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By Howard G. Allen

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The shear strain γ at F I G . 18. Shear deformation of sandwich beam with stiff core. 44 ANALYSIS OF STRUCTURAL SANDWICH PANELS Ρ is therefore du/dz and the shear stress is du r = G^-. 57) may be combined and integrated to yield an expression for u: " - ^ { ^ ( τ - τ ) } · <"» There is no constant o f integration because u and ζ vanish simultaneously. The displacements AA' and BB' are obtained by writing ζ = ±c/2. BB' * - Μ % Λ + ! 10). _Q lEftd Ecc*\ τ + 6 0) ( ^ - - θ [ ~ 2 ~ ~Ϊ~)· · Suppose now that the real core is replaced by a true antiplane core with a shear modulus G', different from G9 but that the correct value o f D is retained.

47) By successive integration the primary bending deformation is given by EIwi = α 6 sinh ax + 2 ό α cosh ax + B3x + B& + B$—5^-. 47) together provide an expression for w'2 which may be integrated at once : Βι . Β2 , _ —EIfW2 = —5sinh αχ Η — ζ - cosh ax + Ba 6 a a? Wx . ~x r2 - . 49) a 38 ANALYSIS OF STRUCTURAL SANDWICH PANELS Similar equations are applicable to regions AB and CD except that the constants BI—BQ are replaced by other constants Αχ—Αβ and Ci — Ce, respectively, and the terms containing W vanish.

28) EIfW2 = ^ . In the foregoing analysis it was tacitly assumed that during the secondary deformation w2, the points d and a (Fig. 6) remained in the same vertical plane. This is true provided that either the beam is loaded and supported in a symmetrical manner, or some suitable physical restraint is applied to the beam (for example, ( 1 6 2) t A similar equation was obtained by N o r r i s ' by different reasoning. 24c) r = ^ G w 2+ G y 0. 24d) Here γ0 is a constant, which is equal ιο the shear strain when w'2 = 0.

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