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Nitsche's method for form‐finding of multipatch isogeometric membrane analysis
Author(s) -
Apostolatos Andreas,
Bletzinger KaiUwe,
Wüchner Roland
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800106
Subject(s) - discretization , structural engineering , stiffness , isogeometric analysis , bending , flexural rigidity , ultimate tensile strength , bending moment , computer science , bending stiffness , mathematics , finite element method , materials science , mathematical analysis , engineering , composite material
Membranes constitute an important category of thin‐walled and in particular tensile structures [1], for which in contrast to shells their structural rigidity is obtained by means of prestress rather than relying on bending stiffness. In particular, the structures considered in this study act in pure membrane state and have no bending stiffness. A big challenge of such structures is finding the shape of static equilibrium. This is not a trivial task since not every shape under any prestress distribution or loading condition renders a static equilibrium configuration. This is even more prominent when prestressed cables are attached to the structure. To overcome this problem for general tensile structures, various types of form‐finding methods were developed [2, 3]. In this study, the Updated Reference Strategy (URS) [4, 5] is presented in combination with multipatch isogeometric analysis [6] as discretization method. The enforcement of the continuity constraints along the common patch interfaces [7] is realized using a Nitsche ‐type method [8] while the results are evaluated and compared with the Penalty‐based approach [9].