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Integration of an equilibrium system in an enhanced theory of bending of elastic plates. (English) Zbl 1090.74037
Summary: The complete integral of the system of partial differential equations governing the equilibrium bending of elastic plates with transverse shear deformation and transverse normal strain is constructed by means of complex variable method. The process helps to elucidate the physical meaning of certain analytic constraints imposed on the asymptotic behavior of the solutions, and shows that in the case of an infinite plate, any analytic solution has finite energy if and only if the bending and twisting moments, the transverse shear force, the displacements in vertical planes, and two other characteristic quantities vanish at infinity. An example is discussed to illustrate the theory.
MSC:
74K20 Plates
74S30 Other numerical methods in solid mechanics (MSC2010)
30C20 Conformal mappings of special domains
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[1] R. Mitric and C. Constanda, An enhanced theory of bending of plates. In: C. Constanda, M. Ahues and A. Largillier (eds.). Integral Methods in Science and Engineering: Analytic and Numerical Techniques. Birkhäuser, Boston (2002) pp. 191–196. · Zbl 1104.74318
[2] N.I. Muskhelishvili, Some Basic Problems in the Mathematical Theory of Elasticity, 3rd edn. P. Noordhoff, Groningen (1949). · Zbl 0041.22601
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