1,721,013 research outputs found
Numerická ilustrace teoretických výsledků pro nelineární semikoercivní nosníkovou úlohu
No full textThe semi-coercive problem of a beam on a unilateral elastic subsoil of Winkler's type is considered. The aim of this contribution is numerically illustrate some basic results of the problem, which are summarised in the contribution. Concretely, we are interested in dependence of the problem solution on an external load, the error estimates of approximated solutions and the convergence properties of used numerical methods subject to the load
Implicit constitutive solution scheme for Mohr-Coulomb plasticity
No full textThis contribution summarizes an implicit constitutive solution\nscheme of the elastoplastic problem containing the Mohr-Coulomb yield cri-\nterion, a nonassociative \now rule, and a nonlinear isotropic hardening. The\npresented scheme builds upon the subdifferential formulation of the \now rule\nleading to several improvements. Mainly, it is possible to detect a position\nof the unknown stress tensor on the Mohr-Coulomb pyramid without blind\nguesswork. Further, a simplifed construction of the consistent tangent opera-\ntor is introduced. The presented results are important for an efficient solution\nof incremental boundary value elastoplastic problems
Limit analysis problem and its penalization
Full text linkThe contribution is focused on solution of the kinematic limit analysis problem within associative perfect plasticity. It is a constrained minimization problem describing a collapse state of an investigated body. Two different penalization methods are presented and interpreted as the truncation method and the indirect incremental method, respectively. It is shown that both methods are meaningful even within the continuous setting of the problem. Convergence with respect to penalty and discretization parameters is discussed. The indirect incremental method can be simply implemented within current elastoplastic codes
Reliable computation and local mesh adaptivity in limit analysis
No full textThe contribution is devoted to computations of the limit load for a perfectly plastic model with the von Mises yield criterion. The limit factor of a prescribed load is defined by a specific variational problem, the so-called limit analysis problem. This problem is solved in terms of deformation fields by a penalization, the finite element and the semismooth Newton methods. From the numerical solution, we derive a guaranteed upper bound of the limit factor. To achieve more accurate results, a local mesh adaptivity is used
Algoritmy pro semikoercivní úlohu s nosníkem na jednostranně pružném podloží
No full textIn this article, so-called "projected" and "non-projected" algorithms for semi-coercive beam problem with a unilateral elastic subsoil of Winkler's type are presented. These algorithms are based on the minimisation of the energy functional for the considered problem. In each the iteration step of the algorithms, the linear problem with bilateral elastic springs is solved. The convergence properties of the algorithms are summarised and demonstrated on numerical examples
Limit analysis problem and its penalization
Full text linkThe contribution is focused on solution of the kinematic limit analysis problem within associative perfect plasticity. It is a constrained minimization problem describing a collapse state of an investigated body. Two different penalization methods are presented and interpreted as the truncation method and the indirect incremental method, respectively. It is shown that both methods are meaningful even within the continuous setting of the problem. Convergence with respect to penalty and discretization parameters is discussed. The indirect incremental method can be simply implemented within current elastoplastic codes
The application of elastic-plastic models in estimating damage zones caused by blasting of deep tunnels
No full textThe paper deals with the continuous modelling of damage zones caused by excavation of tunnels and boreholes in connection with deep repository of spent nuclear fuel in crystalline rocks. For simplicity, elastic and elastic-plastic modelling approaches based on Mohr-Coulomb or Hoek-Brown failure criteria are presented and compared. For the implementation, proper codes were created in Matlab and Python with innovative elements
Estimation of EDZ zones in great depths by elastic-plastic models
Full text linksummary:This contribution is devoted to modeling damage zones caused by the excavation of tunnels and boreholes (EDZ zones) in connection with the issue of deep storage of spent nuclear fuel in crystalline rocks. In particular, elastic-plastic models with Mohr-Coulomb or Hoek-Brown yield criteria are considered. Selected details of the numerical solution to the corresponding problems are mentioned. Possibilities of elastic and elastic-plastic approaches are illustrated by a numerical example
Bending of Beam with Free Ends on Non-linear Subsoil
No full textA semi-coercive problem with a beam on a unilateral elastic subsoil of Winkler type is investigated in the contribution. Firstly, the existence, the uniqueness and the continuous dependence on data of the problem solution are discussed. Secondly, the problem is approximated by the finite element method, where the subsoil is replaced by insulated "springs" due to a numerical quadrature. The relations between the original problem and the family of approximated problems are introduced. Thirdly, suitable numerical methods of Newton type are introduced. The convergence analysis of the methods is investigated. The dependence of the methods on the discretization parameter and the load is also discussed. And finally, some of the theoretical results are illustrated on numerical examples
Robust algorithms for limit load and shear strength reduction methods
Full text linkThis paper is focused on continuation techniques and Newton-like methods
suggested for numerical determination of safety factors within stability
assessment. Especially, we are interested in the stability of slopes and
related limit load and shear strength reduction methods. We build on
computational plasticity and the finite element method, but we mainly work on
an algebraic level to be the topic understandable for broader class of
scientists and our algorithms more transparent. The presented algorithms are
based on the associated plasticity to be more robust. For non-associated
models, we use Davis-type approximations enabling us to apply the associated
approach. A particular attention is devoted to the Mohr-Coulomb
elastic-perfectly plastic constitutive problem. On this example, we explain
some important features of the presented methods which are beyond the algebraic
settings of the problems. We also summarize the Mohr-Coulomb constitutive
solution and some implementation details
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