Abstract
In Ref. 1, we considered theG-closure of some initially given arbitrary setU of the positive-definite, symmetrical plane tensorsD of the 2nd rank, connected with the differential operator ∇ ·D · ∇ in two dimensions. Here, theG-closure procedure is applied to the 4th-order operator ∇∇ ··D ·· ∇∇ in a plane, arising in the theory of plates and containing self-adjoint tensorsD of the 4th rank. The paper generalizes some results obtained earlier in Refs. 2 and 3. The complete solution of the general problem of regularization, which presupposes the arbitrary character of the initially given setU, is not yet obtained.
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References
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Lurie, K.A., Cherkaev, A.V. G-closure of some particular sets of admissible material characteristics for the problem of bending of thin elastic plates. J Optim Theory Appl 42, 305–316 (1984). https://doi.org/10.1007/BF00934301
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DOI: https://doi.org/10.1007/BF00934301