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2 Brigadnov I. A.

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Duality method in limit analysis problem of non-linear elasticity

Brigadnov I. A.

Computer Assisted Mechanics and Engineering Sciences

2003

Vol. 10, No. 4

385-387

The limit analysis problem (LAP) for estimation of mechanical durability for non-linear elastic solids is examined. The appropriate dual problem is formulated. After the standard piecewise linear continuous finite-element approximation, the dual LAP is transformed into the problem of mathematical programming with linear limitations as equalities. This finite dimensional problem is solved by the standard method of gradient projection.

Numerical analysis of dielectrics in powerful electrical fields

Brigadnov I. A.

Computer Assisted Mechanics and Engineering Sciences

2001

Vol. 8, No. 2-3

227-234

The limiting analysis problem for dielectrics in nonhomogeneous powerful electrical fields is considered. In the framework of this problem the external charges for which the appropriate electrostatical variational problem has no solution are calculated, that solution is treated as a beginning of the electrical puncture of dielectric. From the mathematical point of view the limiting analysis problem is non-correct and needs a relaxation. This is achieved using a partial relaxation based on a special discontinuous finite-element approximation.