An algorithm for shakedown analysis with nonlinear yield functions

Zouain, Néstor; Borges, Lisa; Silveira, José Luı́s

doi:10.1016/s0045-7825(01)00374-7

Cited by 96 publications

(55 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For our analyses we employed unstructured meshes created by GiD [61], using settings h gen and h c to control the element sizes in general and on the circumference of the two holes. The coarsest mesh (see Figure 8 and Table IV ) consisted of 604 elements and gave a limit load of 1.783c, which is 0.56% lower than the refined value of Zouain et al [30]. For the second analysis, the value of h gen was reduced substantially (Mesh 2), but the result was almost the same.…”

Section: Block With Asymmetric Holesmentioning

confidence: 87%

See 1 more Smart Citation

Lower bound limit analysis of cohesive‐frictional materials using second‐order cone programming

Makrodimopoulos

Martin

2005

Numerical Meth Engineering

348

163

View full text Add to dashboard Cite

SUMMARYThe formulation of limit analysis by means of the finite element method leads to an optimization problem with a large number of variables and constraints. Here we present a method for obtaining strict lower bound solutions using second-order cone programming (SOCP), for which efficient primaldual interior-point algorithms have recently been developed. Following a review of previous work, we provide a brief introduction to SOCP and describe how lower bound limit analysis can be formulated in this way. Some methods for exploiting the data structure of the problem are also described, including an efficient strategy for detecting and removing linearly dependent constraints at the assembly stage. The benefits of employing SOCP are then illustrated with numerical examples. Through the use of an effective algorithm/software, very large optimization problems with up to 700 000 variables are solved in minutes on a desktop machine. The numerical examples concern plane strain conditions and the Mohr-Coulomb criterion, however we show that SOCP can also be applied to any other problem of lower bound limit analysis involving a yield function with a conic quadratic form (notable examples being the Drucker-Prager criterion in 2D or 3D, and Nielsen's criterion for plates).

show abstract

Section: Block With Asymmetric Holesmentioning

confidence: 87%

“…The plane strain test problem in Figure 7 has been studied by Zouain et al [30], who used mixed six-node triangular elements with continuous quadratic displacements and discontinuous stresses. Within each of their elements the deviatoric stresses varied linearly, but the mean stress was constant.…”

Section: Block With Asymmetric Holesmentioning

confidence: 99%

Lower bound limit analysis of cohesive‐frictional materials using second‐order cone programming

Makrodimopoulos

Martin

2005

Numerical Meth Engineering

348

163

View full text Add to dashboard Cite

show abstract

“…The total strain increment refers to the midside nodes whereas the elastic and plastic strain increments refer to the corner nodes. A rigid-plastic version of this element has been used extensively by Borges, Zouain et al for plastic limit and shakedown analysis [58][59][60][61][62] where it appears to furnish excellent results. Zienkiewicz and Taylor [63] further note its satisfactory performance for linear elasticity and thus, it can be expected to perform well also for elastoplasticity.…”

Section: Numerical Integrationmentioning

confidence: 99%

An interior‐point algorithm for elastoplasticity

Krabbenhøft

Lyamin

Sloan

et al. 2006

Numerical Meth Engineering

121

133

View full text Add to dashboard Cite

SUMMARYThe problem of small-deformation, rate-independent elastoplasticity is treated using convex programming theory and algorithms. A finite-step variational formulation is first derived after which the relevant potential is discretized in space and subsequently viewed as the Lagrangian associated with a convex mathematical program. Next, an algorithm, based on the classical primal-dual interior point method, is developed. Several key modifications to the conventional implementation of this algorithm are made to fully exploit the nature of the common elastoplastic boundary value problem. The resulting method is compared to state-of-the-art elastoplastic procedures for which both similarities and differences are found. Finally, a number of examples are solved, demonstrating the capabilities of the algorithm when applied to standard perfect plasticity, hardening multisurface plasticity, and problems involving softening.

show abstract

“…It remains then only to verify that all yield constraints (35) are fulfilled. If this is the case, the exact solution has been found and if not, the solution is an upper bound.…”

Section: Verification Of Upper Bounds As Exact Solutionsmentioning

confidence: 99%

Bounds to Shakedown Loads for a Class of Deviatoric Plasticity Models

2006

View full text Add to dashboard Cite

The problem of estimating bounds to shakedown loads for problems governed by a class of deviatoric plasticity models including those of Hill, von Mises, and Tresca is addressed. Assuming that an exact elastic solution is available, an upper bound to the elastic shakedown multiplier can be obtained relatively easily using the plastic shakedown theorem. A procedure for computing this upper bound for arbitrary load domains is presented. A number of problems are then examined and it is found that the elastic shakedown factor is given as the minimum of the plastic shakedown factor and the classical limit load factor. Finally, some exact solutions to a number of two dimensional problems are given.

show abstract

An algorithm for shakedown analysis with nonlinear yield functions

Cited by 96 publications

References 15 publications

Lower bound limit analysis of cohesive‐frictional materials using second‐order cone programming

Lower bound limit analysis of cohesive‐frictional materials using second‐order cone programming

An interior‐point algorithm for elastoplasticity

Bounds to Shakedown Loads for a Class of Deviatoric Plasticity Models

Contact Info

Product

Resources

About