Algorithmic Aspects of Isogeometric Shape Optimization

We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more specifically non-uniform rational B-splines (NURBS). This new algorithm enables the solution of partial differential equations within the volumes enclosed by these CAD models using (collocation-based) meshless numerical discretizations. Our hierarchical algorithm first generates quasi-uniform node sets directly on the NURBS surfaces representing the domain boundary, then uses the NURBS representation in conjunction with the surface nodes to generate nodes within the volume enclosed by the NURBS surface. We provide evidence for the quality of these node sets by analyzing them in terms of local regularity and separation distances. Finally, we demonstrate that these node sets are well-suited (both in terms of accuracy and numerical stability) for meshless radial basis function generated finite differences discretizations of the Poisson, Navier-Cauchy, and heat equations. Our algorithm constitutes an important step in bridging the field of node generation for meshless discretizations with isogeometric analysis.

Analysis in computer aided design: Nonlinear isogeometric B-Rep analysis of shell structures

The issue of improving quality, costs and delays indicators in design and manufacturing is more relevant than ever in the industry. After lean manufacturing, well known in production process, the lean engineering approach is being implemented today in the field of design, taking the name of lean product development. The management of knowledge and know-how (existing, new or to be acquired) is the heart of lean engineering. In our suggested methodology this is implemented through a new generation of tools called Knowledge Configuration Management (KCM) and Knowledge Extraction Assistant (KEA). KCM tools are lean engineering components that provide analytical approach to knowledge management and knowledge-based engineering. These tools require a highly integrated approach that involves, for example, predefined geometrical parametric 3D models, such as CAD templates. But this approach cannot be deployed in all engineering sites. We propose to complete this KCM approach introducing a semantic network approach, coupling with Feature Identity Card (FIC). FIC contains a set of metadata and information existing in the Product Data Management (PDM), connected with information extracted from 3D CAD (Computer Aided Design) models. It allows contextualizing information and ensures semantic connections, in order to manipulate the right parameters with mathematical algorithms. Those algorithms will search candidate relationships between design parameters extracted from CAD models. Our suggested approach aims at extracting knowledge in cases where design never came out of Knowledge Based Engineering (KBE) applications. In those situations, it seems important to complete classical knowledge management approach, and to find out the implicit knowledge embedded in 3D CAD models. This is achieved through a global approach, focusing on the product’s 3D definitions. We suggest introducing the latter approach by a suite of digital KEA tools (interfaced with KCM tools). Extracting knowledge from projects information stored in the Product Data Management does this. More precisely, the methodology is based on a commercial 3D similarity search tools for CAD models and on mathematical algorithms that search relationships between extracted design parameters. The goal is to submit new rules to the process and design experts. Implementing this methodology, a deeper knowledge of the product and its associated process can be acquired. This ensures a more productive and efficient design process.

To accurately quantify polyethylene wear in retrieved arthroplasty components, the original geometry of the component must be estimated accurately using a reference geometry such as a computer-aided design (CAD) model or a never-implanted insert. However, differences may exist between the CAD model and manufactured inserts resulting from manufacturing tolerances. We quantified the deviations between CAD models and newly manufactured inserts and determined how these deviations compared with using a never-implanted insert as a reference geometry. We obtained five cruciate-retaining (CR) and five posterior-stabilizing (PS) tibial inserts and their CAD models. The inserts were scanned and reconstructed using microcomputed tomography (micro-CT). Differences in volume and surface geometry were measured among (1) the individual inserts; (2) between the inserts and a CAD model; and (3) between the inserts and a reference geometry constructed from multiple scanned inserts averaged together. The micro-CT volumes were, on average, 0.4% smaller (34-178 mm(3)) than the CAD model volumes. The mean deviation between the CAD model and insert surface geometry was 25.7 μm smaller for CR and 36.8 μm smaller for PS. The mean deviation between the inserts and an averaged reference geometry was 1.4 μm larger for CR and 0.4 μm smaller for PS. Deviations exist between manufactured tibial inserts and CAD models that could cause errors in wear measurements. Scanned inserts may better represent the preimplantation geometry of worn inserts than CAD models, depending on the manufacturing variability between lots. The magnitude of the error in estimation of the preimplantation geometry of a retrieved component could add or subtract the equivalent of 1 year of wear.

