Smooth multi-patch scaled boundary isogeometric analysis for Kirchhoff-Love shells
Authors: Mathias Reichle, Jeremias Arf, Bernd Simeon, Sven Klinkel
Abstract
In this work, a linear Kirchhoff-Love shell formulation in the framework of scaled boundary isogeometric analysis is presented that aims to provide a simple approach to trimming for NURBS-based shell analysis. To obtain a global C1-regular test function space for the shell discretization, an inter-patch coupling is applied with adjusted basis functions in the vicinity of the scaling center to ensure the approximation ability. Doing so, the scaled boundary geometries are related to the concept of analysis-suitable G1 parametrizations. This yields a coupling of patch boundaries in a strong sense that is restricted to G1-smooth surfaces. The proposed approach is advantageous to trimmed geometries due to the incorporation of the trimming curve in the boundary representation that provides an exact representation in the planar domain. The potential of the approach is demonstrated by several problems of untrimmed and trimmed geometries of Kirchhoff-Love shell analysis evaluated against error norms and displacements. Lastly, the applicability is highlighted in the analysis of a violin structure including arbitrarily shaped patches.
The papers around it, by date and closeness
Higher is closer to this paper; left is older. Lines join papers close to each other: groups of lines are sub-topics. Select a point to see why it is there. Back to the summary of this paper
Papers around this one
Ranked by how close their title and abstract are to this paper’s. Select some to read them together.
Closest papers
-
A robust solution strategy for the Cahn-Larché equationsErlend Storvik, Jakub Wiktor Both, Jan Martin Nordbotten et al. · 2022 · Numerical Analysis · AI summary available
Abstract
In this paper we propose a solution strategy for the Cahn-Larch\'e equations, which is a model for linearized elasticity in a medium with two elastic phases that evolve subject to a Ginzburg-Landau type energy functional. The system can be seen as a combination of the Cahn-Hilliard regularized interface equation and linearized elasticity, and is non-linearly coupled, has a fourth order term that comes from the Cahn-Hilliard subsystem, and is non-convex and nonlinear in both the phase-field and displacement variables. We propose a novel semi-implicit discretization in time that uses a standard convex-concave splitting method of the nonlinear double-well potential, as well as special treatment…
-
A Discontinuous Galerkin Method by Patch Reconstruction for Biharmonic ProblemRuo Li, Pingbing Ming, Zhiyuan Sun et al. · 2017 · Numerical Analysis · Not summarized yet
Abstract
We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.
-
Convergence of an adaptive $C^0$-interior penalty Galerkin method for the biharmonic problemAlexander Dominicus, Fernando Gaspoz, Christian Kreuzer · 2019 · Numerical Analysis · AI summary available
Abstract
We develop a basic convergence analysis for an adaptive $\textsf{C}^0\textsf{IPG}$ method for the Biharmonic problem, which provides convergence without rates for all practically relevant marking strategies and all penalty parameters assuring coercivity of the method. The analysis hinges on embedding properties of (broken) Sobolev and BV spaces, and the construction of a suitable limit space. In contrast to the convergence result of adaptive discontinuous Galerkin methods for elliptic PDEs, by Kreuzer and Georgoulis [Math. Comp. 87 (2018), no.~314, 2611--2640], here we have to deal with the fact that the Lagrange finite element spaces may possibly contain no proper $C^1$-conforming subspace.…
-
A robust monolithic solver for phase-field fracture integrated with fracture energy based arc-length method and under-relaxationRitukesh Bharali, Somdatta Goswami, Cosmin Anitescu et al. · 2021 · Numerical Analysis · AI summary available
Abstract
The phase-field fracture free-energy functional is non-convex with respect to the displacement and the phase field. This results in a poor performance of the conventional monolithic solvers like the Newton-Raphson method. In order to circumvent this issue, researchers opt for the alternate minimization (staggered) solvers. Staggered solvers are robust for the phase-field based fracture simulations as the displacement and the phase-field sub-problems are convex in nature. Nevertheless, the staggered solver requires very large number of iterations (of the order of thousands) to converge. In this work, a robust monolithic solver is presented for the phase-field fracture problem. The solver adop…
