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  • Electronic Resource  (2)
  • Mathematics Subject Classification (1991):65N30, 65R20, 73C50  (1)
  • Mathematics and Statistics  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Numerical analysis of the primal problem of elastoplasticity with hardening (1999)
    Springer
    Numerische Mathematik 82 (1999), S. 577-597 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N30, 65R20, 73C50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. The finite element method is a reasonable and frequently utilised tool for the spatial discretization within one time-step in an elastoplastic evolution problem. In this paper, we analyse the finite element discretization and prove a priori and a posteriori error estimates for variational inequalities corresponding to the primal formulation of (Hencky) plasticity. The finite element method of lowest order consists in minimising a convex function on a subspace of continuous piecewise linear resp. piecewise constant trial functions. An a priori error estimate is established for the fully-discrete method which shows linear convergence as the mesh-size tends to zero, provided the exact displacement field u is smooth. Near the boundary of the plastic domain, which is unknown a priori, it is most likely that u is non-smooth. In this situation, automatic mesh-refinement strategies are believed to improve the quality of the finite element approximation. We suggest such an adaptive algorithm on the basis of a computable a posteriori error estimate. This estimate is reliable and efficient in the sense that the quotient of the error by the estimate and its inverse are bounded from above. The constants depend on the hardening involved and become larger for decreasing hardening.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050431
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  • 2
    Electronic Resource
    Electronic Resource
    Interface problem in holonomic elastoplasticity (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 819-835 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The three-dimensional interface problem with the homogeneous Lamé system in an unbounded exterior domain and holonomic material behaviour in a bounded interior Lipschitz domain is considered. Existence and uniqueness of solutions of the interface problem are obtained rewriting the exterior problem in terms of boundary integral operators following the symmetric coupling procedure.The numerical approximation of the solutions consists in coupling of the boundary element method (BEM) and the finite element method (FEM). A Céa-like error estimate is presented for the discrete solutions of the numerical procedure proving its convergence.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161105
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    Paper (German National Licenses)
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