Publication detail

New Formula for Geometric Stiffness Matrix Calculation

NĚMEC, I. TRCALA, M. ŠEVČÍK, I. ŠTEKBAUER, H.

Original Title

New Formula for Geometric Stiffness Matrix Calculation

Type

journal article - other

Language

English

Original Abstract

The standard formula for geometric stiffness matrix calculation, which is convenient for most engineering applications, is seen to be unsatisfactory for large strains because of poor accuracy, low convergence rate, and stability. For very large compressions, the tangent stiffness in the direction of the compression can even become negative, which can be regarded as physical nonsense. So in many cases rubber materials exposed to great compression cannot be analyzed, or the analysis could lead to very poor convergence. Problems with the standard geometric stiffness matrix can even occur with a small strain in the case of plastic yielding, which eventuates even greater practical problems. The authors demonstrate that amore precisional approach would not lead to such strange and theoretically unjustified results. An improved formula that would eliminate the disadvantages mentioned above and leads to higher convergence rate and more robust computations is suggested in this paper. The new formula can be derived from the principle of virtual work using a modified Green-Lagrange strain tensor, or from equilibrium conditions where in the choice of a specific strain measure is not needed for the geometric stiffness derivation (which can also be used for derivation of geometric stiffness of a rigid truss member). The new formula has been verified in practice with many calculations and implemented in the RFEM and SCIA Engineer programs. The advantages of the new formula in comparison with the standard formula are shown using several examples.

Keywords

Geometric Stiffness, Stress Stiffness, Initial Stress Stiffness, Tangent Stiffness Matrix, Finite Element Method, Principle of Virtual Work, Strain Measure

Authors

NĚMEC, I.; TRCALA, M.; ŠEVČÍK, I.; ŠTEKBAUER, H.

Released

27. 4. 2016

Publisher

Scientific Research Publishing

ISBN

2327-4379

Periodical

Journal of Applied Mathematics and Physics

Year of study

2016

Number

4

State

United States of America

Pages from

733

Pages to

748

Pages count

16

URL

http://file.scirp.org/Html/7-1720559_65967.htm

Full text in the Digital Library

http://hdl.handle.net/11012/70141

BibTex

@article{BUT133151,
  author="Ivan {Němec} and Miroslav {Trcala} and Ivan {Ševčík} and Hynek {Štekbauer}",
  title="New Formula for Geometric Stiffness  Matrix Calculation",
  journal="Journal of Applied Mathematics and Physics",
  year="2016",
  volume="2016",
  number="4",
  pages="733--748",
  doi="10.4236//jamp.2016.44084",
  issn="2327-4379",
  url="http://file.scirp.org/Html/7-1720559_65967.htm"
}