Computer-Aided Design最新文献

This paper introduces a novel unsupervised deep learning approach to address the knot placement problem in the field of B-spline approximation, called deep neural network solvers (DNN-Solvers). Given discrete points, the DNN acts as a solver for calculating knot positions in the case of a fixed knot number. The input can be any initial knots and the output provides the desirable knots. The loss function is based on the approximation error. The DNN-Solver converts the lower-dimensional knot placement problem, characterized as a nonconvex nonlinear optimization problem, into a search for suitable network parameters within a high-dimensional space. Owing to the over-parameterization nature, DNN-Solvers are less likely to be trapped in local minima and robust against initial knots. Moreover, the unsupervised learning paradigm of DNN-Solvers liberates us from constructing high-quality synthetic datasets with labels. Numerical experiments demonstrate that DNN-Solvers are excellent in both approximation results and efficiency under the premise of an appropriate number of knots.

Strip-decomposable quadrilateral (SDQ) meshes, i.e., quad meshes that can be decomposed into two transversal strip networks, are vital in numerous fabrication processes; examples include woven structures, surfaces from sheets, custom rebar, or cable-net structures. However, their design is often challenging and includes tedious manual work, and there is a lack of methodologies for editing such meshes while preserving their strip decomposability. We present an interactive methodology to generate and edit SDQ meshes aligned to user-defined directions, while also incorporating desirable properties to the strips for fabrication. Our technique is based on the computation of two coupled transversal tangent direction fields, integrated into two overlapping networks of strips on the surface. As a case study, we consider the fabrication scenario of robotic non-planar 3D printing of free-form surfaces and apply the presented methodology to design and fabricate non-planar print paths.

Topology optimization for engineering problems often requires multiphysics (dual objective functions) and multi-timescale considerations to be coupled with manufacturing constraints across a range of target values. We present a dual neural network approach to topology optimization to optimize a 3-dimensional thermal-electromagnetic device (optical shutter) for maximum temperature rise across a range of extinction ratios while also considering manufacturing tolerances. One neural network performs the topology optimization, allocating material to each sub-pixel within a repeating unit cell. The size of each sub-pixel is selected with manufacturing considerations in mind. The other neural network is trained to predict performance of the device using extinction ratio and temperature rise over a given time period. Training data is generated using a finite element model for both the electromagnetic wave frequency domain and thermal time domain problems. Optimized designs across a range of targets are shown.

We present a specific-purpose globalized and preconditioned Newton-CG solver to minimize a metric-aware curved high-order mesh distortion. The solver is specially devised to optimize curved high-order meshes for high polynomial degrees with a target metric featuring non-uniform sizing, high stretching ratios, and curved alignment — exactly the features that stiffen the optimization problem. To this end, we consider two ingredients: a specific-purpose globalization and a specific-purpose Jacobi-${\text{iLDL}}^{\text{T}}\left(0\right)$ preconditioning with varying accuracy and curvature tolerances (dynamic forcing terms) for the CG method. These improvements are critical in stiff problems because, without them, the large number of non-linear and linear iterations makes curved optimization impractical. First, to enhance the global convergence of the non-linear solver, the globalization strategy modifies Newton’s direction to a feasible step. In particular, our specific-purpose globalization strategy memorizes the length of the feasible step (step-length continuation) between the optimization iterations while ensuring sufficient decrease and progress. Second, to compute Newton’s direction in second-order optimization problems, we consider a conjugate-gradient iterative solver with specific-purpose preconditioning and dynamic forcing terms. To account for the metric stretching and alignment, the preconditioner uses specific orderings for the mesh nodes and the degrees of freedom. We also present a preconditioner switch between Jacobi and ${\text{iLDL}}^{\text{T}}\left(0\right)$ preconditioners to control the numerical ill-conditioning of the preconditioner. In addition, the dynamic forcing terms determine the required accuracy for the Newton direction approximation. Specifically, they control the residual tolerance and enforce sufficient positive curvature for the conjugate-gradients method. Finally, to analyze the performance of our method, the results compare the specific-purpose solver with standard optimization methods. For this, we measure the matrix–vector products indicating the solver computational cost and the line-search iterations indicating the total amount of objective function evaluations. When we combine the globalization and the linear solver ingredients, we conclude that the specific-purpose Newton-CG solver reduces the total number of matrix–vector products by one order of magnitude. Moreover, the number of non-linear and line-search iterations is mainly smaller but of similar magnitude.

