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Invariant imbedding and the reduction of boundary-value problems of thin-plate theory to Cauchy formulations

Technical Report ·
OSTI ID:6179340
Using ideas of invariant imbedding, a classical elliptic boundary value problem, namely the biharmonic equation in a rectangular domain, is reduced to a Cauchy formation, i.e., to an initial value problem. The theory is developed in the contex of elementary thin plate theory. It is shown that a rectangular plate with three edges clamped and the fourth edge free can be completely described by a system of integro-differential equations subject to initial values. The functions defined by these equations are intimately related to the Green's function of the plate. The Betti reciprocity relations are proved in the context of the present theory and some applications of the fundamental solution are considered. It is finally shown that the present Cauchy system can generate a variety of novel numerical schemes including those previously developed.
Research Organization:
University of Southern California, Los Angeles (USA). Dept. of Electrical Engineering
DOE Contract Number:
AT03-76ER70019
OSTI ID:
6179340
Report Number(s):
DOE/ER/70019-T1; ON: DE81026104
Country of Publication:
United States
Language:
English