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Isogeometric Analysis with Geometrically Continuous Functions on Two-Patch Geometries

Basis (linear algebra)

Spline (mathematics)

Isogeometric analysis

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Isogeometric analysis with geometrically continuous functions on two-patch geometries has been studied extensively. The construction of these functions is closely related to the concept of geometric continuity of surfaces, which originated in geometric design. The smoothness of isogeometric functions is found to be equivalent to the geometric smoothness of their graph surfaces, leading to the term "C s -smooth geometrically continuous isogeometric functions" . Recent works have investigated the construction of spline spaces with global C 1 continuity on two or more patches, and it has been shown that these approaches can be combined with hierarchical construction to obtain global C 1 continuous hierarchical splines on two-patch domains . The dimension and basis construction for C 1 -smooth isogeometric function spaces over two-patch domains have also been analyzed, providing important insights for the efficient implementation of the isogeometric method .

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Open access•Posted Content Isogeometric analysis with $C^1$ hierarchical functions on planar two-patch geometries Cesare Bracco, Carlotta Giannelli, Mario Kapl, Rafael Vázquez - Show less +3 more 28 Jan 2019-arXiv: Numerical Analysis 1 Citations	The answer to the query is not in the paper. The paper is about the construction of globally $C^1$ continuous hierarchical splines on two-patch domains in isogeometric analysis.
Open access•Journal Article•DOI Isogeometric analysis with C1 hierarchical functions on planar two-patch geometries Cesare Bracco, Carlotta Giannelli, Mario Kapl, Rafael Vázquez - Show less +3 more 01 Dec 2020-Computers & Mathematics With Applications 14 Citations	The answer to the query is not in the paper. The provided paper is about isogeometric analysis with C1 hierarchical functions on planar two-patch geometries.
Open access•Posted Content Dimension and basis construction for analysis-suitable $G^1$ two-patch parameterizations Mario Kapl, Giancarlo Sangalli, Thomas Takacs - Show less +2 more 23 Jan 2017-arXiv: Numerical Analysis 13 Citations	The provided paper is not about "Isogeometric Analysis with Geometrically Continuous Functions on Two-Patch Geometries".
Open access•Journal Article•DOI Isogeometric analysis with geometrically continuous functions on two-patch geometries Mario Kapl, Vito Vitrih, Bert Jüttler, Katharina Birner - Show less +3 more 01 Oct 2015-Computers & Mathematics With Applications 87 Citations	The paper discusses the construction and analysis of C s -smooth geometrically continuous isogeometric functions on multi-patch domains in isogeometric analysis. It presents a general framework for constructing a basis and explores potential applications.

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Is there any paper treat about solving the wave propagation equation using isogeometric anaysis method ?5 answersYes, there are papers that discuss solving the wave propagation equation using isogeometric analysis. Cromwell and Fraschini both investigate the development of an unconditionally stable space-time isogeometric method for the linear acoustic wave equation. Addo explores the use of isogeometric boundary element analysis (IGABEM) for handling the time harmonic wave propagation equation of Helmholtz in acoustics. Fraschini, Loli, Moiola, and Sangalli focus on high-order space-time isogeometric discretizations of the linear acoustic wave equation using B-splines. These papers propose different approaches and techniques to achieve accurate and efficient solutions for wave propagation problems using isogeometric analysis.

Isogeometric analysis on sandwich plates5 answersIsogeometric analysis (IGA) has been used in several papers to analyze the static, dynamic, and buckling behavior of laminated and functionally graded (FG) sandwich plates. The use of IGA allows for the implementation of nonpolynomial shear deformation theories (NPSDT) and third-order shear deformation theories (TSDT) in the analysis, which consider the nonlinear distribution of transverse shear stresses and satisfy the transverse shear deformation conditions at the top and bottom surfaces of the plates. The multi-patch B-spline basis functions used in IGA ensure C0-continuity at layer interfaces and smoothly varying material properties across each layer thickness. Additionally, a quasi three-dimensional (quasi-3D) shear deformation theory has been proposed, which uses isogeometric analysis and physical neutral surface position to satisfy the free transverse shear stress conditions without the need for shear correction factors. The use of inverse tangent shear deformation theory (ITSDT) in combination with IGA has also been explored for laminated composite and sandwich plates, eliminating the need for shear correction factors and achieving high efficiency. Finally, a fifth-order shear deformation theory (FiSDT) combined with IGA has been used for the analysis of composite sandwich plates, providing accurate results for static, dynamic, and buckling analysis.

Isogeometric analysis on sandwich structures5 answersIsogeometric analysis has been used in several studies to analyze sandwich structures. One study introduced an equilibrium-based stress recovery approach for determining the three-dimensional stress state in composite sandwich plates using isogeometric analysis. Another study performed buckling and vibration studies of sandwich plates with a negative Poisson's ratio honeycomb core using isogeometric analysis. A highly accurate and computationally efficient isogeometric beam element was presented for displacement and stress analysis of thin/thick composite beams. Additionally, effective numerical approaches based on isogeometric analysis were proposed for the static and dynamic analysis of laminated and sandwich composite plates. These studies demonstrate the applicability and advantages of isogeometric analysis in analyzing the behavior of sandwich structures.

Isogeometric analysis of functionally graded sandwich plate4 answersIsogeometric analysis is used to analyze the behavior of functionally graded sandwich plates. Various theories have been developed to accurately model the bending behavior of these plates. One such theory is the hyperbolic quasi-3D shear deformation plate theory, which reduces the number of unknowns and eliminates the need for shear correction factors. Another theory called the spectral displacement formulation (SDF) uses a unique form of the Chebyshev series to express the displacement field, allowing for accurate bending analysis and satisfying traction-free boundary conditions. Stochastic isogeometric analysis (SIGA) is used to analyze functionally graded plates subjected to random distribution loads, modeling the spatial random variation as a homogeneous Gaussian random field. These theories and methods have been shown to be effective in analyzing the bending behavior, free vibration, and thermo-mechanical properties of functionally graded sandwich plates.

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