-
Compatible finite element methods for geophysical fluid dynamicsColin J. Cotter · 2023 · Numerical Analysis · AI summary available
Abstract
This article surveys research on the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's C-grid finite difference scheme to the finite element world. They are constructed from a discrete de Rham complex, which is a sequence of finite element spaces which are linked by the operators of differential calculus. The use of discrete de Rham complexes to solve partial differential equations is well established, but in this article we focus on the specifics of dynamical cores for simulating weather, oceans and climate. The most important consequence of the discrete de Rham complex is the Hodge-Helmholtz d…
-
Thirty years of the finite volume method for solid mechanicsPhilip Cardiff, Ismet Demirdžić · 2018 · Numerical Analysis · AI summary available
Abstract
Since early publications in the late 1980s and early 1990s, the finite volume method has been shown suitable for solid mechanics analyses. At present, there are several flavours of the method, which can be classified in a variety of ways, such as grid arrangement (cell-centred vs staggered vs vertex-centred), solution algorithm (implicit vs explicit), and stabilisation strategy (Rhie-Chow vs Jameson-Schmidt-Turkel vs Godunov upwinding). This article gives an overview, historical perspective, comparison and critical analysis of the different approaches where a close comparison with the de facto standard for computational solid mechanics, the finite element method, is given. The article finish…
-
Low-complexity computation of plate eigenmodes with Vekua approximations and the Method of Particular SolutionsGilles Chardon, Laurent Daudet · 2013 · Numerical Analysis · AI summary available
Abstract
This paper extends the Method of Particular Solutions (MPS) to the computation of eigenfrequencies and eigenmodes of plates. Specific approximation schemes are developed, with plane waves (MPS-PW) or Fourier-Bessel functions (MPS-FB). This framework also requires a suitable formulation of the boundary conditions. Numerical tests, on two plates with various boundary conditions, demonstrate that the proposed approach provides competitive results with standard numerical schemes such as the Finite Element Method, at reduced complexity, and with large flexibility in the implementation choices.
-
An embedded corrector problem for homogenization. Part II: Algorithms and discretizationEric Cancès, Virginie Ehrlacher, Frederic Legoll et al. · 2018 · Numerical Analysis · Not summarized yet
Abstract
This contribution is the numerically oriented companion article of the work [E. Canc\`es, V. Ehrlacher, F. Legoll, B. Stamm and S. Xiang, arxiv preprint 1807.05131]. We focus here on the numerical resolution of the embedded corrector problem introduced in [E. Canc\`es, V. Ehrlacher, F. Legoll and B. Stamm, CRAS 2015; E. Canc\`es, V. Ehrlacher, F. Legoll, B. Stamm and S. Xiang, arxiv preprint 1807.05131] in the context of homogenization of diffusion equations. Our approach consists in considering a corrector-type problem, posed on the whole space, but with a diffusion matrix which is constant outside some bounded domain. In [E. Canc\`es, V. Ehrlacher, F. Legoll, B. Stamm and S. Xiang, arxiv p…
Go further
How are these papers found?
We compare the title and abstract of this paper with those of every paper summarized on this site, and with the papers Semantic Scholar recommends, those it cites and those citing it (for a much-cited paper, its most recent citations and, from OpenAlex, the most cited ones). Among the prior work and the follow-ups, the papers that use each other in depth, a method it uses and the much-cited follow-ups come a little higher. The levels (very close, close, related) come from the similarity of the texts, not from a judgment of quality; * marks a paper without an abstract, compared by its title. The sentence under a paper is written by an AI from the two abstracts: check it in the papers. A paper marked not relevant by three readers leaves the list.
For now only among the papers summarized on this site: search again to add the prior work, the follow-ups and Semantic Scholar’s recommendations.