Geometric optimization of yield-line patterns using a direct search method

Ramsay, A. C. A.; Johnson, David

doi:10.1007/bf01812512

Cited by 7 publications

(2 citation statements)

References 7 publications

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“…A first possibility is to apply an approach proposed in [18] and is based on the direct search method by [6]. On the assembly of the optimization tableau A geometric constraints had to be set for the vertical displacements of the plate.…”

Section: Direct Search Methodsmentioning

confidence: 99%

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Systematic prediction of yield-line configurations for arbitrary polygonal plates

Wüst¹,

Wagner²

2008

Engineering Structures

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In addition to the well-established finite element method in recent years several optimization approaches have been developed concerning the yield-line theory. This paper presents a new systematical algorithm to predict initial yield-line configurations of arbitrary polygonal plates. It contributes a solution to the task of detecting yield-line patterns in advance of an optimization process. For this reason a ciphering of yield-line patterns is proposed and a new application of Catalan numbers and binary trees is demonstrated. After a subsequent refining a triangular element is used in combination with a simplex optimization procedure in order to determine the ultimate load of the considered yield-line configuration. Moreover, further optimization strategies like the direct search method and the conjugate gradient method lead to the final solution of the problem. The use and the efficiency of the new approach are demonstrated with three examples.

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Section: Direct Search Methodsmentioning

confidence: 99%

“…For this reason an extended application of optimization strategies is obvious. [18] presented an approach starting with a regularly triangulated plate structure out of which the active yield-lines are discovered. The final yield-line pattern is detected by a direct search procedure.…”

Section: Introductionmentioning

confidence: 99%

Systematic prediction of yield-line configurations for arbitrary polygonal plates

Wüst¹,

Wagner²

2008

Engineering Structures

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Ein Algorithmus zur Bestimmung und Optimierung von Fließlinienfiguren für beliebige Polygonplatten

Wüst

Wagner

2008

Bautechnik

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Als Ergänzung zur weit verbreiteten Finite‐Element‐Methode wurden in den vergangenen Jahren verschiedene Optimierungsansätze zur Fließlinientheorie entwickelt. Dieser Artikel stellt einen neuartigen, systematisierten Algorithmus vor, um Ausgangskonfigurationen von Fließliniennetzen für beliebig berandete Polygonplatten zu bestimmen. Dem Anwender bietet sich somit eine Lösung für die Aufgabe, im Vorfeld eines Optimierungsprozesses eine geeignete Fließlinienfigur zu wählen. Zu diesem Zweck wird ein Verfahren zur Codierung von Fließlinienfiguren eingeführt und ein bislang unerkannter Aspekt zur Anwendung der Catalanschen Zahlenreihe im Zusammenhang mit Binärbäumen aufgezeigt. Nach einer weiterführenen Verfeinerung des Netzes kommt ein Dreieckselement in Verbindung mit einem Simplex‐Optimierungsverfahren zum Einsatz, um die Traglast der untersuchten Fließlinienkonfiguration zu bestimmen. Darüber hinaus führen andere Optimierungsstrategien wie die direkte Suchmethode oder die konjugierte Gradientenmethode zur endgültigen Lösung des Problems. Die Verwendung und die Leistungsfähigkeit dieses neuen Ansatzes wird anhand von drei Beispielen aufgezeigt.

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Finite element lower bound “yield line” analysis of isotropic slabs using rotation-free elements

Al‐Sabah

Falter

2013

Engineering Structures

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A new lower bound finite element method for slab analysis is presented as a practical substitute to full, non-linear, finite element methods that require expert knowledge and long running times. The method provides a general, safe and efficient lower bound solution for the analysis of reinforced concrete slabs up to failure. As it is finite element based, the method is more general than the yield line and strip methods currently in use. Furthermore, its lower bound nature makes it safer than the yield line method. The method uses a rotation-free, plate finite element modified to allow plastic "yield lines" to pass through at any direction. Yield lines are generated at the principal moment directions when the plastic moment capacity is attained. The material is assumed to be elastic perfectly-plastic. Following the general spirit of yield line analysis, the effects of a yield line are projected to the sides of the triangular element and then used to calculate the bending curvatures. The method's efficiency is achieved by using rotation-free plate elements with a single degree of freedom per node and by the incremental solution that does not require iterations. The method's accuracy and convergence are assessed by comparing standard cases with known results. In all cases, results were close to the theoretical values with difference of less than 1%. It is also used to solve a practical sized flat slab problem in order to demonstrate the method's efficiency, convergence, and speed.

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Geometric optimization of yield-line patterns using a direct search method

Cited by 7 publications

References 7 publications

Systematic prediction of yield-line configurations for arbitrary polygonal plates

Systematic prediction of yield-line configurations for arbitrary polygonal plates

Ein Algorithmus zur Bestimmung und Optimierung von Fließlinienfiguren für beliebige Polygonplatten

Finite element lower bound “yield line” analysis of isotropic slabs using rotation-free elements

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