guidelines, although enhance printability, may not be sufficient for eliminating overheating issues and related defects. Instead, the proposed physics-based method is able to deliver efficient designs with reduced risk of overheating., Computational Design and Mechanics, Mechanical Engineering

An extensive field campaign, the Ems-Dollard Measurements (EDoM), was executed in the Ems Estuary, bordering the Netherlands and Germany, aimed at better understanding the mechanisms that drive the exchange of water and sediments between a relatively exposed outer estuary and a hyper-turbid tidal river. More specifically, the reasons for the large up-estuary sediment accumulation rates and the role of the tidal river on the turbidity in the outer estuary were insufficiently understood. The campaign was designed to unravel the hydrodynamic and sedimentary exchange mechanisms, comprising two hydrographic surveys during contrasting environmental conditions using eight concurrently operating ships and 10 moorings measuring for at least one spring–neap tidal cycle. All survey locations were equipped with sensors measuring flow velocity, salinity, and turbidity (and with stationary ship surveys taking water samples), while some of the survey ships also measured turbulence and sediment settling properties. These observations have provided important new insights into horizontal sediment fluxes and density-driven exchange flows, both laterally and longitudinally. An integral analysis of these observations suggests that large-scale residual transport is surprisingly similar during periods of high and low discharge, with higher river discharge resulting in both higher seaward-directed fluxes near the surface and landward-directed fluxes near the bed. Sediment exchange seems to be strongly influenced by a previously undocumented lateral circulation cell driving residual transport. Vertical density-driven flows in the outer estuary are influenced by variations in river discharge, with a near-bed landward flow being most pronounced in the days following a period with elevated river discharge. The study site is more turbid during winter conditions, when the estuarine turbidity maximum (ETM) is pushed seaward by river flow, resulting in a more pronounced impact of suspended sedimen, Environmental Fluid Mechanics, Mathematical Physics

High-tech equipment critically relies on flexures for precise manipulation and measurement. Through elastic deformation, flexures offer extreme position repeatability within a limited range of motion in their degrees of freedom, while constraining motion in the degrees of constraint. Topology optimization proves a prospective tool for the design of short-stroke flexures, providing maximum design freedom and allowing for application-specific requirements. State-of-the-art topology optimization formulations for flexure synthesis are subject to challenges like ease of use, versatility, implementation complexity, and computational cost, leaving a generally accepted formulation absent. This study proposes a novel topology optimization formulation for the synthesis of short-stroke flexures uniquely based on strain energy measures under prescribed displacement scenarios. The resulting self-adjoint optimization problem resembles great similarity to ‘classic’ compliance minimization and inherits similar implementation simplicity, computational efficiency, and convergence properties. Numerical examples demonstrate the versatility in flexure types and the extendability of additional design requirements. The provided source code encourages the formulation to be explored and applied in academia and industry., Structural Optimization and Mechanics

Metastructures composed of snapping beams are capable of deforming into a series of stable states, enabling them to realize shape reconfigurations. In this paper, we present the design of a metastructure-based morphing surface that is able to exhibit a series of stable configurations with different curvatures. Using theoretical, numerical, and experimental approaches, we study the snap-through transition between the initially flat and the curved stable configurations. Effects of geometric parameters on the snap-through and curvatures are systematically investigated. Results show that the beam thickness is important for tuning the snap-through response, while the curvature can be tuned by changing the beam height and the horizontal span of the structures. Furthermore, an analytical model is developed to investigate the structural nonlinear deformations. It is shown that the proposed model can predict the snap-through transition properly. The structural stability can be controlled by setting proper values for t/L and h/L (t, h, and L represents the beam thickness, height and span, respectively). Finally, it is demonstrated that based on two-dimensional arrangements of bi-stable elements, various stable configurations, like corrugations in different directions, can be imposed to the surface., Structural Optimization and Mechanics, Micro and Nano Engineering

