### Abstract

The linear Reissner–Mindlin shell theory is reformulated in the frame of the tangential differential calculus (TDC)using a global Cartesian coordinate system. The rotation of the normal vector is modelled with a difference vector approach. The resulting equations are applicable to both explicitly and implicitly defined shells, because the employed surface operators do not necessarily rely on a parametrization. Hence, shell analysis on surfaces implied by level-set functions is enabled, but also the classical case of parametrized surfaces is captured. As a consequence, the proposed TDC-based formulation is more general and may also be used in recent finite element approaches such as the TraceFEM and CutFEM where a parametrization of the middle surface is not required. Herein, the numerical results are obtained by isogeometric analysis using NURBS as trial and test functions for classical and new benchmark tests. In the residual errors, optimal higher-order convergence rates are confirmed when the involved physical fields are sufficiently smooth.

Original language | English |
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Pages (from-to) | 172-188 |

Number of pages | 17 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 352 |

DOIs | |

Publication status | Published - 1 Aug 2019 |

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### Keywords

- Isogeometric analysis
- Manifolds
- Shells
- Tangential differential calculus

### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications

### Fields of Expertise

- Information, Communication & Computing

### Cite this

**Reissner–Mindlin shell theory based on tangential differential calculus.** / Schöllhammer, D.; Fries, T. P.

Research output: Contribution to journal › Article › Research › peer-review

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TY - JOUR

T1 - Reissner–Mindlin shell theory based on tangential differential calculus

AU - Schöllhammer, D.

AU - Fries, T. P.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - The linear Reissner–Mindlin shell theory is reformulated in the frame of the tangential differential calculus (TDC)using a global Cartesian coordinate system. The rotation of the normal vector is modelled with a difference vector approach. The resulting equations are applicable to both explicitly and implicitly defined shells, because the employed surface operators do not necessarily rely on a parametrization. Hence, shell analysis on surfaces implied by level-set functions is enabled, but also the classical case of parametrized surfaces is captured. As a consequence, the proposed TDC-based formulation is more general and may also be used in recent finite element approaches such as the TraceFEM and CutFEM where a parametrization of the middle surface is not required. Herein, the numerical results are obtained by isogeometric analysis using NURBS as trial and test functions for classical and new benchmark tests. In the residual errors, optimal higher-order convergence rates are confirmed when the involved physical fields are sufficiently smooth.

AB - The linear Reissner–Mindlin shell theory is reformulated in the frame of the tangential differential calculus (TDC)using a global Cartesian coordinate system. The rotation of the normal vector is modelled with a difference vector approach. The resulting equations are applicable to both explicitly and implicitly defined shells, because the employed surface operators do not necessarily rely on a parametrization. Hence, shell analysis on surfaces implied by level-set functions is enabled, but also the classical case of parametrized surfaces is captured. As a consequence, the proposed TDC-based formulation is more general and may also be used in recent finite element approaches such as the TraceFEM and CutFEM where a parametrization of the middle surface is not required. Herein, the numerical results are obtained by isogeometric analysis using NURBS as trial and test functions for classical and new benchmark tests. In the residual errors, optimal higher-order convergence rates are confirmed when the involved physical fields are sufficiently smooth.

KW - Isogeometric analysis

KW - Manifolds

KW - Shells

KW - Tangential differential calculus

UR - http://www.scopus.com/inward/record.url?scp=85065550924&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2019.04.018

DO - 10.1016/j.cma.2019.04.018

M3 - Article

VL - 352

SP - 172

EP - 188

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

ER -