Computer-Aided Design最新文献

Complex architectural structures may be built in a simple and cost-effective way if their geometry respects the fabrication constraints. Examples of such structures are provided by gridshells that are built from straight and flat slats which are bent on site so that they become tangential or normal to the design surface. Tangential slats follow geodesic curves on the surface, while normal slats are attached along asymptotic curves. Extending work by Frei Otto, Julius Natterer and others, who placed the slats tangentially, Eike Schling proposed structures which also contain slats normal to the reference surface. In the present paper we address those gridshells that consist of three families of bent elements, either tangential or normal to the design surface, and are arranged in a triangular web. We propose algorithms for the computational design of such webs that start from a boundary strip and propagate it, partially under additional guidance, to an entire web.

We present several algorithms for evaluating point containment in constructive solid geometry (CSG) trees with unbounded primitives. Three algorithms are presented based on postfix, prefix, and infix notations of the CSG binary expression tree. We show that prefix and infix notations enable short-circuiting logic, which reduces the number of primitives that must be checked during point containment. To evaluate the performance of the algorithms, each algorithm was implemented in the OpenMC Monte Carlo particle transport code, which relies on CSG to represent solid bodies through which subatomic particles travel. Two sets of tests were carried out. First, the execution time to generate a rasterized image of a 2D slice of three CSG models of varying complexity was measured. Use of both prefix and infix notations offered significant speedup over the postfix notation that has traditionally been used in particle transport codes, with infix resulting in a 6$\times$ reduction in execution time relative to postfix for a model of a tokamak fusion device. We then measured the execution time of neutron transport simulations of the same three models using each of the algorithms. The results and performance improvements reveal the same trends as for the rasterization test, with a 5.52$\times$ overall speedup using the infix notation relative to the original postfix notation in OpenMC for the tokamak model.

This paper addresses two problems needed to support four-dimensional ($3d+t$) spacetime numerical simulations. The first contribution is a general algorithm for producing conforming spacetime meshes of moving geometries. Here, the surface points of the geometry are embedded in a four-dimensional space as the geometry moves in time. The geometry is first tessellated at prescribed time steps and then these tessellations are connected in the parameter space of each geometry entity to form tetrahedra. In contrast to previous work, this approach allows the resolution of the geometry to be controlled at each time step. The only restriction on the algorithm is the requirement that no topological changes to the geometry are made (i.e. the hierarchical relations between all geometry entities are maintained) as the geometry moves in time. The validity of the final mesh topology is verified by ensuring the tetrahedralizations represent a closed 3-manifold. For some analytic problems, the $4d$ volume of the tetrahedralization is also verified. The second problem addressed in this paper is the design of a system to interactively visualize four-dimensional meshes when the $4d$ view changes, including tetrahedra (embedded in $4d$) and pentatopes. Algorithms that either include or exclude a geometry shader are described, and the efficiency of each approach is then compared. Overall, the results suggest that visualizing tetrahedra (either those bounding the domain, or extracted from a pentatopal mesh) using a geometry shader achieves the highest frame rate, realizing interactive frame rates of at least 15 frames per second for meshes with about 50 million tetrahedra.

Porous structures are materials consisting of minuscule pores, where the microstructure morphology significantly impacts their macroscopic properties. Integrating different porous structures through a blending method is indispensable to cater to diverse functional regions in heterogeneous models. Previous studies on blending methods for porous structures have mainly focused on controlling the shape of blending regions, yet they have fallen short in effectively addressing topological errors in blended structures. This paper introduces a new blending method that successfully addresses this issue. Initially, a novel initialization method is proposed, which includes distinct strategies for blending regions of varying complexities. Subsequently, we formulate the challenge of eliminating topological errors as an optimization problem based on persistent homology. Through iterative updates of control coefficients, this optimization problem is solved to generate a blended porous structure. Our approach not only avoids topological errors but also governs the shape and positioning of the blending region while remaining unchanged in the structure outside blending region. The experimental outcomes validate the effectiveness of our method in producing high-quality blended porous structures. Furthermore, these results highlight potential applications of our blending method in biomimetics and the design of high-stiffness mechanical heterogeneous models.

