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Nonelement boundary representation with Bézier surface patches for 3D linear elasticity problems in parametric integral equation system (PIES) and its solving using Lagrange polynomials
Author(s) -
Zieniuk Eugeniusz,
Szerszeń Krzysztof
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22175
Subject(s) - mathematics , parametric surface , parametric statistics , mathematical analysis , boundary value problem , bézier curve , boundary (topology) , singular boundary method , constraint algorithm , representation (politics) , elasticity (physics) , bézier surface , lagrange multiplier , geometry , boundary element method , mathematical optimization , finite element method , statistics , materials science , politics , political science , law , composite material , physics , thermodynamics
In this article, we present a strategy of using rectangular and triangular Bézier surface patches for nonelement representation of 3D boundary geometries for problems of linear elasticity. The boundary generated in this way is directly incorporated in the parametric integral equation system (PIES), which has been developed by the authors. The boundary values on each surface patch are approximated by Lagrange polynomials. Three illustrative examples are presented to confirm the effectiveness of the proposed boundary representation in connection with PIES and to show good accuracy of numerical results.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 34: 51–79, 2018