Computational grid generation for the design of free-form shells with complex boundary conditions

Free-form grid structures have been widely used in various public buildings, and many are bounded by complex curves including internal voids. Modern computational design software enables the rapid creation and exploration of such complex surface geometries for architectural design, but the resulting shapes lack an obvious way for engineers to create a discrete structural grid to support the surface that manifests the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on guideline and surface-flattening methods, which consider complex features and internal boundaries. The method employs a fast and straightforward approach, which achieves fluent lines with bars of balanced length. The parametric domain of a complete nonuniform rational basis spline (NURBS) surface is first divided into a number of patches, and a discrete free-form surface is formed by mapping dividing points onto the surface. The free-form surface is then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the two-dimensional (2D) surface, with grids formed by applying a guideline method. Subsequently, the intersections of the guidelines and the complex boundary are obtained, and the guidelines are divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the three-dimensional (3D) surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes by presenting realistic examples to demonstrate the practical effectiveness of the proposed method.</p

Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions

© 2019 American Society of Civil Engineers. Free-form grid structures have been widely used in various public buildings, and many are bounded by complex curves including internal voids. Modern computational design software enables the rapid creation and exploration of such complex surface geometries for architectural design, but the resulting shapes lack an obvious way for engineers to create a discrete structural grid to support the surface that manifests the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on guideline and surface-flattening methods, which consider complex features and internal boundaries. The method employs a fast and straightforward approach, which achieves fluent lines with bars of balanced length. The parametric domain of a complete nonuniform rational basis spline (NURBS) surface is first divided into a number of patches, and a discrete free-form surface is formed by mapping dividing points onto the surface. The free-form surface is then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the two-dimensional (2D) surface, with grids formed by applying a guideline method. Subsequently, the intersections of the guidelines and the complex boundary are obtained, and the guidelines are divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the three-dimensional (3D) surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes by presenting realistic examples to demonstrate the practical effectiveness of the proposed method

Evaluating the Energy and Mechanical Properties of CSH/nano-CC Interface: An Atomic Investigation

Carbonation of concrete generally leads to decalcification of calcium silicate hydrates (CSH) and generation of calcium carbonate (CC), however, the structure and mechanical properties of CSHCC nano composites are far from being fully addressed. The CC formed by CSH carbonization mainly has three polymorphs, including calcite, vaterite and aragonite. Although different polymorphs have the same chemical composition, they belong to different crystal systems and have completely different unit cell structures. In this paper, the CSH and three polymorphs nano-CC are constructed at the atomic level, and the interface properties between them are explored by reactive molecular dynamics (MD) simulations. The results show the greater interfacial bonding energy, the better the mechanical properties of the CSH-CC composite. Moreover, interface transition region (ITR) emerges between CSH and CC polymorphs, and the ITR thickness is different. The atomic structure in ITR is different from that in the middle region, the former is more disorderly and the coordination number in ITR is significantly reduced, thus showing a metastable state. The findings would deepen the mechanistic understanding of interface properties between CSH and nano-CC

A grid generation procedure for the design of single-layer freeform structures

Computer aided design software enables the rapid creation of any curved surface geometry, whereas it is neither a convenient nor an obvious task for engineers to efficiently create a discrete grid structure on a complex surface that also meets architectural requirements. This emphasizes the importance of grid generating tools and methods in the initial design stage. This paper presents an efficient design tool for the synthesis of free-form grid structures based on the concept of a “guide line”. The process starts with defining a limited number of curves (named the “guide lines”) on the surface, which are then used to determine the directions of the ‘rods’ of the grid. Two variations of this concept are introduced in the paper: the ‘Guide Line Scaling Method’ (GSM) and the ‘Two Guide Lines with Two End Vertices Method’ (2G2VM). Case studies on the British Museum Court Roof are provided which illustrate the successful execution of these procedures. The results show that the free-form grid structures generated with the proposed methods feature a regular shape and fluent lines, thereby satisfying aesthetic requirements. These two methods have been programmed into the software ZDMesher, enabling rapid grid generation for structural design purposes

