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Related papers: An isogeometric method for the Reissner-Mindlin pl…

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We rigorously derive a Blake-Zisserman-Kirchhoff theory for thin plates with material voids, starting from a three-dimensional model with elastic bulk and interfacial energy featuring a Willmore-type curvature penalization. The effective…

Analysis of PDEs · Mathematics 2025-04-09 Manuel Friedrich , Leonard Kreutz , Konstantinos Zemas

The isogeometric approximation of the Stokes problem in a trimmed domain is studied. This setting is characterized by an underlying mesh unfitted with the boundary of the physical domain making the imposition of the essential boundary…

Numerical Analysis · Mathematics 2022-02-02 Riccardo Puppi

We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid variational formulation underlying the DPG method is…

Numerical Analysis · Mathematics 2013-01-28 Victor M. Calo , Nathaniel O. Collier , Antti H. Niemi

We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The…

This work focuses on the coupling of trimmed shell patches using Isogeometric Analysis, based on higher continuity splines that seamlessly meet the $C^1$ requirement of Kirchhoff-Love-based discretizations. Weak enforcement of coupling…

Numerical Analysis · Mathematics 2024-04-15 Giuliano Guarino , Pablo Antolin , Alberto Milazzo , Annalisa Buffa

We define a new theory of discrete Riemann surfaces and present its basic results. The key idea is to consider not only a cellular decomposition of a surface, but the union with its dual. Discrete holomorphy is defined by a straightforward…

Differential Geometry · Mathematics 2016-11-25 Christian Mercat

Penalty methods have proven to be particularly effective for achieving the required $C^1$-continuity in the context of multi-patch isogeometric Kirchhoff-Love shells. Due to their conceptual simplicity, these algorithms are readily…

Numerical Analysis · Mathematics 2021-10-13 Luca Coradello , Josef Kiendl , Annalisa Buffa

In isogeometric analysis, isogeometric function spaces are employed for accurately representing the solution to a partial differential equation (PDE) on a parameterized domain. They are generated from a tensor-product spline space by…

Numerical Analysis · Mathematics 2024-03-29 Dany Rios , Felix Scholz , Thomas Takacs

The purpose of this paper is to present a new mathematical model for the deformation of thin Cosserat elastic plates. Our approach, which is based on a generalization of the classical Reissner plate theory, takes into account the transverse…

Mathematical Physics · Physics 2009-02-18 Lev Steinberg

Although isogeometric analysis exploits smooth B-spline and NURBS basis functions for the definition of discrete function spaces as well as for the geometry representation, the global smoothness in so-called multipatch parametrizations is…

Numerical Analysis · Mathematics 2023-07-26 Jeremias Arf , Mathias Reichle , Sven Klinkel , Bernd Simeon

In this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement and its normal derivative at the boundary of…

Analysis of PDEs · Mathematics 2018-06-25 Antonino Morassi , Edi Rosset , Sergio Vessella

We revisit finite element discretizations of the Reissner-Mindlin plate in the case of non-simply connected (holey) domains with mixed boundary conditions. Guided by the de Rham complex, we develop conditions under which schemes deliver…

Numerical Analysis · Mathematics 2025-06-30 Mark Ainsworth , Charles Parker

The present study investigates a linear-quadratic Dirichlet control problem governed by a non-coercive elliptic equation posed on a possibly non-convex polygonal domain. Tikhonov regularization is carried out in an energy seminorm. The…

Optimization and Control · Mathematics 2026-03-11 Thomas Apel , Mariano Mateos , Arnd Rösch

We consider an optimal shape design problem for the plate equation, where the variable thickness of the plate is the design function. This problem can be formulated as a control in the coefficient PDE-constrained optimal control problem…

Optimization and Control · Mathematics 2015-06-11 Klaus Deckelnick , Michael Hinze , Tobias Jordan

Shell analysis is a well-established field, but achieving optimal higher-order convergence rates for such simulations is a difficult challenge. We present an isogeometric Kirchhoff-Love shell framework that treats every numerical aspect in…

Computational Engineering, Finance, and Science · Computer Science 2020-12-23 Daniel Schöllhammer , Benjamin Marussig , Thomas-Peter Fries

This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner-Mindlin plates. The adaptive discretization is based on the recently developed Geometry Independent Field…

Numerical Analysis · Mathematics 2018-04-17 Peng Yu , Cosmin Anitescu , Satyendra Tomar , Stéphane Bordas , Pierre Kerfriden

This work utilizes the Immersed Boundary Conformal Method (IBCM) to analyze Kirchhoff-Love and Reissner-Mindlin shell structures within an immersed domain framework. Immersed boundary methods involve embedding complex geometries within a…

Numerical Analysis · Mathematics 2024-08-06 Giuliano Guarino , Alberto Milazzo , Annalisa Buffa , Pablo Antolin

The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff-Love type, a detailed review of existing formulations of Kirchhoff-Love and Simo-Reissner…

Computational Engineering, Finance, and Science · Computer Science 2019-05-08 Christoph Meier , Wolfgang A. Wall , Alexander Popp

Trimming is a common operation in CAD, and, in its simplest formulation, consists in removing superfluous parts from a geometric entity described via splines (a spline patch). After trimming the geometric description of the patch remains…

Numerical Analysis · Mathematics 2021-02-11 Annalisa Buffa , Riccardo Puppi , Rafael Vázquez

We present a novel isogeometric collocation method for solving the Poisson's and the biharmonic equation over planar bilinearly parameterized multi-patch geometries. The proposed approach relies on the use of a modified construction of the…

Numerical Analysis · Mathematics 2024-11-21 Mario Kapl , Aljaž Kosmač , Vito Vitrih