In topology optimization, the state of structures is typically obtained by numerically evaluating a discretized PDE-based model. The degrees of freedom of such a model can be partitioned in free and prescribed sets to define the boundary conditions. A multi-partition problem involves multiple partitions of the same discretization, typically corresponding to different loading scenarios. As a result, solving multi-partition problems involves multiple factorization/preconditionings of the system matrix, requiring a high computational effort. In this paper, a novel method is proposed to efficiently calculate the responses and accompanying design sensitivities in such multi-partition problems using static condensation for use in gradient-based topology optimization. A main problem class that benefits from the proposed method is the topology optimization of small-displacement multi-input–multi-output compliant mechanisms. However, the method is applicable to any linear problem. We present its formulation and an algorithmic complexity analysis to estimate computational advantages for both direct and iterative solution methods to solve the system of equations, verified by numerical experiments. It is demonstrated that substantial gains are achievable for large-scale multi-partition problems. This is especially true for problems with both a small set of number of degrees of freedom that fully describes the performance of the structure and with large similarities between the different partitions. A major contribution to the gain is the lack of large adjoint analyses required to obtain the sensitivities of the performance measure., Structural Optimization and Mechanics

We propose a fully immersed topology optimization procedure to design structures with tailored fracture resistance under linear elastic fracture mechanics assumptions for brittle materials. We use a level set function discretized by radial basis functions to represent the topology and the Interface-enriched Generalized Finite Element Method (IGFEM) to obtain an accurate structural response. The technique assumes that cracks can nucleate at right angles from the boundary, at the location of enriched nodes that are added to enhance the finite element approximation. Instead of performing multiple finite element analyses to evaluate the energy release rates (ERRs) of all potential cracks—a procedure that would be computationally intractable—we approximate them by means of topological derivatives after a single enriched finite element analysis of the uncracked domain. ERRs are then aggregated to construct the objective function, and the corresponding sensitivity formulation is derived analytically by means of an adjoint formulation. Several numerical examples demonstrate the technique's ability to tailor fracture resistance, including the well-known benchmark L-shaped bracket and a multiple-loading optimization problem for obtaining a structure with fracture resistance anisotropy., Structural Optimization and Mechanics

Topology optimization methods improve the structural performance of components. However, in food processing, medical, high-precision, and other industries' designs should also fulfil the requirement of being cleanable. An important aspect of cleanability is drainability, which entails that fluids can always run off the structure under just gravity. Therefore, taking drainability into account during the optimization process is essential for many applications. This paper proposes a drainage filter that turns a blueprint design into a drainable design. In a layer-by-layer fashion, the design is adjusted, to ensure fluids can always run down its surface. A smooth minimum and maximum are used in the formulation to allow for consistent sensitivity calculation. To allow for the small runoff angles, typical for practical drainability, a grid refinement is proposed. Moreover, any drainage direction can be considered. The effectiveness of the method is illustrated in 2D and 3D., Structural Optimization and Mechanics, Mechanical, Maritime and Materials Engineering

A novel constraint to prevent local overheating is presented for use in topology optimization (TO). The very basis for the constraint is the Additive Manufacturing (AM) process physics. AM enables fabrication of highly complex topologically optimized designs. However, local overheating is a major concern especially in metal AM processes leading to part failure, poor surface finish, lack of dimensional precision, and inferior mechanical properties. It should therefore be taken into account at the design optimization stage. However, including a detailed process simulation in the optimization would make the optimization intractable. Hence, a computationally inexpensive thermal process model, recently presented in the literature, is used to detect zones prone to local overheating in a given part geometry. The process model is integrated into density-based TO in combination with a robust formulation, and applied in various numerical test examples. It is found that existing AM-oriented TO methods which rely purely on overhang control do not ensure overheating avoidance. Instead, the proposed physics-based constraint is able to suppress geometric features causing local overheating and delivers optimized results in a computationally efficient manner., Structural Optimization and Mechanics, Mechanical, Maritime and Materials Engineering

