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ADVANCES IN COMPUTATIONAL METHODS FOR SIMULATION
Edited by: B.H.V. Topping
An Intersection-Parametrization Technique to Analyse 2-D Structures with Interfaces Governed by Complete Nonmonotone Laws
C.D. Bisbos and C.C. Baniotopoulos
Institute of Steel Structures, Aristotle University, Thessaloniki, Greece
C.D. Bisbos, C.C. Baniotopoulos, "An Intersection-Parametrization Technique to Analyse 2-D Structures with Interfaces Governed by Complete Nonmonotone Laws", in B.H.V. Topping, (Editor), "Advances in Computational Methods for Simulation", Civil-Comp Press, Edinburgh, UK, pp 125-131, 1996. doi:10.4203/ccp.42.3.1
The present paper aims to contribute to the research that concerns the analysis of two-dimensional structures containing interfaces whose structural behaviour is governed by complete nonmonotone boundary laws. Typical examples of the latter laws are the interfacial laws described by one-dimensional serrated stress-strain or load-displacement diagrams along the whole length of the horizontal axis exhibiting a macroscopically nonmonotone, softening-rehardening (saw-tooth) behaviour. The effort to incorporate in an alternative new way the previously mentioned interface action into an effective analysis model is herein presented. In particular, by considering the interfacial forces temporarily as external loads, the corresponding interfacial gaps are related to them by means of a linear function which is similar to the compatibility equation of the classical force method of Structural Mechanics; from a mathematical point of view, the latter describes a linear manifold, whereas from a mechanical point of view, it is the constraint implied by the rest of the structure upon the interface. Since the solution of the problem at hand has to obey the material law of the interface, the solution set is the set of all the intersection points between the aforementioned linear manifold and the softening-rehardening interfacial behaviour curve.
To this end, a numerical technique which combines the previous relations to obtain the complete set of solutions of the problem is herein presented. In addition, in the last part of the paper various computational aspects and a normalization technique are proposed and discussed.
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