Mechanical assemblies can exhibit complex relative motions, during which collisions between moving parts and their surroundings must be avoided. To define feasible design spaces for each part’s shape, “maximal” collision-free pointsets can be computed using configuration space modeling techniques such as Minkowski operations and sweep/unsweep. For example, for a pair of parts undergoing a given relative motion, to make the problem well-posed, the geometry of one part (chosen arbitrarily) must be fixed to compute the maximal shape of the other part by an unsweep operation. Making such arbitrary choices in a multi-component assembly can place unnecessary restrictions on the design space. A broader family of collision-free pairs of parts can be explored, if fixing the geometry of a component is not required. In this paper, we formalize this family of collision-free shapes and introduce a generic method for generating a broad subset of them. Our procedure, which is an extension of the unsweep, allows for co-generation of a pair of geometries which are modified incrementally and simultaneously to avoid collision. We demonstrate the effectiveness and scalability of our procedure in both 2D and 3D by generating a variety of collision-free shapes. Notably, we show that our approach can automatically generate freeform cam and follower profiles, gear teeth, and screw threads, starting from colliding blocks of materials, solely from a specification of relative motion and without the use of any feature-informed heuristics. Moreover, our approach provides continuous measures of collision that can be incorporated into standard gradient-descent design optimization, allowing for simultaneous collision-free and physics-informed co-design of mechanical parts for assembly.

Enforcing connectivity of parts or their complement space during automated design is essential for various manufacturing and functional considerations such as removing powder, wiring internal components, and flowing internal coolant. The global nature of connectivity makes it difficult to incorporate into generative design methods that rely on local decision making, e.g., topology optimization (TO) algorithms whose update rules depend on the sensitivity of objective functions or constraints to locally change the design. Connectivity is commonly corrected for in a post-processing step, which may result in suboptimal designs. We propose a recasting of the connectivity constraint as a locally differentiable violation measure, defined as a “virtual” compliance, modeled after physical (e.g., thermal or structural) compliance. Such measures can be used within TO alongside other objective functions and constraints, using a weighted penalty scheme to navigate tradeoffs. By carefully specifying the boundary conditions of the virtual compliance problem, the designer can enforce connectivity between arbitrary regions of the part’s complement space while satisfying a primary objective function in the TO loop. We demonstrate the effectiveness of our approach using both 2D and 3D examples, show its flexibility to consider multiple virtual domains, and confirm the benefits of considering connectivity in the design loop rather than enforcing it through post-processing.

Design space exploration can reveal the underlying structure of design problems. In a set-based approach, for example, exploration can map sets of designs or regions of the design space that meet specific performance requirements. For some problems, promising designs may cluster in multiple regions of the input design space, and the boundaries of those clusters may be irregularly shaped and difficult to predict. Visualizing the promising regions can clarify the design space structure, but design spaces are typically high-dimensional, making it difficult to visualize the space in three dimensions. To convey the structure of such high-dimensional design regions, a two-stage approach is proposed to (1) identify and (2) visualize each distinct cluster or region of interest in the input design space. This paper focuses on the visualization stage of the approach. Rather than select a singular technique to map high-dimensional design spaces to low-dimensional, visualizable spaces, a selection procedure is investigated. Metrics are available for comparing different visualizations, but the current metrics either overestimate the quality or favor selection of certain visualizations. Therefore, this work introduces and validates a more objective metric, termed preservation, to compare the quality of alternative visualization strategies. Furthermore, a new visualization technique previously unexplored in the design automation community, t-Distributed Neighbor Embedding, is introduced and compared to other visualization strategies. Finally, the new metric and visualization technique are integrated into a two-stage visualization strategy to identify and visualize clusters of high-performance designs for a high-dimensional negative stiffness metamaterials design problem.

