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Boundary Element Analysis of Gradient Elastic Problems

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Recent Advances in Boundary Element Methods

Abstract

A boundary element method (BEM), suitable for solving two dimensional (2D) and three dimensional (3D) gradient elastic problems under static loading, is presented. The simplified Form-II gradient elastic theory (a simple version of Mindlin’s Form II general gradient elastic theory) is employed and the corresponding fundamental solution is exploited for the formulation of the integral representation of the problem. Three noded quadratic line and eight noded quadratic quadrilateral boundary elements are utilized and the discretization is restricted only to the boundary. The boundary element methodology is explained and presented. The importance of satisfying the correct boundary conditions, being compatible with Mindlin’s theory is demonstrated with a simple example. Three numerical examples are reported to illustrate the method and exhibit its merits.

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Author information

Authors and Affiliations

  1. Department of Mechanical and Aeronautical Engineering, University of Patras, GR-26500 Patras, Greece

    G.F. Karlis

  2. Department of Mechanical Engineering, Technological and Educational Institute of Patras, GR-26334 Patras, Greece

    S.V. Tsinopoulos

  3. Department of Mechanical and Aeronautical Engineering, University of Patras, GR-26500 Patras, Greece

    D. Polyzos

  4. Institute of Chemical Engineering and High Temperature Chemical Process, GR-26504 Patras, Greece

    D. Polyzos

Authors
  1. G.F. Karlis
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  2. S.V. Tsinopoulos
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  3. D. Polyzos
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Correspondence to D. Polyzos .

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Editors and Affiliations

  1. Department of Civil Engineering, Aristotle University, 54124 Thessaloniki, Greece

    George D. Manolis (Professor) (Professor)

  2. Department of Mechanical Engineering and Institute of Chemical Engineering&High Temperature Processes, University of Patras, 265 00 Patras, Greece

    D. Polyzos

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Karlis, G., Tsinopoulos, S., Polyzos, D. (2009). Boundary Element Analysis of Gradient Elastic Problems. In: Manolis, G.D., Polyzos, D. (eds) Recent Advances in Boundary Element Methods. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9710-2_16

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  • DOI: https://doi.org/10.1007/978-1-4020-9710-2_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-9709-6

  • Online ISBN: 978-1-4020-9710-2

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