In this chapter, we address various issues related to data processing for rapid prototyping. In contrast to traditional material removal processes, rapid prototyping techniques build a part by incrementally adding materials layer by layer (Kruth 1991, Barequet and Kaplan 1998), so they are also called layer-based manufacturing or layered manufacturing. The processes are fully automatic and offer a number of competitive advantages over traditional manufacturing processes. Hence, they are particularly useful for rapid product development. The entire process for model prototyping is illustrated in Figure 5-1 and can be summarized as follows: CAD modeling: The first step in rapid prototyping is to prepare a computer-aided design (CAD) model of the object to be fabricated using layer based manufacturing processes. For most of the available RP technologies, a solid model with complete topological and geometric information is required. STL interfacing: STL is the de-facto standard for the rapid prototyping industry. It is a file format for approximately defining an object using triangular facets. When a CAD model is available, the entire part geometry is converted into STL format based on a tolerance for accuracy control. Part orientation: Before processing for prototyping, a RP engineer needs to figure out the specific orientation in which the prototype model will be produced. Part accuracy, the amount of supporting material required and ease of post-processing are important factors influencing part orientation determination. Support generation: Depending on the specific RP process to be used, one may need to further define support structures for supporting down-facing areas during part build-up. Support generation can be done on the basis of a STL model or the original CAD model. Model slicing and tool path generation: In contrast to material removal manufacturing technologies, rapid prototyping technologies refer to a class of layer-based material increase manufacturing processes. The digital model of the object and related support structures need to be sliced layer by layer. For each layer, a set of surface contours is obtained and a tool path is defined within the material area for model production in a layer-wise fashion. Model production on a RP machine: The produced tool path is sent to a RP machine for building up the prototype model, including support, layer by layer. Post-processing: Depending on the RP process involved, a post-processing step might be needed for post-curing in the case of stereolithography, for infiltration and furnace sintering in the case of SLS, and/or for removing the support structures and surface polishing in the cases of most other RP processes.

4D CAD model updating using image processing-based construction progress monitoring

Among machining conditions, tool paths exert a significant influence on the final machining outcome. In conventional practice, computer-aided design (CAD) models created from basic dimensions are typically used to generate tool paths within computer-aided manufacturing software. In recent years, 3D annotated models—CAD models enriched with product manufacturing information (PMI)—have become increasingly widespread. However, CAD models are often modified manually to achieve the desired machining results while accounting for machining errors. Consequently, operators consume time and effort in generating tool paths. Moreover, knowledge and experience in machining are required to modify CAD models according to PMI, such as unilateral tolerances. In this study, a method is proposed that leverages operator expertise to automatically modify CAD models and generate tool paths capable of satisfying specified size limits. The method employs a chain expression of dimensions, where the dimensional chain originates from the datum used as a reference for machining. Based on the dimensional chain, the objects requiring shifts are systematically identified. Subsequently, basic dimensions with unilateral tolerances are converted into target dimensions with bilateral tolerances to achieve the desired machining results. Case studies confirm that CAD models can be automatically modified when the target dimension is set to the median value of the size limits. Furthermore, machining experiments demonstrate that the proposed method effectively ensures compliance with the specified size limits.

Adjoint shape optimization has enabled physics-based optimal designs for aerodynamic surfaces. Additive manufacturing (AM) makes it possible to manufacture complex shapes. However, there has been a gap between optimal and manufacturable surfaces due to the inherent limitations of commercial computational fluid dynamics (CFD) codes to implement geometric constraints during adjoint computation. In such cases, the design sensitivities are exported and used to perform constrained shape modifications using parametric information stored in computer aided design (CAD) files to satisfy manufacturability constraints. However, modifying the design using adjoint methods in CFD solvers and performing constrained shape modification in CAD can lead to inconsistencies due to different shape parameterization schemes. This paper describes a method to enable the simultaneous optimization of the fluid domain and impose AM manufacturability constraints, resolving one of the key issues of geometry definition for isogeometric analysis. Similar to a grid convergence study, the proposed method verifies the consistencies between shape parameterization techniques present within commercial CAD and CFD software during mesh movement as a part of the adjoint shape optimization routine. By identifying the appropriate parameters essential to a shape optimization study, the error metric between the different parameterization techniques converges to demonstrate sufficient consistencies for justifiable exchange of data between CAD and CFD. For the identified shape optimization parameters, the error metric to measure the deviation between the two parameterization schemes lies within the AM laser-powder bed fusion (L-PBF) process tolerance. Additionally, comparison for subsequent objective function calculations between iterations of the optimization loop showed acceptable differences within 1% variation between the modified geometries obtained using the two parameterization schemes. This method provides justification for the use of multiphysics guided adjoint design sensitivities computed in CFD software to perform shape modifications in CAD to incorporate AM manufacturability constraints during the shape optimization loop such that optimal designs are also additively manufacturable.