This paper presents the computational design, fabrication, and experimental validation of a mechanical metamaterial in which the damping of the material is significantly increased without decreasing the stiffness by embedding a small volume fraction of negative stiffness (NS) inclusions within it. Unlike other systems that dissipate energy primarily through large‐amplitude deformation of nonlinear structures, this metamaterial dissipates energy by amplifying linear strains in the viscoelastic host material. By macroscopically tuning the pre‐strain of the metamaterial via mechanical loading, the embedded NS inclusions operate about a constrained buckling instability. When further macroscopic vibrational excitation is applied, the inclusions amplify the strains of the surrounding viscoelastic medium. This results in enhanced dissipation of mechanical energy when compared to voided or neat comparison media. Microstereolithography, an emerging high‐resolution additive manufacturing (AM) technology, is employed to fabricate the deeply subwavelength inclusions which ensures broadband damping behavior. The mechanically induced broadband energy dissipation and manufacturing approach further differentiate the metamaterial from other approaches that exploit resonances, large deformations, or non‐mechanical instabilities. The computational design, fabrication, and experimental evaluation reported is the first dynamic demonstration of such a mechanically tunable NS metamaterial, potentially enabling components with integrated structural and damping capabilities.

Additive manufacturing (AM) is making a profound impact on our ability to realize complex metamaterials and structures, but fully realizing the manufacturing freedom afforded by AM requires some significant advances in engineering design methods and tools. For some additive manufacturing applications, simulation-based design tools may be required to explore a hierarchy of features, ranging in size from microns to meters. At the same time, these tools need to provide real-time feedback on the constraints and process-structure-property relationships relevant to specific AM technologies, and this Design-for-AM feedback is needed during the design process, rather than at the end. To address these challenges, a design exploration approach has been established for creating inverse maps of promising regions of a hierarchical structural/material design space. The approach utilizes machine learning classifiers for identifying sets of promising solutions to a materials design problem, combined with statistical characterization of geometric features and material properties to ensure that the designs are robustly manufacturable. The capabilities of the approach are demonstrated by applying it to the hierarchical design of negative stiffness metamaterials for energy absorption applications

Purpose Microstereolithography is capable of producing millimeter-scale polymer parts having micron-scale features. Material properties of the cured polymers can vary depending on build parameters such as exposure. Current techniques for determining the material properties of these polymers are limited to static measurements via micro/nanoindentation, leaving the dynamic response undetermined. The purpose of this paper is to demonstrate a method to measure the dynamic response of additively manufactured parts to infer the dynamic modulus of the material in the ultrasonic range. Design/methodology/approach Frequency-dependent material parameters, such as the complex Young’s modulus, have been determined for other relaxing materials by measuring the wave speed and attenuation of an ultrasonic pulse traveling through the materials. This work uses laser Doppler velocimetry to measure propagating ultrasonic waves in a solid cylindrical waveguide produced using microstereolithography to determine the frequency-dependent material parameters of the polymer. Because the ultrasonic wavelength is comparable with the part size, a model that accounts for both geometric and viscoelastic dispersive effects is used to determine the material properties using experimental data. Findings The dynamic modulus in the ultrasonic range of 0.4-1.3 MHz was determined for a microstereolithography part. Results were corroborated by using the same experimental method for an acrylic part with known properties and by evaluating the natural frequency and storage modulus of the same microstereolithography part with a shaker table experiment. Originality/value The paper demonstrates a method for determining the dynamic modulus of additively manufactured parts, including relatively small parts fabricated with microstereolithography.

One of the challenges in designing metamaterials for additive manufacturing (AM) is accounting for the differences between as-designed and as-built geometries and material properties. From a designer's perspective, these differences can lead to degradation of part and metamaterial performance, which is especially difficult to accommodate in small-lot or one-of-a-kind production. In this context, each part is unique, and therefore, extensive iteration is costly. Designers need a means of exploring the design space while simultaneously considering the reliability of additively manufacturing particular candidate designs. In this work, a design exploration approach, based on Bayesian network classifiers (BNC), is extended to incorporate manufacturing variation into the design exploration process and identify designs that reliably meet performance requirements when this variation is taken into account. The example application is the design of negative stiffness (NS) metamaterials, in which small volume fractions of NS inclusions are embedded within a host material. The resulting metamaterial or composite exhibits macroscopic mechanical stiffness and loss properties that exceed those of the base matrix material. The inclusions are fabricated with microstereolithography with features on the scale of tens of microns, but variability is observed in material properties and dimensions from specimen to specimen. This variability is measured and modeled via design, fabrication, and characterization of metrology parts. The quantified manufacturing variability is incorporated into the BNC approach as a manufacturability classifier to identify candidate designs that achieve performance targets reliably, even when manufacturing variability is taken into account.

