By Donald L. Dean (auth.)
ISBN-10: 3211813772
ISBN-13: 9783211813775
ISBN-10: 3709143608
ISBN-13: 9783709143605
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Additional info for Discrete Field Analysis of Structural Systems
Example text
51 LECTURE Vll ANALYSIS OF MIXED DISCRETE-CONTINUOUS STRUCTURES Ribbed Plates. - A flat plate reinforced by a series of parallel beams, sometimes called an orthotropic plate, is a highly efficient load carrying unit and is a good ftrst example of a mixed discrete-continuous structure for analysis by a discrete fteld method (see Fig. 5). Many mixed discrete-continuous structures are multidimensional lattices with multimensional elements and so are intractable by the micro discrete fteld technique.
2Jn+ll; - 1\Q J+JR2Im+k. 2Jn+ll = (- 1 J (133b,c) for all integer values of I and J. ,~.. 'l'i =1 _ .!. 2 8m(21+ 1) i :i 'l'j = 1 _ _!. fln( 2 J + 1 ) 2 j The two compatibility equations required to find Rk£ and (a Ru are -1 R(r s) = w - r -b s ) m ' n ' a ~ R(r,s) = w[ ~ (r + t)' (133d,e) (134a) *( s + t )] (134b) Transformation of the right-hand sides into the appropriate double finite series in accordance with Eqs. 60b and matching coefficients yields: 62 (135a) in which Wk2 and Cu are as given by Eqs.
The system is symmetric with respect to its middle plane and is loaded antisymmetrically; thus, the top and bottom plates have the same out-of-plane deflections. The plates are simply supported and are proportioned so that in-plane displacements are negligible as compared with out-of-plane displacements.
Discrete Field Analysis of Structural Systems by Donald L. Dean (auth.)
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