Interrogation of spline surfaces with application to isogeometric design and analysis of lattice-skin structures

A case is made that introducing CAD-based geometry prematurely in the aircraft design process actually hinders multidisciplinary design. Consequently, a design process which allows a designer to quickly build and analyze aerospace configurations without CAD or computational meshing specialists is proposed. This allows higher fidelity analyses to be applied at conceptual design and decreases the turnaround time for trade studies and optimizations. The basic premise of conceptual geometry modeling is presented and discussed. Key features and capabilities which are essential for a successful geometry modeler are identified. Desktop Aeronautics' conceptual geometry modeler, RAGE, is described, with emphasis on recent progress and advances in the tool. A preliminary graphical-user-interface is presented along with an application programming interface. Extensibility of the RAGE modeler is discussed along with the importance of this feature. The applicability of RAGE to simple trade studies is demonstrated in an example problem. The precision of the RAGE modeler is also demonstrated on a complex aircraft design. Future plans for the geometry modeler are also discussed. I. Background In the conceptual phase of aircraft design, there is often a wide range of geometric configurations that the designer wishes to consider, analyze, and assess. A designer’s intuition and creativity are crucial to a successful conceptual design, yet are easily inhibited by the modeling and analysis process itself, particularly if high-fidelity analysis is warranted. If the time between inception and assessment of a candidate design is relatively long, a designer may be forced to limit the number of concepts considered. New data revealed in a design iteration may suggest or require significant changes to the geometry configuration. Since the majority of considered design configurations will eventually be discarded, an ideal conceptual design process should involve a highly efficient and easy to use geometry modeler. Significant changes should be allowed without tedious re-work of the geometry model. Exporting the model for analysis should require little effort and have the capability to be automated. Therefore, any modeling application used in this process should be flexible and not restrict the designer’s choice of user interface, analysis method, and design optimization environment. Most current design processes in the aerospace industry rely heavily on computer-aided-design (CAD) applications. As a general design tool, CAD is a powerful geometry modeler capable of precisely representing practically any shape. Unfortunately, this generality is realized at the cost of requiring specialized training to efficiently and effectively use the software. Also, a CAD model is often not easily modified, especially if significant re-work of the geometry is necessary. This can lead to the premature freeze of an aircraft design due to employing excessively high-fidelity geometry modeling too early in the design process. Parametric CAD modeling could address this issue, but creating a well-designed parametric CAD model is difficult. Not only does it require an extremely skilled operator, but also the designer must have some insight into what parameterization may ultimately be desired. Modifying a parametric CAD model is often more difficult than modifying a conventional CAD model. Significant changes, such as adding or removing cross-sections, may invalidate the parameterization in some cases. In most organizations, CAD modeling (whether it be parametric or conventional) is often assigned to a dedicated CAD specialist. Since the conceptual designer is usually not a CAD specialist, the latter must communicate his design intent to the former, often using sketches, dimensions, and word of mouth. When the CAD specialist interprets the sketches, any part or detail not precisely defined usually requires judgment and artistic license. This interpretation may result in loss of design intent and indeterminate iteration between the CAD specialist and designer to obtain a satisfactory result. Because this process is iterative, CAD operators often must recreate similar geometry

This paper describes new algorithms for automatically constructing a computer aided design (CAD) model of a structured scene as imaged by a single camera on a mobile robot. The scene to be modeled is assumed to be composed mostly of linear edges with particular orientations in 3-D. This is the case for most indoor scenes as well as some outdoor urban scenes. The orientation data is used by a motion stereo algorithm to estimate the 3-D structure using a sequence of images. The algorithm assumes that the linear edges are the boundaries of opaque planar patches, such as the floor, the ceiling and the walls. The resulting 3-D description is a CAD model of the scene. Applications of this technique include CAD modeling for architecture and computer graphics, and robot navigation. This paper completes earlier publications and therefore concentrates on the latter parts of processing, including automatically tracking segments, and using the resulting models in different applications. >

