ISOGEOMETRIC ANALYSIS OF SPACE RODS: CONSIDERATIONS ON STRESS LOCKING

Massimo Cuomo (1) , Leopoldo Greco (1)

1 Dipartimento di Ingegneria Civile ed Ambientale

The paper deals with the isogeometric analysis via B-splines of space rods under Kirchhoff-Love hypotheses. The approach has been used for developing space curve element within the framework of the Timoshenko rod model by many authors. In this work we develop a multi-patch isogeometric approach for the numeric analysis of the 3D Kirchhoff-Love rod theory. We use Bezier and B-splines interpolations and we show that they are able to attain very good accuracy for rod structures, particularly for developing a 3D exact curve element with geometric torsion. The patches in general present a Cn-continuity in the interior and are joined with C0-continuity, so that the global tangent stiffness operator in general is singular. In order to avoid the singularity in the stiffness operator several continuity conditions at the joints of the patches are required. Either parametric continuity (C2 or C3) or geometric continuity (G1 or G2) conditions can be imposed. The geometric continuity conditions are weaker than the parametric conditions. The continuity conditions in the CAD -literature are known as the beta-constraints and represent constraint conditions for the displacements of the control points where the scalar beta-quantity represents additional unknowns. In this work, we don't impose the continuity conditions via beta-constraints but directly by means of the Lagrange's multipliers method.

Domaines: Mécanique [physics.med-ph]

Massimo Cuomo, Leopoldo Greco. ISOGEOMETRIC ANALYSIS OF SPACE RODS: CONSIDERATIONS ON STRESS LOCKING. 2012. ⟨hal-00877888⟩