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Limit Analysis (limit + analysis)

Distribution by Scientific Domains
Engineering100%

Kinds of Limit Analysis

  • bound limit analysis
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    Terms modified by Limit Analysis

  • limit analysis problem
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    Selected Abstracts

    Lower bound limit analysis with adaptive remeshing

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005
    Andrei V. Lyamin
    Abstract The objective of this work is to present an adaptive remeshing procedure for lower bound limit analysis with application to soil mechanics. Unlike conventional finite element meshes, a lower bound grid incorporates statically admissible stress discontinuities between adjacent elements. These discontinuities permit large stress jumps over an infinitesimal distance and reduce the number of elements needed to predict the collapse load accurately. In general, the role of the discontinuities is crucial as their arrangement and distribution has a dramatic influence on the accuracy of the lower bound solution (Limit Analysis and Soil Plasticity, 1975). To ensure that the discontinuities are positioned in an optimal manner requires an error estimator and mesh adaptation strategy which accounts for the presence of stress singularities in the computed stress field. Recently, Borges et al. (Int. J. Solids Struct. 2001; 38:1707,1720) presented an anisotropic mesh adaptation strategy for a mixed limit analysis formulation which used a directional error estimator. In the present work, this strategy has been tailored to suit a discontinuous lower bound formulation which employs the stresses and body forces as primary unknowns. The adapted mesh has a maximum density of discontinuities in the direction of the maximum rate of change in the stress field. For problems involving strong stress singularities in the boundary conditions (e.g. a strip footing), the automatic generation of discontinuity fans, centred on the singular points, has been implemented. The efficiency of the proposed technique is demonstrated by analysis of two classical soil mechanics problems; namely the bearing capacity of a rigid strip footing and the collapse of a vertical cut. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Limit analysis and convex programming: A decomposition approach of the kinematic mixed method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2009
    Franck Pastor
    Abstract This paper proposes an original decomposition approach to the upper bound method of limit analysis. It is based on a mixed finite element approach and on a convex interior point solver using linear or quadratic discontinuous velocity fields. Presented in plane strain, this method appears to be rapidly convergent, as verified in the Tresca compressed bar problem in the linear velocity case. Then, using discontinuous quadratic velocity fields, the method is applied to the celebrated problem of the stability factor of a Tresca vertical slope: the upper bound is lowered to 3.7776,value to be compared with the best published lower bound 3.772,by succeeding in solving non-linear optimization problems with millions of variables and constraints. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    DEM analysis of bonded granular geomaterials

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 17 2008
    S. Utili
    Abstract In this paper, the application of the distinct element method (DEM) to frictional cohesive (c, ,) geomaterials is described. A new contact bond model based on the Mohr,Coulomb failure criterion has been implemented in PFC2D. According to this model, the bond strength can be clearly divided into two distinct micromechanical contributions: an intergranular friction angle and a cohesive bond force. A parametric analysis, based on several biaxial tests, has been run to validate the proposed model and to calibrate the micromechanical parameters. Simple relationships between the macromechanical strength parameters (c, ,) and the corresponding micromechanical quantities have been obtained so that they can be used to model boundary value problems with the DEM without need of further calibration. As an example application, the evolution of natural cliffs subject to weathering has been studied. Different weathering scenarios have been considered for an initially vertical cliff. Firstly, the case of uniform weathering has been studied. Although unrealistic, this case has been considered in order to validate the DEM approach by comparison against analytical predictions available from limit analysis. Secondly, non-uniform weathering has been studied. The results obtained clearly show that with the DEM it is possible to realistically model boundary value problems of bonded geomaterials, which would be overwhelmingly difficult to do with other numerical techniques. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Bearing capacity of two interfering footings

    INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2008
    Jyant Kumar
    Abstract By using an upper bound limit analysis in conjunction with finite elements and linear programming, the ultimate bearing capacity of two interfering rough strip footings, resting on a cohesionless medium, was computed. Along all the interfaces of the chosen triangular elements, velocity discontinuities were employed. The plastic strains were incorporated using an associated flow rule. For different clear spacing (S) between the two footings, the efficiency factor (,,) was determined, where ,, is defined as the ratio of the failure load for a strip footing of given width in the presence of the other footing to that of a single isolated strip footing having the same width. The value of ,, at S/B = 0 becomes equal to 2.0, and the maximum ,, occurs at S/B = ,Scr/B. For S/B,Scr/B, the ultimate failure load for a footing becomes almost half that of an isolated footing having width (2B + S), and the soil mass below and in between the two footings deforms mainly in the downward direction. In contrast, for S/B>Scr/B, ground heave was noticed along both the sides of the footing. As compared to the available theories, the analysis provides generally lower values of ,, for S/B>Scr/B. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Three-dimensional Mohr,Coulomb limit analysis using semidefinite programming

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2008
    K. Krabbenhøft
    Abstract Recently, Krabbenhøft et al. (Int. J. Solids Struct. 2007; 44:1533,1549) have presented a formulation of the three-dimensional Mohr,Coulomb criterion in terms of positive-definite cones. The capabilities of this formulation when applied to large-scale three-dimensional problems of limit analysis are investigated. Following a brief discussion on a number of theoretical and algorithmic issues, three common, but traditionally difficult, geomechanics problems are solved and the performance of a common primal,dual interior-point algorithm (SeDuMi (Appl. Numer. Math. 1999; 29:301,315)) is documented in detail. Although generally encouraging, the results also reveal several difficulties which support the idea of constructing a conic programming algorithm specifically dedicated to plasticity problems. Copyright © 2007 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]

