resumé de séminaire : Kristian Krabbenhoft 2006-11-02 [19,4 ko]

Problems of engineering plasticity are usually solved using methods more or less directly derived from the basic finite element procedure for linear elasticity. From a mathematical point of view these procedures are less than satisfactory. More seriously, however, is that their performance for all but the simplest problems leaves much to be desired in terms of efficiency and robustness. The generally poor performance of conventional algorithms for plasticity problems (elastoplasticity, limit analysis, etc) is significantly worsened for problems involving non-smooth yield criteria (Drucker-Prager, Mohr-Coulomb, etc). Such yield criteria are an integral part of geotechnical engineering analysis and design and the development of robust and efficient algorithms capable of treating these criteria is therefore highly desirable. Recently, a number of advances have been made in the field of mathematical programming which opens for the development of suitable algorithms for the above mentioned yield criteria as well as a number of others that traditionally are considered difficult. I will summarize the background of these algorithms historically, mathematically, and implementation wise and demonstrate their applicability to a wide range of plasticity problems. I will further summarize other recent work by the Newcastle Geotechnical Research Group on computational limit and shakedown analysis. Topics include finite element technology (upper and lower bound elements, discontinuities), adaptive mesh refinement, some novel limit design procedures, and some new analytical solutions for shakedown problems involving cohesive-frictional materials.

1. Hjiaj M, Huang WX, Krabbenhoft K, et al., Formulation of non-standard dissipative behavior of geomaterials (vol 52, pg 147, 2005), JOURNAL OF ENGINEERING MATHEMATICS 2. Lyamin AV, Sloan SW, Krabbenhoft K, et al., Lower bound limit analysis with adaptive remeshing, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 63 (14):1961-1974 AUG 14 2005 3. Hjiaj M, Huang WX, Krabbenhoft K, et al., Formulation of non-standard dissipative behavior of geomaterials, JOURNAL OF ENGINEERING MATHEMATICS 52 (1-3): 147-165 JUL 2005 4. Krabbenhoft K, Lyamin AV, Hjiaj M, et al., A new discontinuous upper bound limit analysis formulation, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 63 (7):1069-1088 JUN 21 2005 5. Krabbenhoft K, Damkilde L, Krabbenhoft S, Ultimate limit state design of sheet pile walls by finite elements and nonlinear programming, COMPUTERS & STRUCTURES 83 (4-5): 383-393 JAN 2005