Computer analysis of elastic-plastic structures

Franchi, Alberto; Cohn, M. Z.

doi:10.1016/0045-7825(80)90098-5

Cited by 41 publications

(12 citation statements)

References 3 publications

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“…The structure is then kinematically indeterminate. Our computational scheme for dealing with these events is the same as described, for instance, by Franchi and Cohn [9] and Maier et al [26]. It is also important to note that such a nonholonomic-based implementation of holonomy is computationally attractive, in view of the significant reduction in variables (and hence of MCP problem size) as compared with a traditional holonomic analysis formulated using all variables.…”

Section: Algorithm For Exact Nonholonomic Analysismentioning

confidence: 97%

“…(d) At variance with most existing schemes (see e.g. [9,13]) that construct at each step a new diagonal (active) matrix H, we employ a nonsymmetric (holonomic and constant) matrix H. In particular, we extend the single stress model of Tin-Loi and Xia [21] to the case of combined stresses. Of course, the active set strategy implies that only active submatrices of H are used to update A aa , A ab , A bb , and A ba .…”

Section: Algorithm For Exact Nonholonomic Analysismentioning

confidence: 99%

“…Various procedures proposed by Franchi and Cohn [9] for perfect plasticity elastoplastic analysis and later extended to softening structures by Bolzon et al [13] are employed. In addition, we have developed and incorporated several new techniques for the present purpose.…”

Section: Algorithm For Exact Nonholonomic Analysismentioning

confidence: 99%

“…The various computational treatments for classical stable plasticity (perfect or hardening plasticity) are well established (see e.g. [8][9][10][11]). A recurring mathematical structure in all these approaches is that of complementarity.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A complementarity approach for elastoplastic analysis of strain softening frames under combined bending and axial force

Tangaramvong¹,

Tin‐Loi²

2007

Engineering Structures

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Section: Algorithm For Exact Nonholonomic Analysismentioning

confidence: 97%

Section: Algorithm For Exact Nonholonomic Analysismentioning

confidence: 99%

Section: Algorithm For Exact Nonholonomic Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A complementarity approach for elastoplastic analysis of strain softening frames under combined bending and axial force

Tangaramvong¹,

Tin‐Loi²

2007

Engineering Structures

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“…In an attempt to provide general purpose computer programs Franchi and Cohn [7] produced a rather involved PLCP based algorithm and applied it to a single storey plane frame. Kaneko [8] used the same formulation but worked directly on incremental quantities and was able to assess nonholonomic plasticity without having to make any computational adjustments (as in [5,6]).…”

Section: Introductionmentioning

confidence: 99%

An efficient mathematical programming method for the elastoplastic analysis of frames

Spiliopoulos

Patsios

2010

Engineering Structures

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Multilevel Formulations in the Limit Analysis and Design of Structures With Bilateral Contact Constraints

Muralidhar

Rao

Badhrinath

et al. 1996

Int. J. Numer. Meth. Engng.

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SUMMARYIn this paper, we study the rich class of formulations that arise in the limit analysis and design of elastic/plastic structures in the presence of contact constraints. It is well-known that in the absence of contacts, both the limit analysis and limit design problems can be written as linear programs. However, when contact constraints are present, the structure effectively exhibits both softening and stiffening behaviour under monotonically increasing loading. The resulting limit analysis and limit design problems are non-convex and are difficult to solve due to the presence of complementary type of equality constraints. We show that by using a mixed form of the minimum principle, we can restate the limit analysis and h i t design problems as two-and three-level formulations, respectively. Further, under a strong assumption on the problem and solution data, we can take advantage of the underlying convexity to reduce both these multilevel formulations to equivalent linear programs. While it may not be possible to always verify this assumption in practice, we show that a two-step iterative procedure is effective in reaching a solution to the limit design problem.

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Computer analysis of elastic-plastic structures

Cited by 41 publications

References 3 publications

A complementarity approach for elastoplastic analysis of strain softening frames under combined bending and axial force

A complementarity approach for elastoplastic analysis of strain softening frames under combined bending and axial force

An efficient mathematical programming method for the elastoplastic analysis of frames

Multilevel Formulations in the Limit Analysis and Design of Structures With Bilateral Contact Constraints

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