# Analysis and Design of Structural Sandwich Panels by Howard G. Allen PDF

By Howard G. Allen

ISBN-10: 008012870X

ISBN-13: 9780080128702

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26) H>{" and must be continuous in consequence. However, the only three conditions which provide independent equations are the continuity of w'v w'2 and w". ( x ) w[ continuous at Β 2 Ci öL L C 2 . L aL WL „ T „ B± n —1 cosh — + —1 s i n h — + — - + C 3 L + C 4 = - 0 -2 + JS4. a 2 a 2 16 a (xi) vv2 continuous at Β aL ^ . aL W C i c o s h - y + C 2 sinh — + y = Βλ. ( x i i ) w[' continuous at Β . öZ/ aL I WL _ \ „ Λ C i s i n h — + C 2 c o s h - ^ - + l — - + 2 C 3 U = B2 + 2B3a. A. 31). The total deflection, w, may therefore be expressed as a function of χ in the region AB.

When the faces are thick and the core is weak, however, this simple view is no longer valid and the central region no longer bends in the arc o f a circle. W H- f 2Lo t S k ^ Β ι k lw « (b) F I G . 14. (a) Beam with four-point loading, (b) Right-hand half of the beam. 6, applied to the right-hand half of the beam (Fig. 14b). By symmetry, γο is zero. The shear force Q is equal to + W in BC and zero in AB and BC. 27) for BC is -Qi = Bi cosh ax+B2 sinh ax+ W. 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^-.

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. The foregoing analysis may be repeated except that G is replaced by G' and 2sc vanishes.