No 1, Vol. 3, 2001 
 

DISPERSION ANALYSIS AND ELEMENT-FREE GALERKIN
SIMULATIONS OF HIGHER-ORDER STRAIN GRADIENT MODELS

H. Askes¹, A.S.J. Suiker² and L.J. Sluys³

Koiter Institute Delft/Delft University of Technology,
Faculties of Civil Engineering and Geosciences¹³ and of Aerospace Engineering²,
P.O. Box 5048, 2600 CA Delft, The Netherlands
¹h.askes@cintg.tudelft.nl
²a.s.j.suiker@lr.tudelft.nl
³l.j.sluys@citg.tudelft.nl

Abstract

The role of strain gradients in continuum mechanics has been studied. Distinction is made between stabilizing and destabilizing gradients. A combined model is proposed to investigate the interaction of the two effects. Dispersion analysis and numerical simulations are used to compare the various formats of the model in a qualitative and a quantitative manner. It is shown that a destabilizing second-order gradient has a devastating effect on the numerical response, even if a stabilizing second-order gradient is present. For this class of models only the absence of destabilizing terms guarantees convergent numerical responses.

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