The design of high-precision motion stages, which must exhibit high dynamic performance, is a challenging task. Manual design is difficult, time-consuming, and leads to sub-optimal designs that fail to fully exploit the extended geometric freedom that additive manufacturing offers. By using topology optimization and incorporating all manufacturing steps (printing, milling, and assembly) into the optimization formulation, high-quality optimized and manufacturable designs can be obtained in an automated manner. With a special focus on overhang control, minimum feature size, and computational effort, the proposed methodology is demonstrated using a case study of an industrial motion stage, optimized for maximum eigenfrequencies. For this case study, an optimized design can be obtained in a single day, showing a substantial performance increase of around 15% as compared to a conventional design. The generated design is manufactured using laser powder-bed fusion in aluminum and experimentally validated within 1% of the simulated performance. This shows that the combination of additive manufacturing and topology optimization can enable significant gains in the high-tech industry., Structural Optimization and Mechanics, Mechanical, Maritime and Materials Engineering

A remarkable elastic anisotropy in plates of austenitic stainless steel produced by the Wire and Arc Additive Manufacturing process is recently reported. The Young's modulus depends on the angle of orientation with respect to the material deposition direction. Here, for the first time, this anisotropy is exploited to maximize structural stiffness by simultaneously optimizing the structural design layout and the local deposition path direction for WAAM. The results obtained indicate deposition that is commonly preferred along the load-path directions for WAAM is sub-optimal and stiffness can be increased at least 53% upon optimizing the deposition directions., Computational Design and Mechanics

In this paper, a novel alternative method of stiffness compensation in buckled mechanisms is investigated. This method involves the use of critical load matching, i.e., matching the first two buckling loads of a mechanism. An analytical simply supported five-bar linkage model consisting of three rigid links, a prismatic slider joint, and four torsion springs in the revolute joints is proposed for the analysis of this method. It is found that the first two buckling loads are exactly equal when the two grounded springs are three times stiffer than the two ungrounded springs. The force–deflection characteristic of this linkage architecture showed statically balanced behavior in both symmetric and asymmetric actuation. Using modal analysis, it was shown that the sum of the decomposed strain energy per buckling mode is constant throughout the motion range for this architecture. An equivalent lumped-compliant mechanism is designed; finite element and experimental analysis showed near-zero actuation forces, verifying that critical load matching may be used to achieve significant stiffness compensation in buckled mechanisms., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Micro and Nano Engineering, Computational Design and Mechanics

Hoe deze lessenserie werkt Je leest nu de docenthandleiding, hier vind je een overzicht van de opbouw van de lessenserie en de bijbehorende materialen. Deze lessenserie bestaat uit zes thema’s. Ieder thema duurt een week en heeft eigen doelen op het gebied van samenwerken en programmeren. Bij ieder thema hoort een docentkaart en leerlingkaarten. Op de docentkaart staan de leerdoelen en wat jouw rol is gedurende dat thema. Op de leerlingkaarten staan opdrachten voor de leerlingen. Op deze kaarten staan ook alle benodigdheden. Voor zowel de vaardigheid samenwerken als het werken met de robot zijn hulpkaarten voor de leerlingen aanwezig. De hulpkaarten kunnen de leerlingen helpen de problemen zelfstandig op te lossen voordat ze jou om hulp hoeven te vragen. Iedere les volgt dezelfde opzet: introductie, opdracht en reflectie. Deze onderdelen staan hieronder toegelicht. De kinderen werken tijdens de lessen in twee- of drietallen., Science Education and Communication

Science Education and Communication

Professionals are increasingly involved in attempts to under- stand and address problems with wicked tendencies, which require crossing boundaries between disciplines, organisa- tions and stakeholder perspectives. This multiple-case study investigated six higher professional education courses in order to develop better understanding of how teachers fos- ter the development of students’ boundary-crossing exper- tise through enhancing relevant learning processes in courses focussing on wicked-problem-solving in interdisci- plinary and multi-stakeholder contexts. We viewed students’ relevant learning processes as learning mechanisms that foster boundary awareness (identification and reflection) and boundary work (coordination and transformation) and considered teachers to be enablers of such learning pro- cesses. Data came from semi-structured interviews with tea- chers, students and stakeholders, observations and document study. We identified nine interrelated enabling strategies teachers used. To foster students’ observation of wickedness through boundary awareness, they encouraged mutual acquaintance, open exploration, opportunities for learning, and multi-perspectivity. To foster students’ action through boundary work, they encouraged initial contact, joint action and multifaceted perspectives on value creation. To foster the interplay between boundary awareness and work, they encouraged successive refinement and structure while embracing wickedness. Balancing the tension that stu- dents experience at boundaries when navigating complexity, uncertainty and value divergence was identified as an impor- tant element of these enabling strategies., Science Education and Communication

