Classification and Comparison of LP Formulations for the Plastic Design of Frames

Tam, T.K.H.; Jennings, A.

doi:10.1007/978-94-017-2490-6_10

Cited by 2 publications

(1 citation statement)

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“…The reason that this kinematic program is chosen to be solved is that, for its solution using the simplex method, it is the least demanding in terms of storage and computing time of any of the other linear programs that could be formulated by either using the force or the displacement method of analysis (Munro 1979, Tam andJennings 1989). Once the solution of the above program is obtained for the current iteration, the simplex multipliers of its optimal solution give directly a set of design variables M H p and a set of p r , which are then used for the next iteration.…”

Section: Optimal Shakedown Design Using the Force Methodsmentioning

confidence: 99%

A fully automatic force method for the optimal shakedown design of frames

Spiliopoulos

1999

Computational Mechanics

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The paper presents a fully automatic way to handle the problem of the optimal shakedown design of planar frames. The evaluation of the elastic moments is essential for this design problem and due to the fact that they are design dependent, a classical iterative procedure is followed which updates these moments at the beginning of each iteration. A linear programming problem is then solved inside each iteration. The formulation adopted here is based on the force method which has computational advantages against the displacement method for this type of problems. Within the framework of the force method, the statical basis is provided by an easy to implement algorithm which selects a near minimal mesh basis for any planar graph. This basis is ef®ciently used, in a novel way, to ®nd the¯exibility matrix of the frame in a skyline form amenable to standard algorithms for its decomposition. The quickest way to the ground of each load is used to form the right hand side of the elastic compatibility equations for each load pattern. These equations are ef®-ciently solved by standard back-substitution algorithms and the elastic bending moments to be introduced at the beginning of each iteration is established. Examples of application are also included.

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Section: Optimal Shakedown Design Using the Force Methodsmentioning

confidence: 99%