By E. H. Mansfield
Written by means of one of many world's best gurus on plate habit, this examine offers a transparent actual perception into elastic plate habit. Small-deflection idea is handled partly 1 in chapters facing simple equations: together with thermal results and multi-layered anisotropic plates, oblong plates, round and different formed plates, plates whose barriers are amenable to conformal transformation, plates with variable thickness, and approximate tools. Large-deflection concept is taken care of partially 2 in chapters facing uncomplicated equations and targeted suggestions; approximate tools, together with post-buckling habit; and asymptotic theories for extraordinarily skinny plates, together with rigidity box idea and inextensional concept. The mathematical content material is inevitably excessive, making the fashion of the e-book acceptable to engineers and utilized mathematicians. E.H. Mansfield is a Fellow of the Royal Society, a founder member of the Fellowship of Engineering, and the writer of over a hundred courses.
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Additional resources for The Bending and Stretching of Plates, 2nd edition
Example text
Reissner and Stavsky (1961) and Stavsky (1961). We note first that the concept of a neutral surface has, in general, no part to play in the analysis of multi-layered plates because of coupling between moments and planar strains. 1 Coupled stress-strain and moment-curvature relations Consider an element of a multi-layered plate bounded by surfaces at z= ±%t and subjected to constant moments and middle-surface forces. 90) where the Etj vary from layer to layer so that E is a function of z. The stresses a may be integrated through the thickness of the plate to yield the following resultant middle-surface forces N and moments M per unit length, where and -r.
Mnx . 1) D where qmn are constants and m, n are integers. Such a series can, of course, represent any distribution of applied loading. In using a Fourier series representation for the deflexion, care must be exercised to ensure that no unjustifiable differentiations of the series are carried out. This difficulty was overcome by Hopkins (1945) by representing d8w/dx4'dy4 as a double Fourier series, d8w " (mn\ 3(nn\3 « L£M ) 3 ) . mnx . sinsm nny ^ 3 in which the factor (mn/a) (nn/b) is introduced merely for convenience.
No. 2234. O. (June 1945). Levy, M. Compt. , 129, pp. 535-9 (1899). Morley, L. S. D. Simple series solution for the bending of a clamped rectangular plate under uniform normal load. Quart. J. Mech. Appl. , 16, pp. 109-14 (1963). Bending of clamped rectilinear plates. Quart. J. Mech. Appl. , 16, pp. 293-317 (1964). Nadai, A. Elastische Flatten. Berlin, 1925. Thompson, J. M. T. General theory of elastic stability. Wiley-Interscience, 1973. Timoshenko, S. Theory of elastic stability. 1st ed. McGraw-Hill, 1936.