Topology optimization typically generates designs that exhibit significant geometrical complexity, which can pose difficulties for manufacturing and assembly. The number of occurrences of an important design feature, in particular intersections, increases with geometrical complexity. Intersections are essential for load transfer in many engineering structures. For certain upcoming manufacturing processes, such as direct metal deposition, the size of an intersection plays a role. During metal deposition, slim intersections are more prone to manufacturing defects than bulkier ones. In this study, a computationally tractable methodology is proposed to both control occurrence and size of intersections in topology optimization. To identify intersections, a stress-based quantity is proposed, denoted as Intersection Indicator. This quantity is based on the local degree of multi-axiality of the stress state, and identifies material points at intersections. The proposed intersection indicator can identify intersections in both single as well as multi-load case problems. To detect the relative size of intersections, the average density in the vicinity of an intersection is used to penalize or promote intersection sizes of interest. The corresponding sensitivity analysis involves solving a set of adjoint equations for each load case. Numerical 2D experiments demonstrate a controllable reduction of penalized slim intersections compared to the designs obtained from conventional compliance minimization. The overall geometrical complexity of the design is reduced due to the promotion of bulkier intersections which leads to an increase in compliance. The designs obtained are more suitable for manufacturing processes such as direct metal deposition., Computational Design and Mechanics, Mechanical Engineering

The design of high-precision motion stages, which must exhibit high dynamic performance, is a challenging task. Manual design is difficult, time-consuming, and leads to sub-optimal designs that fail to fully exploit the extended geometric freedom that additive manufacturing offers. By using topology optimization and incorporating all manufacturing steps (printing, milling, and assembly) into the optimization formulation, high-quality optimized and manufacturable designs can be obtained in an automated manner. With a special focus on overhang control, minimum feature size, and computational effort, the proposed methodology is demonstrated using a case study of an industrial motion stage, optimized for maximum eigenfrequencies. For this case study, an optimized design can be obtained in a single day, showing a substantial performance increase of around 15% as compared to a conventional design. The generated design is manufactured using laser powder-bed fusion in aluminum and experimentally validated within 1% of the simulated performance. This shows that the combination of additive manufacturing and topology optimization can enable significant gains in the high-tech industry., Computational Design and Mechanics, Mechanical Engineering

Topology optimization methods improve the structural performance of components. However, in food processing, medical, high-precision, and other industries' designs should also fulfil the requirement of being cleanable. An important aspect of cleanability is drainability, which entails that fluids can always run off the structure under just gravity. Therefore, taking drainability into account during the optimization process is essential for many applications. This paper proposes a drainage filter that turns a blueprint design into a drainable design. In a layer-by-layer fashion, the design is adjusted, to ensure fluids can always run down its surface. A smooth minimum and maximum are used in the formulation to allow for consistent sensitivity calculation. To allow for the small runoff angles, typical for practical drainability, a grid refinement is proposed. Moreover, any drainage direction can be considered. The effectiveness of the method is illustrated in 2D and 3D., Computational Design and Mechanics, Mechanical Engineering

A novel constraint to prevent local overheating is presented for use in topology optimization (TO). The very basis for the constraint is the Additive Manufacturing (AM) process physics. AM enables fabrication of highly complex topologically optimized designs. However, local overheating is a major concern especially in metal AM processes leading to part failure, poor surface finish, lack of dimensional precision, and inferior mechanical properties. It should therefore be taken into account at the design optimization stage. However, including a detailed process simulation in the optimization would make the optimization intractable. Hence, a computationally inexpensive thermal process model, recently presented in the literature, is used to detect zones prone to local overheating in a given part geometry. The process model is integrated into density-based TO in combination with a robust formulation, and applied in various numerical test examples. It is found that existing AM-oriented TO methods which rely purely on overhang control do not ensure overheating avoidance. Instead, the proposed physics-based constraint is able to suppress geometric features causing local overheating and delivers optimized results in a computationally efficient manner., Computational Design and Mechanics, Mechanical, Maritime and Materials Engineering

