Variational principles and convergence of finite element approximations of a holonomic elastic-plastic problem. (English) Zbl 0618.73034
It is shown that a boundary-value problem based on a holonomic elastic- plastic constitutive law, due to B. D. Reddy, J. B. Martin and T. B. Griffin [Extremal paths and holonomic constitutive laws in elastoplasticity, Quart Appl. Math. (to appear)], may be formulated equivalently as a variational inequality of the second kind. A regularized form of the problem is analyzed, and finite element approximations are considered. It is shown that solutions based on finite element approximation of the regularized problem converge.
MSC:
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 49J40 | Variational inequalities |
Keywords:
boundary-value problem; holonomic elastic-plastic constitutive law; inequality of the second kind; regularised problemReferences:
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