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Generalized J-integral method for sensitivity analysis of static shape design

Ohtsuka K., Chludnev A.

Control and Cybernetics

2000

Vol. 29, no 2

513-533

The paper analyses the concept of GJ-integral. This concept is linked with the derivative of the energy functional with respect to a general perturbation of the domain and it is useful in studying many problems of sensitivity analysis. Applications of the GJ-integral method to numerous linear and nonlinear problems are indicated.

On solvability of boundary value problems in elastoplasticity

Chludnev A., Sokołowski J.

Control and Cybernetics

1998

Vol. 27, no 2

311-330

In the paper the existence of a solution to the thress-dimensional elastoplastic problem with the Prandtl-Reuss constitutive law and the Neumann boundary conditions is established. The proof is based on a suitable combination of the parabolic regularization of equations and the penalty method for the elastoplastic yield condition. The method is applied in the case of the domain with smooth boundary as well as in the case of an interior crack. It is shown that the weak solutions to the elastoplastic problem satisfying the variational inequality meet all boundary conditions.