In topology optimization, the state of structures is typically obtained by numerically evaluating a discretized PDE-based model. The degrees of freedom of such a model can be partitioned in free and prescribed sets to define the boundary conditions. A multi-partition problem involves multiple partitions of the same discretization, typically corresponding to different loading scenarios. As a result, solving multi-partition problems involves multiple factorization/preconditionings of the system matrix, requiring a high computational effort. In this paper, a novel method is proposed to efficiently calculate the responses and accompanying design sensitivities in such multi-partition problems using static condensation for use in gradient-based topology optimization. A main problem class that benefits from the proposed method is the topology optimization of small-displacement multi-input–multi-output compliant mechanisms. However, the method is applicable to any linear problem. We present its formulation and an algorithmic complexity analysis to estimate computational advantages for both direct and iterative solution methods to solve the system of equations, verified by numerical experiments. It is demonstrated that substantial gains are achievable for large-scale multi-partition problems. This is especially true for problems with both a small set of number of degrees of freedom that fully describes the performance of the structure and with large similarities between the different partitions. A major contribution to the gain is the lack of large adjoint analyses required to obtain the sensitivities of the performance measure., Computational Design and Mechanics

High-tech equipment critically relies on flexures for precise manipulation and measurement. Through elastic deformation, flexures offer extreme position repeatability within a limited range of motion in their degrees of freedom, while constraining motion in the degrees of constraint. Topology optimization proves a prospective tool for the design of short-stroke flexures, providing maximum design freedom and allowing for application-specific requirements. State-of-the-art topology optimization formulations for flexure synthesis are subject to challenges like ease of use, versatility, implementation complexity, and computational cost, leaving a generally accepted formulation absent. This study proposes a novel topology optimization formulation for the synthesis of short-stroke flexures uniquely based on strain energy measures under prescribed displacement scenarios. The resulting self-adjoint optimization problem resembles great similarity to ‘classic’ compliance minimization and inherits similar implementation simplicity, computational efficiency, and convergence properties. Numerical examples demonstrate the versatility in flexure types and the extendability of additional design requirements. The provided source code encourages the formulation to be explored and applied in academia and industry., Computational Design and Mechanics

Metastructures composed of snapping beams are capable of deforming into a series of stable states, enabling them to realize shape reconfigurations. In this paper, we present the design of a metastructure-based morphing surface that is able to exhibit a series of stable configurations with different curvatures. Using theoretical, numerical, and experimental approaches, we study the snap-through transition between the initially flat and the curved stable configurations. Effects of geometric parameters on the snap-through and curvatures are systematically investigated. Results show that the beam thickness is important for tuning the snap-through response, while the curvature can be tuned by changing the beam height and the horizontal span of the structures. Furthermore, an analytical model is developed to investigate the structural nonlinear deformations. It is shown that the proposed model can predict the snap-through transition properly. The structural stability can be controlled by setting proper values for t/L and h/L (t, h, and L represents the beam thickness, height and span, respectively). Finally, it is demonstrated that based on two-dimensional arrangements of bi-stable elements, various stable configurations, like corrugations in different directions, can be imposed to the surface., Computational Design and Mechanics, Micro and Nano Engineering

We propose a fully immersed topology optimization procedure to design structures with tailored fracture resistance under linear elastic fracture mechanics assumptions for brittle materials. We use a level set function discretized by radial basis functions to represent the topology and the Interface-enriched Generalized Finite Element Method (IGFEM) to obtain an accurate structural response. The technique assumes that cracks can nucleate at right angles from the boundary, at the location of enriched nodes that are added to enhance the finite element approximation. Instead of performing multiple finite element analyses to evaluate the energy release rates (ERRs) of all potential cracks—a procedure that would be computationally intractable—we approximate them by means of topological derivatives after a single enriched finite element analysis of the uncracked domain. ERRs are then aggregated to construct the objective function, and the corresponding sensitivity formulation is derived analytically by means of an adjoint formulation. Several numerical examples demonstrate the technique's ability to tailor fracture resistance, including the well-known benchmark L-shaped bracket and a multiple-loading optimization problem for obtaining a structure with fracture resistance anisotropy., Computational Design and Mechanics

