# Limit Analysis Problem (limit + analysis_problem)

Distribution by Scientific Domains

## Selected Abstracts

### Solving limit analysis problems: an interior-point method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2005
F. Pastor
Abstract This paper exposes an interior-point method used to solve convex programming problems raised by limit analysis in mechanics. First we explain the main features of this method, describing in particular its typical iteration. Secondly, we show and study the results of its application to a concrete limit analysis problem, for a large range of sizes, and we compare them for validation with existing results and with those of linearized versions of the problem. As one of the objectives of the work, another classical problem is analysed for a Gurson material, to which linearization or conic programming does not apply. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### A general non-linear optimization algorithm for lower bound limit analysis

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003
Kristian Krabbenhoft
Abstract The non-linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound load optimization problem, and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non-linear yield criteria. Copyright © 2002 John Wiley & Sons, Ltd. [source]

### Solving limit analysis problems: an interior-point method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2005
F. Pastor
Abstract This paper exposes an interior-point method used to solve convex programming problems raised by limit analysis in mechanics. First we explain the main features of this method, describing in particular its typical iteration. Secondly, we show and study the results of its application to a concrete limit analysis problem, for a large range of sizes, and we compare them for validation with existing results and with those of linearized versions of the problem. As one of the objectives of the work, another classical problem is analysed for a Gurson material, to which linearization or conic programming does not apply. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### Convergence analysis and validation of sequential limit analysis of plane-strain problems of the von Mises model with non-linear isotropic hardening

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005
S.-Y. Leu
Abstract The paper presents sequential limit analysis of plane-strain problems of the von Mises model with non-linear isotropic hardening by using a general algorithm. The general algorithm is a combined smoothing and successive approximation (CSSA) method. In the paper, emphasis is placed on its convergence analysis and validation applied to sequential limit analysis involving materials with isotropic hardening. By sequential limit analysis, the paper treats deforming problems as a sequence of limit analysis problems stated in the upper bound formulation. Especially, the CSSA algorithm was proved to be unconditionally convergent by utilizing the Cauchy,Schwarz inequality. Finally, rigorous validation was conducted by numerical and analytical studies of a thick-walled cylinder under pressure. It is found that the computed limit loads are rigorous upper bounds and agree very well with the analytical solutions. Copyright © 2005 John Wiley & Sons, Ltd. [source]