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CivilComp Proceedings
ISSN 17593433 CCP: 86
PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 98
Numerical Experiment for Determination of Critical Hole Length P.G. Papadopoulos, P. Lambrou and D. Plasatis
Department of Civil Engineering, Aristotle University of Thessaloniki, Greece P.G. Papadopoulos, P. Lambrou, D. Plasatis, "Numerical Experiment for Determination of Critical Hole Length", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 98, 2007. doi:10.4203/ccp.86.98
Keywords: critical hole length, hole mouth opening displacement, truss model, mesh refinement, global loaddeformation curve, yield concentration.
Summary
The usual finite elements have complicated stiffness matrices and present particular difficulties in handling nonlinear problems [1]. Alternatively, truss models can be used for the analysis of structures [2,3]. A bar of a truss is the finite element with the simplest local stiffness matrix. And a truss has a simple global stiffness matrix.
The bars of a truss model obey nonlinear uniaxial stressstrain laws; so, the whole truss can, in a simple way, describe material nonlinearities. On the other hand, by writing the equilibrium conditions with respect to the deformed truss, we can, in a simple way too, take into account geometric nonlinearities. The proposed truss model can be proved as a simple and useful computational tool in fracture mechanics. A numerical experiment is performed on a typical problem of fracture mechanics, that of a plate with central hole, subject to uniaxial tension [4,5], for five gradually increasing values of the hole length. A local mesh refinement of the truss is simply constructed around and near the hole, in order to study, in more detail, the stress and strain concentrations in this region. It is observed that this local mesh refinement plays a role similar to that of other defects (voids, cracks, stiffer or more flexible inclusions), which cause stress concentrations; thus it slightly reduces the global stiffness and the strength of the plate. The value of the critical hole length of the plate under consideration is detected in three ways:
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