Design space exploration can reveal the underlying structure of design problems of interest. In a set-based approach, for example, exploration can identify sets of designs or regions of the design space that meet specific performance requirements. For some problems, promising designs may cluster in multiple regions of the design space, and the boundaries of those clusters may be irregularly shaped and difficult to predict. Visualizing the promising regions can clarify the design space structure, but design spaces are typically high-dimensional, making it difficult to visualize the space in three dimensions. Techniques have been introduced to map high-dimensional design spaces to low-dimensional, visualizable spaces. Before the promising regions can be visualized, however, the first task is to identify how many clusters of promising designs exist in the high-dimensional design space. Unsupervised machine learning methods, such as spectral clustering, have been utilized for this task. Spectral clustering is generally accurate but becomes computationally intractable with large sets of candidate designs. Therefore, in this paper a technique for accurately identifying clusters of promising designs is introduced that remains viable with large sets of designs. The technique is based on spectral clustering but reduces its computational impact by leveraging the Nyström Method in the formulation of self-tuning spectral clustering. After validating the method on a simplified example, it is applied to identify clusters of high performance designs for a high-dimensional negative stiffness metamaterials design problem.

Modern design problems present both opportunities and challenges, including multifunctionality, high dimensionality, highly nonlinear multimodal responses, and multiple levels or scales. These factors are particularly important in materials design problems and make it difficult for traditional optimization algorithms to search the space effectively, and designer intuition is often insufficient in problems of this complexity. Efficient machine learning algorithms can map complex design spaces to help designers quickly identify promising regions of the design space. In particular, Bayesian network classifiers (BNCs) have been demonstrated as effective tools for top-down design of complex multilevel problems. The most common instantiations of BNCs assume that all design variables are independent. This assumption reduces computational cost, but can limit accuracy especially in engineering problems with interacting factors. The ability to learn representative network structures from data could provide accurate maps of the design space with limited computational expense. Population-based stochastic optimization techniques such as genetic algorithms (GAs) are ideal for optimizing networks because they accommodate discrete, combinatorial, and multimodal problems. Our approach utilizes GAs to identify optimal networks based on limited training sets so that future test points can be classified as accurately and efficiently as possible. This method is first tested on a common machine learning data set, and then demonstrated on a sample design problem of a composite material subjected to a planar sound wave.

Microstereolithography is capable of producing millimeter-scale polymer parts having micron-scale features. Material properties of the cured polymers can vary depending on build parameters such as exposure time and laser power. Current techniques for determining the material properties of these polymers are limited to static measurements via micro/nanoindentation, leaving the dynamic response undetermined. Frequency-dependent material parameters, such as the complex Young’s modulus, have been determined for other relaxing materials by measuring the wave speed and attenuation of an ultrasonic pulse traveling through the materials. This method is now applied to determine the frequency-dependent material parameters of polymers manufactured using microstereolithography. Because the ultrasonic wavelength is comparable to the part size, a model that accounts for both geometric and viscoelastic effects is used to determine the material properties using experimental data.

Design exploration methods seek to identify sets of candidate designs or regions of the design space that yield desirable performance. Commonly, the dimensionality of the design space exceeds the limited dimensions supported by standard graphical techniques, making it difficult for human designers to visualize or understand the underlying structure of the design space. With standard visualization tools, it is sometimes challenging to visualize a multi-dimensional Pareto frontier, but it is even more difficult to visualize the collections of design (input) variable values that yield those Pareto solutions. It is difficult for a designer to determine not only how many distinct regions of the design (input) space may offer desirable performance but also how those design spaces are structured. In this paper, a form of spectral clustering known as ε-neighborhood clustering is proposed for identifying satisfactory regions in the design spaces of multilevel problems. By exploiting properties of graph theory, the number of satisfactory design regions can be determined accurately and efficiently, and the design space can be partitioned. The method is demonstrated to be effective at identifying clusters in a 10 dimensional space. It is also applied to a multilevel materials design problem to demonstrate its efficacy on a realistic design application. Future work intends to visualize each individually identified design region to produce an intuitive mapping of the design space.

