Computation of collapse states with von Mises type yield condition

Christiansen, Edmund; Andersen, Knud D.

doi:10.1002/(sici)1097-0207(19991120)46:8<1185::aid-nme743>3.3.co;2-e

Cited by 30 publications

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“…Several other element combinations are possible (see References [7; 1; 2]), but based on the computational experience in Reference [2] no other combination can be expected to perform signiÿcantly better.…”

Section: Remarksmentioning

confidence: 99%

“…The execution of step 1 above is completely described in Reference [2]. Methods for the solution of the discrete problem in step 2 are still being developed.…”

Section: Remarksmentioning

confidence: 99%

“…The ow rule is deÿned by the optimality conditions on the saddle point. For details we refer to Reference [2]. For completeness we give a brief review of step 1 above in the following section.…”

Section: Remarksmentioning

confidence: 99%

“…The details can be found in Reference [2]. Our computational experiments are in the plane strain model and in order to be explicit we shall restrict the notation to this case.…”

Section: Discretization On a Given Meshmentioning

confidence: 99%

“…It is shown in Reference [2] that (12) and (15) are dual optimization problems and can be solved e ciently by the method described in Reference [8]. …”

Section: Discretization On a Given Meshmentioning

confidence: 99%

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Automatic mesh refinement in limit analysis

Christiansen

Pedersen²

2001

Int. J. Numer. Meth. Engng.

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A strategy for automatic mesh refinement in limit analysis is combined with a recently developed computational method. In the absence of estimates of the local error the strategy can be based on the deformations and on slack in the yield condition. The approach is tested on standard problems in plane strain, including the classical punch problem. Very accurate results are obtained with the use of moderate computational power. This way we obtain new and improved results for classical problems in limit analysis. Copyright © 2001 John Wiley & Sons, Ltd.

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Section: Remarksmentioning

confidence: 99%

“…The execution of step 1 above is completely described in Reference [2]. Methods for the solution of the discrete problem in step 2 are still being developed.…”

Section: Remarksmentioning

confidence: 99%

Section: Remarksmentioning

confidence: 99%

“…The details can be found in Reference [2]. Our computational experiments are in the plane strain model and in order to be explicit we shall restrict the notation to this case.…”

Section: Discretization On a Given Meshmentioning

confidence: 99%

“…It is shown in Reference [2] that (12) and (15) are dual optimization problems and can be solved e ciently by the method described in Reference [8]. …”

Section: Discretization On a Given Meshmentioning

confidence: 99%

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Automatic mesh refinement in limit analysis

Christiansen

Pedersen²

2001

Int. J. Numer. Meth. Engng.

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Failure analysis of engineering structures in undergraduate courses using optimization

Sivaselvan

2011

Comp Applic In Engineering

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In the design process for engineering structures, it is often of interest to determine the largest magnitude of a given form of load that can be applied on a structure before causing failure. This gives the factor of safety against failure. Determining the factor of safety entails analysis of a structure on the verge of failure, and is known as limit analysis. It is well known that limit analysis can be formulated as a constrained optimization problem. With robust computational tools for optimization having become readily available, it is possible to introduce the optimization-based approach to limit analysis at various stages in the undergraduate civil engineering curriculum. In this article, we present three instances of limit analysis using an optimizationbased approach from (i) a sophomore level Statics course, (ii) a junior level Structural Analysis course, and (iii) a senior level Advanced Solid Mechanics course. These are based on materials presented by the author in undergraduate mechanics courses at the University of Colorado at Boulder. In each case, we develop a mathematical formulation and implement the computations in MATLAB. We use two optimization tools, one from the MATLAB Optimization Toolbox and the other called SeDuMi. Classroom experience has shown that the optimization-based approach helps students recognize the underlying thread in seemingly disparate limit analysis problems. ß

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A unified mathematical programming formulation of strain driven and interior point algorithms for shakedown and limit analysis

Garcea

Leonetti

2011

Numerical Meth Engineering

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SUMMARYA mathematical programming formulation of strain-driven path-following strategies to perform shakedown and limit analysis for perfectly elastoplastic materials in an FEM context is presented. From the optimization point of view, standard arc-length strain-driven elastoplastic analyses, recently extended to shakedown, are identified as particular decomposition strategies used to solve a proximal point algorithm applied to the static shakedown theorem that is then solved by means of a convergent sequence of safe states. The mathematical programming approach allows: a direct comparison with other non-linear programming methods, simpler convergence proofs and duality to be exploited. Owing to the unified approach in terms of total stresses, the strain-driven algorithms become more effective and less non-linear with respect to a self-equilibrated stress formulation and easier to implement in the existing codes performing elastoplastic analysis. The elastic domain is represented avoiding any linearization of the yield function so improving both the accuracy and the performance. Better results are obtained using two different finite elements, one with a good behavior in the elastic range and the other suitable for performing elastoplastic analysis. The proposed formulation is compared with a specialized implementation of the primal-dual interior point method suitable to solve the problems at hand.

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Computation of collapse states with von Mises type yield condition

Cited by 30 publications

References 0 publications

Automatic mesh refinement in limit analysis

Automatic mesh refinement in limit analysis

Failure analysis of engineering structures in undergraduate courses using optimization

A unified mathematical programming formulation of strain driven and interior point algorithms for shakedown and limit analysis

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