8th GRACM International Congress on Computational Mechanics Volos, 12 July – 15 July 2015
ENCLOSING ELLIPSOID ESTIMATIONS OF VARIABLE ELASTIC STRESS DOMAINS IN THE SHAKEDOWN ANALYSIS OF OFFSHORE JACKET PLATFORMS Orestis Ioannou, Lazaros Mavridis, Konstantinos D. Nikolaou and Christos D. Bisbos Dep. Civil Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124 Greece e-mails:
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Keywords: shakedown analysis, mathematical programming, offshore platforms, minimum enclosing ellipsoids, wave loading. ABSTRACT Jacket platforms are one of the most commonly used type of offshore oil exploration structures. They constitute of steel space frames with circular hollow section members. Environmental loads contain, among others, current and wave loads. Due to the cyclic nature of the wave loading, shakedown analysis of the jacket platforms is an important tool in the assessment of the safety margins against plastic collapse1. Shakedown analysis is performed using mathematical programming techniques. In classical approach, the load variability is modeled via the so-called variable load polyhedrons, yielding respectively local polyhedral variable elastic stress domains for each stress check point. Usually the apexes of the load polyhedrons are welldefined and their number is very small. Unfortunately, a peculiarity of offshore structures under wave loading is the fact that load apexes cannot be defined. Moreover, the elastic analysis of the platform under a single wave instant is an essentially nonlinear and tedious procedure (Morison equations). This aspect has restricted the straightforward application of standard shakedown techniques in offshore structures to academic examples2. In a previous work by the authors3, shakedown analysis of real world jacket platforms is considered. The elastic stresses at each stress check point are computed directly for several wave instants. These constitute the apexes of a local polyhedral elastic stress domain. Linear plastic Ν-VY-VZ-MT-MY-MZ interaction is assumed and the resulting large-scale linear programming problem is solved by a two-level technique. The present paper follows a different approach. Firstly, the local elastic stresses are computed for several wave instants3. Then, we consider as local variable elastic stress domains, the minimum volume ellipsoids, enclosing the respective polyhedra. The enclosing ellipsoids are computed via a semidefinite programming technique4. This way, the mathematical programming problem corresponding to the shakedown analysis of the platform turns to be a nonlinear optimization problem, even for linear plastic interaction criteria. In the sequel, a bi-level technique5 is applied to solve this nonlinear problem. An example is presented and results are compared with the previously obtained ones3.
1 Hellan
O, Skallerud B, Amdahl J and Moan T, Reassesment of offshore steel structures: Shakedown and cyclic nonlinear FEM analyses, Proc. of the 1st IOPE Conference, Edinburgh, pp. 34 - 43 (1991). 2 Fadaee MJ, Saffari H, Tabatabaei R, Mathematical modelling for shakedown analysis of offshore structures, American. J. of Applied Sciences, vol. 4 (7) pp. 449-455 (2007). 3 Mavridis L, Ioannou O, Nikolaou K and Bisbos C, 3D Shakedown analysis of offshore jacket platforms, CD-ROM proceedings of the 8th National Conference of Steel Structures, Tripoli, Greece (2014). 4 Boyd S and Vandenberghe, Convex optimisation, Cambridge University Press (2009). 5 Bisbos C and Ampatzis A, Shakedown analysis of spatial frames with parametrized load domain, Engineering Structures, 30 (11) pp. 3119-3128 (2008).
