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Institutional Repository [SANDBOX]
Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/2DDBDFFC-FDDC-4FB9-B4F7-6F1C98D55A8C | ||
| Year | 1994 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
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| Bibliographic Citation | G.E Stavroulakis, P.D Panagiotopoulos, "A new class of multilevel decomposition algorithms for non monotone problems based on the quasidifferentiability concept," Comp.Methods in Applied Mech. and Engin. vol. 117, no. 3–4,, pp. 289–307. Aug.1994.doi: 10.1016/0045-7825(94)90119-8 https://doi.org/10.1016/0045-7825(94)90119-8 | ||
| Appears in Collections |
A convex, multilevel decomposition approach is proposed for the solution of static analysis problems involving non-monotone, possibly multivalued laws. The theory is developed here for model problems of structures having non-monotone interface or boundary conditions. First we decompose appropriately the non-monotone laws writing them as a difference of monotone constituents. In the general case, this is related to the quasidifferentiability concept. This permits us to obtain a system of convex variational inequalities, the solution s) of which describe the position s) of static equilibrium of the considered structure. Then the problems are formulated as min-min problems for appropriately defined Lagrangian functions. Convex optimization algorithms of various complexity are used in a multilevel scheme for the numerical solution of the considered structural analysis problem. Numerical results concerning the calculation of an elastic contact problem and an elastic stamp problem illustrate the theory.
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