A practical grid generation procedure for the design of free-form structures

Computer aided design software enables the rapid conceptual creation of a curved surface geometry, whereas it is neither a convenient nor an obvious task for engineers to create a discrete grid structure on a complex surface that meets architectural and aesthetic requirements. This emphasizes the importance of grid generating tools and methods in the initial design stage. This paper presents an efficient design tool for the synthesis of free-form grid structures based on the "guide line" method, employing a fast and straightforward approach which achieves grids with rods of balanced length and fluent lines. The process starts with defining a limited number of curves (named the "guide lines") on the surface, which are then used to determine the directions of the 'rods' of the grid. Two variations of this concept are introduced in this paper: the ‘Guide Line Scaling Method’ (GSM) and the 'Two Guide Lines with Two End Vertices Method' (2G2VM). Case studies are provided which illustrate the successful execution of these procedures. The results show that the free-form grid structures generated with the proposed methods feature a regular shape and fluent lines, thereby satisfying aesthetic requirements. These two methods have been programmed into the software ZD-Mesher, enabling rapid grid generation for structural design purposes

Twisted van der Waals Quantum Materials: Fundamentals, Tunability and Applications

Twisted vdW quantum materials have emerged as a rapidly developing field of 2D semiconductors. These materials establish a new central research area and provide a promising platform for studying quantum phenomena and investigating the engineering of novel optoelectronic properties such as single-photon emission, non-linear optical response, magnon physics, and topological superconductivity. These captivating electronic and optical properties result from, and can be tailored by, the interlayer coupling using moir\'e patterns formed by vertically stacking atomic layers with controlled angle misorientation or lattice mismatch. Their outstanding properties and the high degree of tunability position them as compelling building blocks for both compact quantum-enabled devices and classical optoelectronics. This article offers a comprehensive review of recent advancements in the understanding and manipulation of twisted van der Waals structures and presents a survey of the state-of-the-art research on moir\'e superlattices, encompassing interdisciplinary interests. It delves into fundamental theories, synthesis and fabrication, and visualization techniques, and the wide range of novel physical phenomena exhibited by these structures, with a focus on their potential for practical device integration in applications ranging from quantum information to biosensors, and including classical optoelectronics such as modulators, light emitting diodes (LEDs), lasers, and photodetectors. It highlights the unique ability of moir\'e superlattices to connect multiple disciplines, covering chemistry, electronics, optics, photonics, magnetism, topological and quantum physics. This comprehensive review provides a valuable resource for researchers interested in moir\'e superlattices, shedding light on their fundamental characteristics and their potential for transformative applications in various fields.Comment: 179 pages, 42 figures, Chemical Review

Digital and automatic design of free-form single-layer grid structures

Grid shells have been widely used in various long-span public buildings, and many of them are defined over free-form surfaces with complex boundaries. This emphasizes the importance of general and digitalised grid generation and optimization methods in the initial design stage to achieve visually sound grid shells. In this paper, a framework is presented for the development of a digital tool and to generate regular and fluent grids for structural design over free-form surfaces, especially those with complex boundaries. Both triangular and quadrilateral grid generation are addressed. To generate regular and fluent grids for free-form surfaces, a simple yet practical framework is proposed based on a spring-mass model. Firstly, an initial casual quadrilateral grid is tiled on the surface based on surface discretization and mesh parameterization. Secondly, the distribution of the initial grid vertices is adjusted by a dynamic relaxation procedure, assuming the grid as a spring-mass system. Thirdly, the grid vertices corresponding to the adjusted particles in the equilibrium state are then reconnected to produce a grid with a predefined pattern (triangular or quadrilateral). Finally, the generated grid is relaxed with the spring-mass model, alongside additional geometric operations including grid size adjustment and filtering techniques, to further improve the grid regularity and fluency. As part of its contribution, this paper also broadens the application scope of the fluency index, which can be used to quantitatively evaluate the suitability of a given triangular or quadrilateral grid for architectural and structural expression. Examples are presented and show that the proposed framework is effective for the triangular and quadrilateral grid generation over various surfaces and to optimize the resulted grids along complex boundaries. The method proposed can be useful for rapid design and performance evaluation of free-form grid structures.</p