Stiffened shells and plates are widely used in engineering. Their performance is highly influenced by the arrangement, or layout, of stiffeners on the base shell or plate and the geometric features, or topology, of these stiffeners. Moreover, modular design is beneficial, since it allows for increased quality control and mass production. In this work, a method is developed that simultaneously optimizes the topology of stiffeners and their layout on a base shell or plate. This is accomplished by introducing a fixed number of modular stiffeners, which are subject to density-based topology optimization and a mapping of these modules to a ground structure. To illustrate potential applications, several stiffened plates and shell examples are presented. All examples demonstrated that the proposed method is able to generate clear topologies for any number of modules and a distinct layout of the stiffeners on the base shell or plate., Structural Optimization and Mechanics

Multi-stable metastructures composed of curved beams can switch to a series of stable configurations via elastic snap-through transitions. The elastic deformations allow metastructures to function as reusable energy absorbers. However, conventional metastructure designs based on solid beams often result in relatively low energy dissipation. In this work, it is found that by increasing the beam unit's bending stiffness while keeping the volume/mass constant, energy dissipation of the metastructure can be largely improved. Based on this observation, we propose two types of structural designs (lattice and hollow cross-section design) as building blocks for multi-stable metastructures. The lattice design is realized by incorporating lattice structures into pre-shaped beams while for the hollow cross-section design, a box-shaped cross section is adopted. The proposed structures are experimentally characterized under cyclic loading and are shown to exhibit sequential snap-through transitions with relatively large energy dissipation. Results show the snap-through behavior can be further tailored through tuning structural in-plane thickness. Effects of geometric parameters on snap-through, local buckling and bi-stability are investigated, and the feasible design domains for selecting proper lattice and cross-section geometries are identified. In addition, we demonstrate that the proposed design is not restricted to beams, and can be extended to shell structures., Micro and Nano Engineering, Structural Optimization and Mechanics

Although additive manufacturing (AM) allows for a large design freedom, there are some manufacturing limitations that have to be taken into consideration. One of the most restricting design rules is the minimum allowable overhang angle. To make topology optimization suitable for AM, several algorithms have been published to enforce a minimum overhang angle. In this work, the layer-by-layer overhang filter proposed by Langelaar (Struct Multidiscip Optim 55(3):871–883, 2017), and the continuous, front propagation-based, overhang filter proposed by van de Ven et al. (Struct Multidiscipl Optim 57(5):2075–2091, 2018) are compared in detail. First, it is shown that the discrete layer-by-layer filter can be formulated in a continuous setting using front propagation. Then, a comparison is made in which the advantages and disadvantages of both methods are highlighted. Finally, the continuous overhang filter is improved by incorporating complementary aspects of the layer-by-layer filter: continuation of the overhang filter and a parameter that had to be user-defined are no longer required. An implementation of the improved continuous overhang filter is provided., Structural Optimization and Mechanics

Rivers, Ports, Waterways and Dredging Engineering

An important cause of failure in powder bed additive manufacturing is the distortion of the part due to thermal shrinkage during printing and the relaxation of residual stresses after its release from the base plate. In this paper, Additive Manufacturing simulations are coupled with Topology Optimization in order to generate designs that are not susceptible to failure associated with distortion. Two possible causes of failure are accounted for: recoater collision and global distortion of the product. Both are considered by simulation of the build process and defined as constraints in the context of a Solid Isotropic Material with Penalization method based topological optimization. The adjoint method is used to derive the sensitivities of the additive manufacturing constraints. The method is demonstrated with the 2D and 3D optimization of a bracket. Next to global topological changes, the obtained designs show features that are aimed at facilitating the printing process. These features resemble supports that are routinely applied to powder bed additive manufacturing. The formulated constraints were found to prevent excessive part distortion and associated build failures in all cases, against a modest increase in the compliance of the bracket., Structural Optimization and Mechanics

