Possibilities and drawbacks using arbitrary precision numbers for structural analysis

PAMM, vol. 20

Abstract

Abstract In various areas of computational mechanics, rounding errors can have a considerable influence on the quality of the simulation results; in some cases, these lead to the termination of the numerical calculation. Rounding errors are caused by limited accuracy in the representation of floating point numbers. Current codes usually use double precision numbers (p = 16 significant digits). Until now, modern multi‐precision libraries with which floating‐point numbers can be processed with arbitrary accuracy are largely unused. The aim of this article is to show the possibilities and limitations of such libraries in the context of computational mechanics. The accuracy of computations from p = 8 up to p = 128 will be investigated. Examples will be selected which are particularly sensitive to rounding errors. On the basis of a first academic example it is examined which calculation accuracy is necessary to carry out a static analysis on a cantilever beam with a slenderness of up to 1049 with a standard beam FE formulation. In a second example, a load‐bearing structure is analyzed in which the stiffness of its supporting members differs by several powers. Finally, the disadvantages associated with the higher calculation accuracy (CPU time, memory requirements) are discussed.

Authors 2

1. Simon Klarmann corresponding Aachen Chair of Structural Analysis and Dynamics

   RWTH Aachen University

   Affiliation as printed

   Chair of Structural Analysis and Dynamics RWTH Aachen University Germany

   Chair of Structural Analysis and Dynamics, RWTH Aachen University, Germany

   Simon Klarmann

   Telephone: +49 241 80 25085

2. Jens Wackerfuß

   University of Kassel

   Affiliation as printed

   Institute of Structural Analysis University of Kassel Germany

   Institute of Structural Analysis, University of Kassel, Germany