Details
| Original language | English |
|---|---|
| Pages (from-to) | 2371-2404 |
| Number of pages | 34 |
| Journal | Archive of applied mechanics |
| Volume | 94 |
| Issue number | 9 |
| Early online date | 26 Apr 2024 |
| Publication status | Published - Sept 2024 |
Abstract
We develop low-order triangular virtual elements for linear Kirchhoff–Love shells from an engineering point of view. Flat element geometry is considered, which enables a direct shell discretization with no need for a curvilinear coordinate system or predefined initial mapping. Along with the assumed linearity of the problem, the superposition of the uncoupled membrane and plate energies is performed by unifying aspects of the virtual element method when applied to linear two-dimensional elasticity and plate bending problems. We explore low-order cases, namely linear to quadratic membrane displacements and quadratic to cubic deflection polynomial approximations such that no internal degrees of freedom are needed. For all elements, a single stabilization available in the literature is employed to stabilize the element formulations. Numerical examples of static problems show that the presented formulation is capable of solving complex shell problems. Possible extensions are discussed in future works.
Keywords
- Elasticity, Kirchhoff–Love, Linearity, Shells, Virtual element method
ASJC Scopus subject areas
- Engineering(all)
- Mechanical Engineering
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In: Archive of applied mechanics, Vol. 94, No. 9, 09.2024, p. 2371-2404.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On triangular virtual elements for Kirchhoff–Love shells
AU - Wu, T. P.
AU - Pimenta, P. M.
AU - Wriggers, P.
N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
PY - 2024/9
Y1 - 2024/9
N2 - We develop low-order triangular virtual elements for linear Kirchhoff–Love shells from an engineering point of view. Flat element geometry is considered, which enables a direct shell discretization with no need for a curvilinear coordinate system or predefined initial mapping. Along with the assumed linearity of the problem, the superposition of the uncoupled membrane and plate energies is performed by unifying aspects of the virtual element method when applied to linear two-dimensional elasticity and plate bending problems. We explore low-order cases, namely linear to quadratic membrane displacements and quadratic to cubic deflection polynomial approximations such that no internal degrees of freedom are needed. For all elements, a single stabilization available in the literature is employed to stabilize the element formulations. Numerical examples of static problems show that the presented formulation is capable of solving complex shell problems. Possible extensions are discussed in future works.
AB - We develop low-order triangular virtual elements for linear Kirchhoff–Love shells from an engineering point of view. Flat element geometry is considered, which enables a direct shell discretization with no need for a curvilinear coordinate system or predefined initial mapping. Along with the assumed linearity of the problem, the superposition of the uncoupled membrane and plate energies is performed by unifying aspects of the virtual element method when applied to linear two-dimensional elasticity and plate bending problems. We explore low-order cases, namely linear to quadratic membrane displacements and quadratic to cubic deflection polynomial approximations such that no internal degrees of freedom are needed. For all elements, a single stabilization available in the literature is employed to stabilize the element formulations. Numerical examples of static problems show that the presented formulation is capable of solving complex shell problems. Possible extensions are discussed in future works.
KW - Elasticity
KW - Kirchhoff–Love
KW - Linearity
KW - Shells
KW - Virtual element method
UR - http://www.scopus.com/inward/record.url?scp=85191751734&partnerID=8YFLogxK
U2 - 10.1007/s00419-024-02591-9
DO - 10.1007/s00419-024-02591-9
M3 - Article
AN - SCOPUS:85191751734
VL - 94
SP - 2371
EP - 2404
JO - Archive of applied mechanics
JF - Archive of applied mechanics
SN - 0939-1533
IS - 9
ER -