An immersed enriched finite element method is proposed for the analysis of phononic crystals (PnCs) with finite element (FE) meshes that are completely decoupled from geometry. Particularly, a technique is proposed to prescribe Bloch–Floquet periodic boundary conditions strongly on non-matching edges of the periodic unit cell (PUC). The enriched finite element formulation effectively transforms a periodic non-confirming discretization into an enriched node-to-node periodic discretizations where periodicity is enforced by any standard procedure. The enriched formulation is also used to describe the interior material interface. This completely eliminates the tedious process of generating matching or fitted meshes during the design process, as it allows changing the inclusion's geometry as well as the PnC's lattice type without changing the FE mesh. The proposed approach, which is used to analyze phononic crystals in 1-D, 2-D, and 3-D using structured meshes, exhibits the same performance as the standard finite element analysis on fitted meshes., Structural Optimization and Mechanics

Additive manufacturing (AM) and topology optimization (TO) have a synergetic relation, as AM can produce complex TO designs, and TO provides high-performance parts that utilize the form freedom provided by AM. Recently, TO has been tailored more toward AM with the inclusion of the minimum allowable overhang angle as a design constraint: resulting designs can be built without any support structures. This work is an extension thereof, by allowing support structures only if they are accessible, such that they can be removed after manufacturing. This is achieved by applying a conventional overhang filter twice, combined with basic operations such as geometry inversion, union, and intersection. The result is an accessibility-aware overhang filter that can be incorporated in TO. Compared with conventional overhang filtered designs, the accessibility filter results in increased part performance and better convergence behavior. Furthermore, a modular filter structure is presented to easily construct the accessibility filter, and its effectiveness is demonstrated on several numerical cases., Structural Optimization and Mechanics

Enriched finite element methods have gained traction in recent years for modeling problems with material interfaces and cracks. By means of enrichment functions that incorporate a priori behavior about the solution, these methods decouple the finite element (FE) discretization from the geometric configuration of such discontinuities. Taking advantage of this greater flexibility, recent studies have proposed the adoption of Non-Uniform Rational B-Splines (NURBS) to preserve the interfaces' exact geometries throughout the analysis. In this article, we investigate NURBS-based geometries in the context of the Discontinuity-Enriched Finite Element Method (DE-FEM) based on linear field approximations. While optimal convergence is retained for problems with weak discontinuities without singularities, representing exact geometry via NURBS does not yield noticeable improvements when extracting stress intensity factors of cracked specimens. For low-order elements, we conclude that the benefits of exact geometry representation do not outweigh the increased complexity in formulation and implementation. The choice of linear FEs hinders the accuracy of the proposed formulation, suggesting that its full potential may only be unleashed by increasing the field representation order., Structural Optimization and Mechanics

Metastructures consisting of planar arrangements of bi-stable snap-through beams are able to exhibit multiple stable configurations. Apart from the expected translational state transition, when all beam elements snap through, rotational states may exist as well. In this paper we explore the rotational properties of multi-stable metastructures on the basis of both experimental and theoretical investigations, and define the conditions for achieving rotational stable states. Results show that the metastructure is able to realize both translational and rotational states, while the rotational transitions require less energy as compared to their translational counterparts. The influence of geometric parameters on rotational stability is investigated via parametric studies. Furthermore, to determine the design criteria for rotational stability, a theoretical investigation based on mode superposition principle is performed to predict the nonlinear-deformation of a unit cell. The theoretical analysis predicts well the rotational snap-through transitions that are observed in finite element simulations. It is found that the rotational stability is determined by setting proper values for h/L and t/L (h, t, L represent apex height, thickness and span of the bi-stable beam structure, respectively). Finally, we experimentally demonstrate that the proposed metastructure with multiple layers is able to achieve large rotations and translations., Materials and Environment, Micro and Nano Engineering, Structural Optimization and Mechanics