This in vitro study evaluated the dimensional accuracy of three 3D printers and one milling machine with their respective polymeric materials using a simplified geometrical model. A simplified computer-aided design (CAD) model was created. The test samples were fabricated with three 3D printers: a dental desktop stereolithography (SLA) printer, an industrial SLA printer, and an industrial fused deposition modeling (FDM) printer, as well as a 5-axis milling machine. One polymer material was used per industrial printer and milling machine while two materials were used with the dental printer for a total of five study groups. Test specimens were then digitized using a laboratory scanner. The virtual outer caliper method was used to measure the linear dimensions of the digitized 3D printed and milled specimens in x-, y-, and z-axes, and compare them to the known values of the CAD model. Data were analyzed with Kruskal-Wallis one-way ANOVA on Ranks followed by the Tukey's test. Milled specimens were not significantly different from the CAD model in any dimension (p > 0.05). All 3D printed specimens were significantly different from the CAD model in all dimensions (p = 0.01), except the dental SLA 3D printer with one of the polymers tested (Bis-GMA) which was not significantly different in two (x and z) dimensions (p = 0.4 and p = 0.12). The milling technology tested provided greater dimensional accuracy than the selected 3D printing. Printer, printing technology, and material selection affected the accuracy of the printed model.

Digital manufacturing (DM) is actively adopted to the production lifecycles of a variety of critical industries, and this rapid growth has resulted in exponential increase of 3D computer-aided design (CAD) models. Unfortunately, counterfeiting of intellectual property becomes a prominent threat as many 3D designs are accessible online, combined with the proliferation of cheap consumer 3D printers that enable malicious actors to produce non-authentic parts. State-of-the-art techniques to secure manufacturing processes mostly rely on watermarking, which embeds hidden information inside CAD models to prove ownership and authenticity. Nevertheless, such techniques tamper with the model itself, while existing attacks allow removing such watermarks altogether. To address these shortcomings, we integrate signal processing and cryptographic techniques and describe a tailored solution for CAD model ownership and supply chain management. Our approach generates unique identifiers for 3D designs using frequency-domain transforms and employs non-fungible tokens (NFTs) that persist on public distributed ledgers. Our NFTs are implemented on the Ethereum blockchain using smart contracts and their functionality is twofold: (a) authenticate the owner of a CAD model, and (b) enable ownership transfer. To validate our technique, we deployed our smart contract on Ethereum's proof-of-work Ropsten network and demonstrated the applicability of our methodology.

In this paper, a method of reconstructing 3D (three dimensional) models from the original scanned point cloud using priori templates is proposed. Different from previous reconstruction methods that triangulate and fit the original scanning point cloud directly, we construct a priori template based on the CAD (computer aided design) model and guide the reconstruction of the original scanning point cloud with the priori template. Given a CAD model, the basic geometric elements are used as the basic units to extract the set elements of 3D shapes. Then the geometric elements are meshed, and the normal vectors at the mesh nodes are extracted. The corresponding point cloud data of each basic element are extracted from the original point cloud. The point cloud data near the normal of the guide point are searched, and the Gaussian weighted average value of the searched point represents the actual geometric parameters of the part at the guide point. Finally, the geometric elements of the basic unit are reconstructed locally by Non-Uniform Rational B-Splines surface fitting, and the complete reconstruction model is obtained by integrating the local reconstruction. Experiments show that our method can solve the problems of high quality reconstruction, sharp feature preservation, and detail recovery in surface reconstruction.

Nickel and nickel-alloy microparts sized on the order of 5–1000 microns have been imaged in three dimensions using a new microscopic technique, Digital Volumetric Imaging (DVI). The gears were fabricated using Sandia National Laboratories’ LIGA technology (lithography, molding, and electroplating). The images were taken on a microscope built by Resolution Sciences Corporation by slicing the gear into one-micron thin slices, photographing each slice, and then reconstructing the image with software. The images were matched to the original CAD (computer aided design) model, allowing LIGA designers, for the first time, to see visually how much deviation from the design is induced by the manufacturing process. Calibration was done by imaging brass ball bearings and matching them to the CAD model of a sphere. A major advantage of DVI over scanning techniques is that internal defects can be imaged to very high resolution. In order to perform the metrology operations on the microcomponents, high-speed and high-precision algorithms are developed for coordinate metrology. The algorithms are based on a least-squares approach to data registration the {X,Y,Z} point clouds generated from the component surface onto a target geometry defined in a CAD model. Both primitive geometric element analyses as well as an overall comparison of the part geometry are discussed. Initial results of the micromeasurements are presented in the paper.