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Isogeometric analysis of 3D solids in boundary representation for problems in nonlinear solid mechanics and structural dynamics
Author(s) -
Chasapi Margarita,
Mester Leonie,
Simeon Bernd,
Klinkel Sven
Publication year - 2021
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6893
Subject(s) - isogeometric analysis , nonlinear system , boundary representation , representation (politics) , galerkin method , boundary (topology) , basis function , finite element method , boundary value problem , boundary element method , mathematics , solid mechanics , basis (linear algebra) , mathematical analysis , geometry , structural engineering , physics , engineering , thermodynamics , quantum mechanics , politics , political science , law
This contribution presents an isogeometric approach in three dimensions for nonlinear problems in solid mechanics and structural dynamics. The proposed approach aligns with the boundary representation modeling technique in CAD. Isogeometric analysis is combined with the parameterization of the scaled boundary finite element method. In this way, the boundary description of 3D solids in CAD can be directly utilized for the analysis in an isogeometric framework. The approximation of the solution on the boundary is based on bi‐variate NURBS. We also approximate the interior of the solid with uni‐variate B‐splines to facilitate the solution of nonlinear problems. The nonlinear case is extended to three dimensions in this present work. The method is further extended to dynamic problems. The mass and damping matrices are derived using the same basis functions. The solution of the entire solid is obtained with the Galerkin method. We study several nonlinear and dynamic problems with simple geometries and arbitrary number of boundaries. Moreover, a fiber reinforced composite serves as demonstration for complex shapes.