Multi-stable metastructures composed of curved beams can switch to a series of stable configurations via elastic snap-through transitions. The elastic deformations allow metastructures to function as reusable energy absorbers. However, conventional metastructure designs based on solid beams often result in relatively low energy dissipation. In this work, it is found that by increasing the beam unit's bending stiffness while keeping the volume/mass constant, energy dissipation of the metastructure can be largely improved. Based on this observation, we propose two types of structural designs (lattice and hollow cross-section design) as building blocks for multi-stable metastructures. The lattice design is realized by incorporating lattice structures into pre-shaped beams while for the hollow cross-section design, a box-shaped cross section is adopted. The proposed structures are experimentally characterized under cyclic loading and are shown to exhibit sequential snap-through transitions with relatively large energy dissipation. Results show the snap-through behavior can be further tailored through tuning structural in-plane thickness. Effects of geometric parameters on snap-through, local buckling and bi-stability are investigated, and the feasible design domains for selecting proper lattice and cross-section geometries are identified. In addition, we demonstrate that the proposed design is not restricted to beams, and can be extended to shell structures., Micro and Nano Engineering, Computational Design and Mechanics

Stiffened shells and plates are widely used in engineering. Their performance is highly influenced by the arrangement, or layout, of stiffeners on the base shell or plate and the geometric features, or topology, of these stiffeners. Moreover, modular design is beneficial, since it allows for increased quality control and mass production. In this work, a method is developed that simultaneously optimizes the topology of stiffeners and their layout on a base shell or plate. This is accomplished by introducing a fixed number of modular stiffeners, which are subject to density-based topology optimization and a mapping of these modules to a ground structure. To illustrate potential applications, several stiffened plates and shell examples are presented. All examples demonstrated that the proposed method is able to generate clear topologies for any number of modules and a distinct layout of the stiffeners on the base shell or plate., Computational Design and Mechanics

An important cause of failure in powder bed additive manufacturing is the distortion of the part due to thermal shrinkage during printing and the relaxation of residual stresses after its release from the base plate. In this paper, Additive Manufacturing simulations are coupled with Topology Optimization in order to generate designs that are not susceptible to failure associated with distortion. Two possible causes of failure are accounted for: recoater collision and global distortion of the product. Both are considered by simulation of the build process and defined as constraints in the context of a Solid Isotropic Material with Penalization method based topological optimization. The adjoint method is used to derive the sensitivities of the additive manufacturing constraints. The method is demonstrated with the 2D and 3D optimization of a bracket. Next to global topological changes, the obtained designs show features that are aimed at facilitating the printing process. These features resemble supports that are routinely applied to powder bed additive manufacturing. The formulated constraints were found to prevent excessive part distortion and associated build failures in all cases, against a modest increase in the compliance of the bracket., Computational Design and Mechanics

Although additive manufacturing (AM) allows for a large design freedom, there are some manufacturing limitations that have to be taken into consideration. One of the most restricting design rules is the minimum allowable overhang angle. To make topology optimization suitable for AM, several algorithms have been published to enforce a minimum overhang angle. In this work, the layer-by-layer overhang filter proposed by Langelaar (Struct Multidiscip Optim 55(3):871–883, 2017), and the continuous, front propagation-based, overhang filter proposed by van de Ven et al. (Struct Multidiscipl Optim 57(5):2075–2091, 2018) are compared in detail. First, it is shown that the discrete layer-by-layer filter can be formulated in a continuous setting using front propagation. Then, a comparison is made in which the advantages and disadvantages of both methods are highlighted. Finally, the continuous overhang filter is improved by incorporating complementary aspects of the layer-by-layer filter: continuation of the overhang filter and a parameter that had to be user-defined are no longer required. An implementation of the improved continuous overhang filter is provided., Computational Design and Mechanics

Rivers, Ports, Waterways and Dredging Engineering

An immersed enriched finite element method is proposed for the analysis of phononic crystals (PnCs) with finite element (FE) meshes that are completely decoupled from geometry. Particularly, a technique is proposed to prescribe Bloch–Floquet periodic boundary conditions strongly on non-matching edges of the periodic unit cell (PUC). The enriched finite element formulation effectively transforms a periodic non-confirming discretization into an enriched node-to-node periodic discretizations where periodicity is enforced by any standard procedure. The enriched formulation is also used to describe the interior material interface. This completely eliminates the tedious process of generating matching or fitted meshes during the design process, as it allows changing the inclusion's geometry as well as the PnC's lattice type without changing the FE mesh. The proposed approach, which is used to analyze phononic crystals in 1-D, 2-D, and 3-D using structured meshes, exhibits the same performance as the standard finite element analysis on fitted meshes., Computational Design and Mechanics