Meshfree methods for shear-deformable structures based on mixed weak forms

Hale, Jack

Reference : Meshfree methods for shear-deformable structures based on mixed weak forms


	Document type :	Scientific congresses, symposiums and conference proceedings : Unpublished conference
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics Engineering, computing & technology : Multidisciplinary, general & others
	Focus Areas :	Computational Sciences
	To cite this reference:	http://hdl.handle.net/10993/17084

Title :	Meshfree methods for shear-deformable structures based on mixed weak forms
Language :	English
Author, co-author :	Hale, Jack [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit > ; Imperial College London > Department of Aeronautics]
Publication date :	24-Jul-2014
Peer reviewed :	Yes
On invitation :	Yes
Audience :	International
Event name :	PhD Olympiad at the 11th. World Congress on Computational Mechanics
Event date :	20-07-2013 to 25-07-2013
Event place (city) :	Barcelona
Event country :	Spain
Keywords :	[en] meshfree ; mixed forms ; shear-deformable ; beams ; plates
Abstract :	[en] Similarly to the finite element method, meshfree methods must be carefully designed to overcome the shear-locking problem when discretising the shear-deformable structural theories. Many successful treatments of shear-locking in the finite element literature are constructed through the application of a mixed variational form, where the shear stress is treated as an independent variational quantity in addition to the usual displacements. Because of its sound mathematical underpinnings this is the methodology I have chosen to solve the shear-locking problem when using meshfree basis functions. In this talk I will discuss the mathematical origins of the shear-locking problem and the applicability of the celebrated LBB stability condition for designing well-behaved mixed meshfree approximation schemes. I will show results from two new formulations that demonstrate the effectiveness of this approach. The first method is a meshfree formulation for the Timoshenko beam problem that converges to a classic inf-sup stable finite element method when using Maximum- Entropy basis functions. The second method is a generalised displacement meshfree method for the Reissner- Mindlin problem where the shear stress is eliminated prior to the solution of the linear system using a local patch-projection technique, resulting in a linear system expressed in terms of the original displacement unknowns only. Stability is ensured by using a stabilised weak form which is necessary due to the loss of kernel coercivity for the Reissner-Mindlin problem.
Research centres :	Imperial College London
Funders :	EPSRC
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/17084
Other URL :	http://orbilu.uni.lu/handle/10993/12057

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Open access	Jack_Samuel_HALE_PhD_Olympiad_Abstract.pdf		Publisher postprint	77.27 kB	View/Open

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Open access	HALE_wccm_2014_olympiad_presentation.pdf	Presentation	5.94 MB	View/Open

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