We present an approach for systematic design of generalized Plesiohedra, a new type of 3D space-filling shapes that can even include unchained handlebodies. We call these handlebody plesiohedra unchained, since they are topologically interlocked, i.e., they can be assembled and disassembled without breaking any of the solids apart and they can keep in place with a set of boundary constraints. These space-filling shapes (i.e. congruent prototiles) are obtained from the Voronoi decomposition of symmetric Delone (Delaunay) point sets. To create this new class of shapes, we generalize the design space of classical Plesiohedra by introducing two novel geometric steps: (a) extension of point sites to piecewise linear approximations of higher-dimensional geometries and (b) extension of symmetries to 3D crystallographic symmetries. We show how these specific collections of higher-dimensional geometries can admit the symmetric Delone property. A Voronoi partitioning of 3D space using these specific collections of higher-dimensional shapes as Voronoi sites naturally results in congruent prototiles. This generalizes the idea of classical Plesiohedra by allowing for piecewise linear approximation of curved edges and faces, non-convex boundaries, and even handlebodies with positive genus boundaries to provide truly volumetric material systems in contrast to traditional planar or shell-like systems. To demonstrate existence of these solid shapes, we produced a large set of unchained congruent space-filling handlebodies as proofs of concept. For this, we focused our investigation using isometries of some space-filling polyhedra, such as a cube and a truncated octahedron with circles, and curve complexes as Voronoi sites. These results point to a rich and vast parametric design space of unchained handlebody plesiohedra making them an excellent representations for engineering applications such as topologically interlocked architectured materials.

This article introduces a novel computer-aided procedure to design optimised coated structures with precise shell thickness control using the Smallest Univalue Segment Assimilating Nucleus operator and a novel augmentation-projection technique. Structures with heterogeneous sections, or coated structures, combine two different materials for the nucleus and the shell, which are generally chosen so that the material in the infill is lighter and the material in the coating is stiffer, which in this work are supposed homogeneous. Solving the interface problem requires material properties interpolation equations that consider three material phases, accurate placement of the coating over the base material, and precise control over the coating's thickness. The formation of the coating is controlled by the Smallest Univalue Segment Assimilating Nucleus, an edge detection operator developed in Digital Image Processing. The coating's thickness is controlled by an innovative methodology consisting of the projection of an augmented contour field, which is shown to create a constant thickness coating around the material domain. The optimisation problem is solved with the Sequential Element Rejection and Admission method. The validity of the procedure has been verified by solving various numerical application examples.

Recovering geometric regularities from scanned mesh models with various types of surface features has always been a challenging task in reverse engineering. To address this problem, this paper presents a regularity detection and enhancement framework for surface mesh reconstruction. Initially, surface patches are identified by decomposing the original model into planar, quadric and freeform surface patches. Similar surface patches are aligned with each other by pairwise registration, and symmetry patterns are detected from the accumulated affine transformations using an improved grid fitting method. Regular relations between symmetry patterns and individual surface patches are enumerated and progressively strengthened by orientation, dimension and placement optimizations. Finally, the resultant model with enhanced regularities is obtained by projecting surface patches onto the optimized parametric surfaces iteratively. Comparative experiments on test models demonstrate that the proposed method outperforms existing methods in recovering both lower- and higher-level regularities of engineering models, especially those with freeform surfaces.

This paper presents a novel mesh denoising approach designed specifically for developable models with curved folds, going beyond traditional denoising metrics to focus on restoring the model’s developability. We introduce a metric based on normal variation to assess mesh developability and integrate it into an optimization problem that aims to increase the sparsity of the normal vector field, leading to a dedicated mesh denoising algorithm. The performance of our method is evaluated across a wide range of criteria, including standard metrics and surface developability determined through Gaussian curvature. Through testing on a variety of noisy models and comparison with several state-of-the-art mesh denoising and developability optimization techniques, our approach demonstrates superior performance in both traditional metrics and the enhancement of mesh developability.

Functionally Graded Cellular Materials (FGCM) with variable volume fractions have demonstrated significant advantages, including weight reduction, improved stiffness, and enhanced load distribution, when compared to uniform density counterparts. Their design is often characterized by the application of a density distribution to locally modify Representative Volume Elements (RVEs). Current studies have explored the application of Triply Periodic Minimal Surfaces (TPMS) topologies, given their capability to create seamless and interconnected structures, thus avoiding stress concentration issues commonly encountered in traditional lattice configurations. Consequently, this paper introduces a design methodology tailored to TPMS-based FGCM allowing for independent or simultaneous adjustments of RVE thickness and size. Models for predicting relative density as a function of the RVE design parameters of Primitive and Gyroid topologies are presented and discussed. These models are employed to adapt the topologies to three-dimensional density distributions. The proposed method is implemented as a set of design tools and is illustrated for the studied TPMS topologies.