Topology optimization of hexahedral (hex) meshes has been a widely studied topic, with the primary goal of optimizing the singularity structure. Previous works have focused on simplifying complex singularity structures by collapsing sheets/chords. However, these works require a large number of checks during the process to prevent illegal operations. Moreover, the employed simplification strategies are not based on the topological characteristics of the structure, but rather on the rank of the components that can be simplified. To overcome these problems, we analyze how topology operations affect the degree of edges in hex meshes, and introduce a fast and automatic algorithm to simplify the singularity structure of hex meshes. The algorithm relies on sheet operations, using mesh volume as a metric to assess the degree of simplification. Moreover, it designs constraints to prevent illegal operations and employs integer linear program to plan the overall optimization strategy for a mesh. After that, we relax the singularity constraints to further simplify the structure, and handle unreasonable singularities via sheet inflation operation. Our algorithm can also improve singularity structure without merging singularities by adjusting the singularity constraint conditions. Numerous experiments demonstrate the effectiveness and efficiency of our algorithm.

Modular floor slabs must be subdivided into prefabricable, transportable segments. This slab segmentation process conventionally uses a rectangular pattern, particularly for timber buildings. Regular segmentation patterns and strict column grids are ideal for rectangular building shapes, but restrict timber buildings to only some architectural uses, and are unideal for urban infill. Unfortunately, planning and constructing multi-storey wood buildings without a strict grid is still challenging. There is therefore a conflict between the desired column placement and the constraints imposed by building systems. This article investigates novel methods for segmenting timber floors supported by irregular column layouts. It proposes six different segmentation methods that are informed through Co-Design by structural, material waste, and transportation requirements. Co-Design allows for the direct integration and automated feedback of such diverse criteria into the early building design phase. These methods are based on three well-known computational approaches: Single-Objective Optimisation, Parametric Modelling, and Agent-Based Modelling. They could also be applied to other non-timber prefabricated floor systems. The segmentation methods are demonstrated on two example floor slabs with irregular column layouts, one with a rectilinear and the other with an irregular outline. The methods are compared using quantitative proxies for cost, fabrication time, architectural adaptability, and assembly complexity. More benchmark testing is needed, but initial results showed that the most efficient segmentations cannot adapt to irregular layouts, emphasising the need for a more adaptable approach to modular timber construction.

The goal of this document is to survey existing methods for recovering or extracting CSG (Constructive Solid Geometry) representations from unstructured data such as 3D point-clouds or polygon meshes. We review and discuss related topics such as the segmentation and fitting of the input data. We cover techniques from solid modeling for the conversion of a polyhedron to a CSG expression and for the conversion of a B-rep to a CSG expression. We look at approaches coming from program synthesis, evolutionary techniques (such as genetic programming or genetic algorithm), and deep learning. Finally, we conclude our survey with a discussion of techniques for the generation of computer programs involving higher-level constructs, representations, and operations for representing solids.

This work presents the first method for generating triangular surface meshes in three dimensions for the NURBS-enhanced finite element method. The generated meshes may contain triangular elements that span across multiple NURBS surfaces, whilst maintaining the exact representation of the CAD geometry. This strategy completely eliminates the need for de-featuring complex watertight CAD models and, at the same time, eliminates any uncertainty associated with the simplification of CAD models. In addition, the ability to create elements that span across multiple surfaces ensures that the generated meshes are highly compliant with the requirements of the user-specified spacing function, even if the CAD model contains very small geometric features. To demonstrate the capability, the proposed strategy is applied to a variety of CAD geometries, taken from areas such as solid/structural mechanics, fluid dynamics and wave propagation.

As an inherent flaw in the kinematic chain mechanism of 5-axis machine tools, singularity can induce dramatic changes in machine axes motion and unfavorable fluctuations in feedrate. For effective singularity avoidance, it is desirable to first achieve accurate and efficient singularity detection and then eliminate the singularity without impairing tool orientation smoothness. This paper presents a novel approach for accurately detecting and smoothly avoiding the singularity in 5-axis CNC machining. In the detection method, two exclusion criteria are presented to efficiently exclude most non-singular segments of the tool orientation spline, and a curve intersection-based algorithm is thus developed to accurately identify the singular segments. In the singularity avoidance method, a concept of admissible tool orientation annulus (ATOA) is introduced, which serves to confine the range and magnitude of the tool orientation spline’s adjustments, and a local adjustment algorithm is then developed to enable the escape of the tool orientation from the singular region with controllable direction and deviation, while maintaining its continuity and smoothness. The effectiveness of singularity avoidance and the kinematic performance of the tool orientation modified by our method, are comparable to a state-of-the-art singularity avoidance algorithm. Finally, the conducted experiments validate the proposed method.

Given a 3D point cloud, we propose a method for suitably resampling the cloud while reconstructing and preserving the feature curves to which some points are identified to belong. The first phase of our strategy enriches the cloud by approximating the curvilinear profiles outlined by the feature points with piece-wise polynomial parametric space curves through the use of the Hough transform. The second phase describes how the removal of a point or its insertion can be performed without affecting the approximated profiles and preserving the enriched structure of the cloud. The combination of the two steps provides multiple possibilities for processing a point cloud by varying its size or improving its density homogeneity without affecting the retrieved feature curves. The various capabilities of our approach are investigated to produce simplification, refinement, and resampling techniques whose effectiveness is evaluated through experiments and comparisons.