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Siedlungswasserwirtschaft
(2015)
Nachfolgende Ausführungen und Berechnungsbeispiele beziehen sich auf Kapitel 19 Siedlungswasserwirtschaft im „Wendehorst: Bautechnische Zahlentafeln 35. Auflage 2015“ (abgekürzt: BZ). Für den Bau von Anlagen der Siedlungswasserwirtschaft sind ebenso die Grundlagen der Hydraulik zu berücksichtigen. Aus diesem Grunde sind auch die entsprechenden Ausführungen zur Hydraulik zu beachten.
In this paper we propose a stochastic programming method to analyse limit and shakedown of structures under uncertainty condition of strength. Based on the duality theory, the shakedown load multiplier formulated by the kinematic theorem is proved actually to be the dual form of the shakedown load multiplier formulated by static theorem. In this investigation a dual chance constrained programming algorithm is developed to calculate simultaneously both the upper and lower bounds of the plastic collapse limit and the shakedown limit. The edge-based smoothed finite element method (ES-FEM) with three-node linear triangular elements is used for structural analysis.
Shakedown analysis of Reissner-Mindlin plates using the edge-based smoothed finite element method
(2014)
This paper concerns the development of a primal-dual algorithm for limit and shakedown analysis of Reissner-Mindlin plates made of von Mises material. At each optimization iteration, the lower bound of the shakedown load multiplier is calculated simultaneously with the upper bound using the duality theory. An edge-based smoothed finite element method (ES-FEM) combined with the discrete shear gap (DSG) technique is used to improve the accuracy of the solutions and to avoid the transverse shear locking behaviour. The method not only possesses all inherent features of convergence and accuracy from ES-FEM, but also ensures that the total number of variables in the optimization problem is kept to a minimum compared with the standard finite element formulation. Numerical examples are presented to demonstrate the effectiveness of the present method.