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A correlation study of methods of matrix structural analysis by Richard H Gallagher; Rattinger Ivan.; John S Archer; North

By Richard H Gallagher; Rattinger Ivan.; John S Archer; North Atlantic Treaty Organization. Advisory Group for Aeronautical Research and Development. Structures and Materials Panel

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Extra info for A correlation study of methods of matrix structural analysis : report to the 14th Meeting, Paris, France, July 6, 1962

Sample text

E. vertical shear deformation would be disregarded. Analyses of the subject wing models have been performed in this manner and reported in Ref. 7 ; vertical shear deflection effects were approximated. *3) In general, these formulations are not those of an equivalent plate idealization but do approach the latter under special circumstances. Subsequent sections provide detailed descriptions of the theoretical bases for the above idealizations and their application to the analysis of the four model wings, as well as factors pertinent to their choice for comparison purposes.

This definition is applicable to all subsequent developments of this chapter. Substitution of Eqs. (20) and (32) into Eq. (28a) yields: hi = SA\A\> [Β-ψ [D\r [E] [D] [B]-i {Δ }« tàA (28b) or, since the matrix [B] contains only constants : hi = \Α\ΐ[Β-ψ [ U [DY [E] [D] tàA] [B] -i {Δ}« (28c) The significance of the row matrix [Δ\1 is that it contains a one in the location corresponding to the displacement j and zeros elsewhere. (See discussion of Eq. ) The column matrix {Δ }* is similarly defined.

The stress pattern must be consistent with the state of displacement but need not satisfy equilibrium requirements. ) The disregard of equilibrium requirements does not imply, however, that assumptions in accord with equilibrium requirements are not amenable to treatment with the subject technique. Use of the assumptions of Eqs. (19) (representing an equilibrium condition) in connection with the unit displacement formulation Eq. (28a), will yield a completely satisfactory element stiff ess matrix, albeit of different value from that obtained previously.

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