By P. G. Lowe Ph.D., M.I.C.E (auth.)
Adding one other quantity, whether just a slender one, to the technical books already released calls for a few justification. Mine is, first of all, that plate concept isn't good represented within the on hand ordinary texts, and secondly that no present textual content safely covers smooth functions. the current account is meant to be undemanding (though this can be a relative time period) whereas nonetheless supplying stimulation and worthy event for the reader. precise beneficial properties of curiosity will i am hoping be the therapy of geometry of surfaces and the makes an attempt round the finish of the paintings to take a position a bit. The precise remedy of geometry of surfaces has been put in an appendix the place it will possibly comfortably be talked about via the reader. My curiosity in plate concept extends again decades to the full of life and stimulating discussions with my manager, Professor R. W. Tiffen, at Birkbeck collage, London, and a debt to him continues to be. curiosity was once rekindled for me by way of Dr R. E. Melchers whilst I supervised him in Cambridge a few ten years in the past, and extra lately my remain at Strathclyde college and encouragement and stimulation within the Civil Engineering division led me to adopt the current paintings. The typescript was once ready by way of Ms Catherine Drummond and that i thank her warmly for this and different guidance, consistently cheerfully provided. My thank you additionally to the publishers and the referees for priceless reviews and suggestion. P.G.L.
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4). 4 Rectangular plate, mixed edge conditions. ELASTIC PLATES 55 According to the (Levy) procedure described above, the simply supported edge conditions are satisfied by a variation in the y direction of Cos nnyfa. 0) is a suitable form for the displacement when n is odd. 0). 0). It remains to construct the value for ¢n(x) such that the fixed edge conditions should also be satisfied. 1 ) withn odd. 2) where n is odd, and the individual equations for ¢n(x) have been obtained by separately equating to zero the coefficients of the respective terms in Cos (nny/a).
This symmetry corresponds to independence for all the dependent quantities from change of 34 BASIC PRINCIPLES OF PLATE THEORY . 9 dQr Q +-·dr r dr dM rr + dr· dr · , ® Circular plate-element forces. the angular coordinate, e-termed axial symmetry. This feature has been incorporated in the stress resultant array on Fig. 9. Since only variation with respect to r is now possible, so ordinary rather than partial differentials are indicated. Also, this form of symmetry ensures that Qo = O. It is left as an exercise for the reader to construct and demonstrate the correctness of Fig.
13 this curvature is associated with a centre of curvature O 2 which is given by the point where the normal intersects the axis of revolution. Take the surface coordinates to be rand B. By this is meant that the point P is located in plan by the choice at rand B, then P', the point required on STATICS AND KINEMATICS OF PLATE BENDING 37 the deflected surface is vertically below P, a distance w(r), the amount by which the point originally at P deflects to P'. Now, the operation (.. )'r does not affect any of the orthogonal unit vectors I, J, K; however, (.