An efficient assumed strain formulation for avoiding the membrane locking of non polar shells is developed in the context of B-spline interpolation. Assumed membrane strains are introduced locally in each element with a local L2-projection, and then a spline reconstruction algorithm, developed by Thomas et al. in [1], is employed for reconstructing the membrane strain at the global patch level. In this way, a banded stiffness matrix is obtained that strongly reduces the computational cost with respect to the standard ¯B formulation for isogeometric analysis. The main advantages of the proposed method are: the reproduction of regular membrane strain fields, an accurate membrane locking-free solution and an high computational efficiency with respect to standard ¯B formulation. The method can be applied for any polynomial degree of the B-spline interpolation. The effectiveness of the proposed method is demonstrated analyzing some bending and membrane dominated problem, commonly employed as benchmark in the shell literature.

A reconstructed local Bbar formulation for isogeometric Kirchhoff–Love shells

greco leopoldo
;
cuomo massimo;contrafatto loredana
2018-01-01

Abstract

An efficient assumed strain formulation for avoiding the membrane locking of non polar shells is developed in the context of B-spline interpolation. Assumed membrane strains are introduced locally in each element with a local L2-projection, and then a spline reconstruction algorithm, developed by Thomas et al. in [1], is employed for reconstructing the membrane strain at the global patch level. In this way, a banded stiffness matrix is obtained that strongly reduces the computational cost with respect to the standard ¯B formulation for isogeometric analysis. The main advantages of the proposed method are: the reproduction of regular membrane strain fields, an accurate membrane locking-free solution and an high computational efficiency with respect to standard ¯B formulation. The method can be applied for any polynomial degree of the B-spline interpolation. The effectiveness of the proposed method is demonstrated analyzing some bending and membrane dominated problem, commonly employed as benchmark in the shell literature.
2018
Kirchhoff-Love shells, B-spline interpolation, assumed strain method, spline reconstruction, membrane locking
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/316164
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