Second-order cone programming with warm start for elastoplastic analysis with von Mises yield criterion

Yonekura, Kazuo; Kanno, Yoshihiro

doi:10.1007/s11081-011-9144-4

Cited by 39 publications

(37 citation statements)

References 48 publications

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“…We note that in recent work, Krabbenhoft et al [66] solved the primal problem by an interior point method, and Wieners [67] and Bilotta et al [1] by a sequential quadratic programming approach. When c is quadratic (corresponding to linear elastic and linear hardening models) and when the yield function is of the form of a 2-norm (as is the case with the von Mises function), then Equation (2) can be recast as a second order cone program (SOCP) [5]. This can in turn be reformulated as a semi-definite program [68], which can be solved by efficient interior point methods that have been recently developed.…”

Section: Primal Problem Of Incremental State Updatementioning

confidence: 99%

“…In recent years, there has been renewed interest in application of mathematical programming approaches to nonlinear mechanics problems [1][2][3][4][5][6], fueled by advances in optimization algorithms and solvers. These approaches build on generalizations of classical energy theorems [7][8][9][10][11], on the one hand, and upper-bound and lower-bound theorems [12][13][14][15][16][17][18][19] and shakedown theorems [20][21][22] on the other.…”

Section: Introductionmentioning

confidence: 99%

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A projected Newton algorithm for the dual convex program of elastoplasticity

Lotfian

Sivaselvan

2014

Numerical Meth Engineering

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SUMMARYIn this paper, we study a dual optimization problem that arises when taking a mathematical programming approach to incremental state update in nonlinear problems. The mathematical programming approach stems from energy-based descriptions of constitutive models. We describe a projected Newton algorithm to solve the dual optimization problem. This algorithm requires solution of an unconstrained optimization problem at the integration point level, rather than a constrained one as carried out by classical return-mapping schemes. Especially, implementation of multi-surface plasticity models is no more involved than that of single-surface models. We explore characteristics and performance of the projected Newton algorithm through numerical examples. Insights gained from such a further exploration of mathematical programming algorithms are likely to aid in development of successive convex programming approaches to geometric nonlinear and other non-convex problems such as non-associated flow models.

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Section: Primal Problem Of Incremental State Updatementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A projected Newton algorithm for the dual convex program of elastoplasticity

Lotfian

Sivaselvan

2014

Numerical Meth Engineering

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“…See, for example, Alizadeh and Goldfarb [17] and Anjos and Lasserre [18] for fundamentals of SOCP; applications of SOCP in applied mechanics and structural engineering are found in [37][38][39][40]. Note that the constraints in (12b) are called second-order cone constraints.…”

Section: Discrete Damping Coefficientsmentioning

confidence: 99%

“…A continuous optimization problem with a linear objective function and some second-order cone constraints are called an SOCP problem. See, for example, Alizadeh and Goldfarb [17] and Anjos and Lasserre [18] for fundamentals of SOCP; applications of SOCP in applied mechanics and structural engineering are found in [37][38][39][40].…”

Section: Discrete Damping Coefficientsmentioning

confidence: 99%

Damper placement optimization in a shear building model with discrete design variables: a mixed‐integer second‐order cone programming approach

Kanno

2013

Earthq Engng Struct Dyn

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SUMMARY Supplemental damping is known as an efficient and practical means to improve seismic response of building structures. Presented in this paper is a mixed‐integer programming approach to find the optimal placement of supplemental dampers in a given shear building model. The damping coefficients of dampers are treated as discrete design variables. It is shown that a minimization problem of the sum of the transfer function amplitudes of the interstory drifts can be formulated as a mixed‐integer second‐order cone programming problem. The global optimal solution of the optimization problem is then found by using a solver based on a branch‐and‐cut algorithm. Two numerical examples in literature are solved with discrete design variables. In one of these examples, the proposed method finds a better solution than an existing method in literature developed for the continuous optimal damper placement problem. Copyright © 2013 John Wiley & Sons, Ltd.

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“…The main operation is to recast the quadratic terms in the objective function to linear ones, subject to a quadratic constraint, and to reform the yield function as a cone. Owing to the attractive advantages presented in the introduction, a variety of mechanics problems have been formulated and solved in such a manner, including computational limit analysis of solids and plates [39][40][41], static/dynamic analysis of elastoplastic frames and solids [19,[42][43][44], analysis of steady-state non-Newtonian fluid flows [45], consolidation analysis [21] and the analysis of granular contact dynamics [38,46,47]. 973…”

mentioning

confidence: 99%

Lagrangian modelling of large deformation induced by progressive failure of sensitive clays with elastoviscoplasticity

Xue

Sheng

Sloan

et al. 2017

Numerical Meth Engineering

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International audienceThis paper presents a Lagrangian formulation of elastoviscoplasticity, based on the Particle Finite Element Method, for progressive failure analysis of sensitive clays. The sensitive clay is represented by an elastoviscoplastic model which is a mixture of the Bingham model, for describing rheological behaviour, and the Tresca model with strain softening for capturing the progressive failure behaviour. The finite element formulation for the incremental elastoviscoplastic analysis is reformulated, through the application of the Hellinger-Reissner variational theorem, as an equivalent optimization program that can be solved efficiently using modern algorithms such as the interior-point method. The recast formulation is then incorporated into the framework of the Particle Finite Element Method for investigating progressive failure problems related to sensitive clays, such as the collapse of a sensitive clay column and the retrogressive failure of a slope in sensitive clays, where extremely large deformation occurs

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Second-order cone programming with warm start for elastoplastic analysis with von Mises yield criterion

Cited by 39 publications

References 48 publications

A projected Newton algorithm for the dual convex program of elastoplasticity

A projected Newton algorithm for the dual convex program of elastoplasticity

Damper placement optimization in a shear building model with discrete design variables: a mixed‐integer second‐order cone programming approach

Lagrangian modelling of large deformation induced by progressive failure of sensitive clays with elastoviscoplasticity

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