Strong and weak form meshless methods in computational biomechanics

Research output: Chapter in Book/Conference paperChapter

Abstract

Meshless methods (MMs) were introduced in the late 1970s to solve problems in astrophysics. In MMs the spatial domain is represented by a set of nodes (cloud of points) and not discretized by elements as in most of the mesh-based methods (finite difference method, finite element method, finite volume method); consequently, there is no need for predefined connectivity between the nodes. In this chapter we are going to give an overview of applications, advantages, and disadvantages of various MMs developed and applied in the context of computational biomechanics. Strong and weak formulations will be presented, focusing on the novel interpolation schemes such as modified moving least squares and discretization correction particle strength exchange method, along with the meshless total Lagrangian explicit dynamics method. The applicability of the methods in multiscale problems and their inherent parallelization will be depicted through various applications, along with their advantages over the traditional mesh-based numerical methods. MMs can be considered as mainstream numerical methods able to tackle demanding engineering applications. Intensive and rigorous research in the field will make MMs robust enough to be used by industry.
Original languageEnglish
Title of host publicationNumerical Methods and Advanced Simulation in Biomechanics and Biological Processes
EditorsMiguel Cerrolaza, Sandra J. Shefelbine, Diego Garzon-Alvarado
PublisherAcademic Press
Chapter18
Pages325
Number of pages339
ISBN (Electronic)978-0-12-811718-7
Publication statusPublished - 6 Oct 2017

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biomechanics
numerical method
method
finite volume method
astrophysics
finite difference method
finite element method
interpolation
connectivity
engineering

Cite this

Bourantas, G., Joldes, G., Wittek, A., & Miller, K. (2017). Strong and weak form meshless methods in computational biomechanics. In M. Cerrolaza, S. J. Shefelbine, & D. Garzon-Alvarado (Eds.), Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes (pp. 325). Academic Press.
Bourantas, Georgios ; Joldes, Grand ; Wittek, Adam ; Miller, Karol. / Strong and weak form meshless methods in computational biomechanics. Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes. editor / Miguel Cerrolaza ; Sandra J. Shefelbine ; Diego Garzon-Alvarado. Academic Press, 2017. pp. 325
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Bourantas, G, Joldes, G, Wittek, A & Miller, K 2017, Strong and weak form meshless methods in computational biomechanics. in M Cerrolaza, SJ Shefelbine & D Garzon-Alvarado (eds), Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes. Academic Press, pp. 325.

Strong and weak form meshless methods in computational biomechanics. / Bourantas, Georgios; Joldes, Grand; Wittek, Adam; Miller, Karol.

Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes. ed. / Miguel Cerrolaza; Sandra J. Shefelbine; Diego Garzon-Alvarado. Academic Press, 2017. p. 325.

Research output: Chapter in Book/Conference paperChapter

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Bourantas G, Joldes G, Wittek A, Miller K. Strong and weak form meshless methods in computational biomechanics. In Cerrolaza M, Shefelbine SJ, Garzon-Alvarado D, editors, Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes. Academic Press. 2017. p. 325