    Interior point optimization and limit analysis: an application

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2003
    Joseph Pastor
    Abstract The well-known problem of the height limit of a Tresca or von Mises vertical slope of height h, subjected to the action of gravity stems naturally from Limit Analysis theory under the plane strain condition. Although the exact solution to this problem remains unknown, this paper aims to give new precise bounds using both the static and kinematic approaches and an Interior Point optimizer code. The constituent material is a homogeneous isotropic soil of weight per unit volume ,. It obeys the Tresca or von Mises criterion characterized by C cohesion. We show that the loading parameter to be optimized, ,h/C, is found to be between 3.767 and 3.782, and finally, using a recent result of Lyamin and Sloan (Int. J. Numer. Meth. Engng. 2002; 55: 573), between 3.772 and 3.782. The proposed methods, combined with an Interior Point optimization code, prove that linearizing the problem remains efficient, and both rigorous and global: this point is the main objective of the present paper. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Limit analysis and convex programming: A decomposition approach of the kinematic mixed method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2009
    Franck Pastor
    Abstract This paper proposes an original decomposition approach to the upper bound method of limit analysis. It is based on a mixed finite element approach and on a convex interior point solver using linear or quadratic discontinuous velocity fields. Presented in plane strain, this method appears to be rapidly convergent, as verified in the Tresca compressed bar problem in the linear velocity case. Then, using discontinuous quadratic velocity fields, the method is applied to the celebrated problem of the stability factor of a Tresca vertical slope: the upper bound is lowered to 3.7776,value to be compared with the best published lower bound 3.772,by succeeding in solving non-linear optimization problems with millions of variables and constraints. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Upper and lower bounds in limit analysis: Adaptive meshing strategies and discontinuous loading

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009
    J. J. Muñoz
    Abstract Upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimization problems. The membership constraints for Von Mises and Mohr,Coulomb plasticity criteria are written as a set of quadratic constraints, which permits one to solve the optimization problem using specific algorithms for Second-Order Conic Program (SOCP). From the stress field at the lower bound and the velocities at the upper bound, we construct a novel error estimate based on elemental and edge contributions to the bound gap. These contributions are employed in an adaptive remeshing strategy that is able to reproduce fan-type mesh patterns around points with discontinuous surface loading. The solution of this type of problems is analysed in detail, and from this study some additional meshing strategies are also described. We particularise the resulting formulation and strategies to two-dimensional problems in plane strain and we demonstrate the effectiveness of the method with a set of numerical examples extracted from the literature. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Lower-bound limit analysis by using the EFG method and non-linear programming

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2008
    Shenshen Chen
    Abstract Intended to avoid the complicated computations of elasto-plastic incremental analysis, limit analysis is an appealing direct method for determining the load-carrying capacity of structures. On the basis of the static limit analysis theorem, a solution procedure for lower-bound limit analysis is presented firstly, making use of the element-free Galerkin (EFG) method rather than traditional numerical methods such as the finite element method and boundary element method. The numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the domain under consideration. The reduced-basis technique is adopted to solve the mathematical programming iteratively in a sequence of reduced self-equilibrium stress subspaces with very low dimensions. The self-equilibrium stress field is expressed by a linear combination of several self-equilibrium stress basis vectors with parameters to be determined. These self-equilibrium stress basis vectors are generated by performing an equilibrium iteration procedure during elasto-plastic incremental analysis. The Complex method is used to solve these non-linear programming sub-problems and determine the maximal load amplifier. Numerical examples show that it is feasible and effective to solve the problems of limit analysis by using the EFG method and non-linear programming. Copyright © 2007 John Wiley & Sons, Ltd. [source]

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

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2006
    A. Makrodimopoulos
    Abstract The 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 primal-dual 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). 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]

    Lower bound limit analysis with adaptive remeshing

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005
    Andrei V. Lyamin
    Abstract The objective of this work is to present an adaptive remeshing procedure for lower bound limit analysis with application to soil mechanics. Unlike conventional finite element meshes, a lower bound grid incorporates statically admissible stress discontinuities between adjacent elements. These discontinuities permit large stress jumps over an infinitesimal distance and reduce the number of elements needed to predict the collapse load accurately. In general, the role of the discontinuities is crucial as their arrangement and distribution has a dramatic influence on the accuracy of the lower bound solution (Limit Analysis and Soil Plasticity, 1975). To ensure that the discontinuities are positioned in an optimal manner requires an error estimator and mesh adaptation strategy which accounts for the presence of stress singularities in the computed stress field. Recently, Borges et al. (Int. J. Solids Struct. 2001; 38:1707,1720) presented an anisotropic mesh adaptation strategy for a mixed limit analysis formulation which used a directional error estimator. In the present work, this strategy has been tailored to suit a discontinuous lower bound formulation which employs the stresses and body forces as primary unknowns. The adapted mesh has a maximum density of discontinuities in the direction of the maximum rate of change in the stress field. For problems involving strong stress singularities in the boundary conditions (e.g. a strip footing), the automatic generation of discontinuity fans, centred on the singular points, has been implemented. The efficiency of the proposed technique is demonstrated by analysis of two classical soil mechanics problems; namely the bearing capacity of a rigid strip footing and the collapse of a vertical cut. 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]