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Shape Functions

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Meshless Methods in Biomechanics

Part of the book series: Lecture Notes in Computational Vision and Biomechanics ((LNCVB,volume 16))

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Abstract

This chapter explicitly shows how to construct shape functions for meshless methods. The chapter starts with the introduction of the “support-domain” concept which permits to identify the field nodes contributing to the construction of the shape function. Afterwards, the most popular approximation function is presented: the moving least square (MLS) approximation function. The construction procedure is presented in detail as well as the most important numerical properties of the MLS approximation function. Additionally the importance of the weight function used in the construction of the MLS shape function is shown. Then, the radial point interpolation (RPI) functions are presented. Again, an exhaustive description of the RPI shape function construction is presented supported by examples and explicative algorithms. The most important numerical properties of the RPI shape function are demonstrated. In addition, it is shown the relevance of the radial basis function (RBF) used to construct the RPI shape function, as well as the influence of the RBF shape parameters on the final solution.

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Authors and Affiliations

  1. Mechanical Engineering Department, Universidade do Porto, Porto, Portugal

    Jorge Belinha

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  1. Jorge Belinha
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Correspondence to Jorge Belinha .

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Belinha, J. (2014). Shape Functions. In: Meshless Methods in Biomechanics. Lecture Notes in Computational Vision and Biomechanics, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-319-06400-0_4

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  • DOI: https://doi.org/10.1007/978-3-319-06400-0_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06399-7

  • Online ISBN: 978-3-319-06400-0

  • eBook Packages: EngineeringEngineering (R0)

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