A composite material system comprised of a monostable negative stiffness (NS) structure within a polymer matrix was designed, fabricated, and experimentally evaluated. The monostable negative stiffness (NS) structure was designed using a combination of analytical and numerical models and manufactured in stainless steel. The NS structure was arranged in parallel with different polymer matrices to experimentally evaluate the effects of the matrix properties on the overall stiffness and energy dissipation of the composite NS-matrix system when loaded in uniaxial compression. A strong influence of the matrix properties on the stiffness and energy absorption capacity of the composite system was observed. Unlike conventional composites for which there is a natural tradeoff between stiffness and energy absorption capacity, the composite NS-matrix system enhanced stiffness while simultaneously improving energy absorption relative to a neat matrix, but only when the stiffness of the matrix was carefully matched to the stiffness of the NS structure.

Micro-stereolithography is capable of producing polymer parts on the scale of millimeters that contain micron-scale features. Accurate prediction of the dynamic performance of components produced using micro-sterolithography requires knowledge of the as-fabricated material properties, but very little published material property data exist for these materials. This is complicated by the fact that the properties vary as a function of build parameters (i.e., laser exposure time). Designers therefore have limited useful material property information for part design. Frequency-dependent material parameters are often determined by measuring the wave speed and attenuation of an ultrasonic pulse as it propagates through the material. This work employs laser Doppler vibrometry to detect extensional waves in a solid polymer rod of circular cross-section that is excited by a longitudinal ultrasonic contact transducer. Transverse motion associated with extensional waves propagating along the rod axis is measured at multiple surface points. The time series gathered from all locations are used to produce a frequency-wavenumber spectrum. These data, coupled with a forward model that accounts for both viscoelastic and geometric waveguide effects, are then used to invert for the lossy material properties from 0.4 to 1.2 MHz.

Recent research has indicated that embedding small volume fractions of negative stiffness (NS) inclusions within a host material can create composites with macroscopic mechanical stiffness and loss properties that exceed conventional, composites. To design these composites, a multi-level, set-based approach that employs Bayesian network classifiers was developed to identify sets of satisfactory designs at each level of the multilevel design space. In this paper, manufacturing uncertainties are incorporated to further refine the design space mappings created by the set-based approach. Manufacturing uncertainty refers to the random deviations in dimensions and other properties that often arise when fabricating a specimen. Joint probability distributions are used to model this manufacturing uncertainty. The joint probability distributions are formulated as kernel density estimates that can be based on manufacturing data. The joint probability distributions are incorporated within the set-based approach to identify sets of designs that not only yield satisfactory performance but also offer robustness to manufacturing uncertainty. The approach is demonstrated in the context of hierarchical composite materials, but it can be applied to other multi-level design problems to efficiently yield sets of robustly manufacturable, high performance designs.

A set-based approach is presented for exploring multilevel design problems. The approach is applied to design negative stiffness metamaterials with mechanical stiffness and loss properties that surpass those of conventional composites. Negative stiffness metamaterials derive their properties from their internal structure, specifically by embedding small volume fractions of negative stiffness inclusions in a continuous host material. Achieving high stiffness and loss from these materials by design involves managing complex interdependencies among design variables across a range of length scales. Hierarchical material models are created for length scales ranging from the structure of the microscale negative stiffness inclusions to the effective properties of mesoscale metamaterials to the performance of an illustrative macroscale component. Bayesian network classifiers (BNCs) are used to map promising regions of the design space at each hierarchical modeling level, and the maps are intersected to identify sets of multilevel solutions that are likely to provide desirable system performance. The approach is particularly appropriate for highly efficient, top-down, performance-driven, multilevel design, as opposed to bottom-up, trial-and-error multilevel modeling.

In this paper, we present the design of prototypes and experimental results from implementing these prototypes to demonstrate a novel online diagnostic technique for probing the integrity of concentric neutral wires (CNs) in underground power distribution cables. Our technique uses anisotropic magneto-resistive (AMR) magnetic sensors that rotate around the circumference of the cable and record the corresponding emanating magnetic field. This magnetic field is a function of the currents passing through the CNs (as well as the central conductor, CC), and can be used to detect signatures of damaged (non-conductive) CNs. We describe the implementation of the prototypes, including the radios that ensure electrical isolation between the data repository (a laptop computer), and the energized cable. We further show experimental results from applying the prototypes to detect fabricated faults on cables in our lab underground cable test-bed under various CN current conditions. The results show that we can detect breaks in CNs in with 1 A RMS return-current per CN, and at least up to 95 feet from the failure side (the maximum length of the cables in our test-bed).