The Bending and Stretching of Plates by E. H. Mansfield

By E. H. Mansfield

Written via one of many world's major gurus on plate habit, this research offers a transparent actual perception into elastic plate habit. Small-deflection conception is taken care of partially 1 in chapters facing easy equations: together with thermal results and multi-layered anisotropic plates, oblong plates, round and different formed plates, plates whose obstacles are amenable to conformal transformation, plates with variable thickness, and approximate tools. Large-deflection conception is handled partially 2 in chapters facing uncomplicated equations and precise ideas; approximate equipment, together with post-buckling habit; and asymptotic theories for extraordinarily skinny plates, together with pressure box concept and inextensional idea. The mathematical content material is unavoidably excessive, making the fashion of the publication applicable 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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50 Ζ,(<τ)ω'(1/<χ) where the coefficients u_k9 v_k need not be evaluated. 52 These relations suffice to determine the coefficients an and hence the function φλ(ζ). 4 Square Plate with Rounded Corners As an illustrative example consider the uniformly loaded and clamped plate shown in Fig. ). 53 48 λ = 25' (b) (a) FIG. 54 T = <1

7 FIG. 8 REFERENCES S. D . POISSON, Memoirs of the Academy. 8 (Paris, 1829). S. P. TIMOSHENKO and S. WOINOWSKY-KRIEGER, Theory of Plates and Shells. 2nd ed. Chaps. 3, 9 (MCGRAW-HILL, 1959). Ε. T. WHITTAKER and G . N. WATSON, A Course of Modern Analysis. , 356-378 (Cambridge, 1940). W. FLÜGGE, Bauingenieur. 10, 221 (1929). G . F. CARRIER, The bending of the clamped sectorial plate. / . , 6 6 , A-134 (1944). S. , 4, 254 (1933). ADDITIONAL REFERENCES S. WOINOWSKY-KRIEGER, The bending of a wedge-shaped plate.

22 subject to the boundary conditions ΝΘ,α == Γ ^ Ί =ο . 23) is simply 4 w1 = tf v i qm . \ —sin m* Dt& Z-J mnx . 24 As for the functions Ym9 they are now chosen to satisfy the boundary conditions at y = ±\b together with the equation _4(4 Tr . mnx) V r ms i n — 4 = 0 which, on differentiation and division throughout by ûn{mnxja\ gives « - - i / Ü t f E S + ^ V . - O . 26 The four constants A M , BM9 CM, D M are to be determined from the conditions along y — ± lb. If the boundary conditions there are the same the deflexion will be symmetrical in y, and A M = DM= 0.

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