Shell structures with high stiffness-to-weight ratios are desirable in various engineering applications. Topology optimization serves as a popular and effective tool for generating optimal shell structures. The solid isotropic material with ...

• An IGA-based SIMP method using NURBS for both density and shell models is proposed to design shell structures.
• An automated post-processing step is proposed to get explicit and fair boundaries.
• Numerical experiments confirm the ...

Owing to the rapid development in additive manufacturing, the potential to fabricate intricate structures has become a reality, emphasizing the importance of designing structures conducive to additive manufacturing processes. A crucial ...

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• Analytical conditions for non-self-supporting constraints are derived based on the implicit B-spline representation.
• Several acceleration techniques are employed to achieve high computational performance.
• The self-supporting ...

Shell structures refer to structural elements that derive strength and load-bearing capacity from their thin and curved geometry. In practical applications, shell structures are commonly composed of multiple patches to represent intricate and ...

• The paper presents a general framework for multi-patch Reissner-Mindlin shell structures topology optimization based on IGA-SIMP method.
• C 0 continuity is ensured by patch splitting and reparameterization along interfaces, ensuring ...

One prominent step in isogeometric analysis (IGA) is known as domain parameterization, that is, finding a parametric spline representation for a computational domain. Typically, domain parameterization is divided into two separate steps: ...

• A fast parameterization method is proposed via generalization of neural networks.
• Our method simultaneously parametrizes the boundary and interior of a domain.
• We achieve results as good as the prior work with two orders of ...

This paper studies the stability of the dimension of the spline space S d ( T ) of bi-degree ( d , d ) with highest order of smoothness over a T-mesh T. By decomposing the T-connected component of T into a diagonalizable component and a non-...

In isogeometric analysis (IGA), domain parameterization plays a crucial role as it significantly impacts the results of subsequent numerical analyses. Previous literature has often treated domain parameterization as two separate processes: ...

• A domain parameterization method is proposed based on deep learning.
• Our method simultaneously parameterize the boundary and interior of a domain.
• Our approach produces results with lower distortion and higher bijectivity ratio.

Moving planes have been widely recognized as a potent algebraic tool in various fundamental problems of geometric modeling, including implicitization, intersection computation, singularity calculation, and point inversion of parametric surfaces. ...

• An efficient approach to computing a set of moving planes that follow the given rational parametric surface is proposed.
• The moving planes are significant to surface implicitization, surface intersection, inversion formula, etc.
• ...

Computing the intersection curves of two quadrics (QSIC) is a fundamental problem in computer aided design system, where the topology analysis of the QSIC is an essential task to realize the robust computation. In this paper, a new method is ...

• A new method is presented to classify the topology of the intersection curves of two quadrics.
• The classification is determined by a set of discriminants to provide explicit representations.
• The new method can be applied even when ...

With the advent of additive manufacturing (AM), topology optimization (TO) has become increasingly important in structural design. A key component of structural design is generating the interior shape of an object under predefined ...

• A framework is developed to create porous structures with a high self-supporting ratio based on TPMS.

Singularity computation is a fundamental problem in Computer Graphics and Computer Aided Geometric Design, since it is closely related to topology determination, intersection, mesh generation, rendering, simulation, and modeling of curves and surfaces. In ...

Constructing a high-quality parameterization of a computational domain is a fundamental research problem in isogeometric analysis, which has been extensively investigated so far. However, most of the current approaches employ non-...

• A novel parameterization method for planar domains is presented.
• The ...

In this paper, a robust and efficient algorithm is proposed to calculate the intersection points of two planar algebraic curves with guaranteed tolerance. The proposed method takes advantage of the fundamental methods in the fields of ...

• An algorithm is proposed to calculate the intersection of two algebraic curves.

• A constructional method for proving the validity of implicitization of rational surfaces is provided.

This paper provides an elementary and constructive treatment to implicitizing tensor product rational surfaces whose base point locus is a local complete intersection (lci) by the method of moving planes and moving quadrics. The ...

Domain parameterization, i.e., constructing a map from a parameter domain to a computational domain, is a key step in isogeometric analysis. Before parameterizing the interior of the computational domain, the boundary correspondence ...

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• An automatic method to compute a correspondence of volumetric domains is presented.

Handling stress constraints is an important topic in topology optimization. In this paper, we introduce an interpretation of stresses as optimization variables, leading to an augmented Lagrangian formulation. This formulation takes two sets of ...

Porous structures are widely used in our daily life due to their special properties such as higher rigidity and lightweight. With the popularity of additive manufacturing (AM), producing porous structures by AM shows great advantages ...

• An implicit representation is proposed to model a type of porous structures.
• A ...

Constructing a volumetric spline parameterization of a three dimensional domain with given boundary is a fundamental problem in isogeometric analysis. Recently it is shown that the rank of the parameterization has great impact in ...

• A low-rank spline parameterization method for volumetric models is presented.
• ...

Domain parameterization is the process of setting up a map from a parametric domain to a computational domain. It is a key step in isogeometric analysis and has regained much attention in recent years. A prerequisite for domain ...

• An automatic approach to compute a correspondence of planar domains is presented.

• A tensor product rational surface of bidegree ( m , n ) without base points can always be implicitized by moving quadrics together with moving planes.

It was proven by Cox, Goldman and Zhang that a tensor product rational surface without base points can be implicitized by moving quadrics whenever the rational surface doesn't contain low degree moving planes following it. However, ...

We propose an algorithm for computing injective IGA-suitable planar parameterizations with as uniform and orthogonal as possible iso-parametric structure. Central to this approach is a PolySquare-enhanced domain partition procedure ...