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

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13a). First, from Eq. (43), where the element is supported: {FE} = [fV1 {as} (43a) Hence, [ / ] - 1 = [ICEE]· The relationships for [kss] are next obtained by writing equations for the static equilibrium of the supported element. The conditions of static equilibrium provide a set of equations which can be written as follows : {Fs} = [R] {FE} (54) and by substitution of Eq. (43a) into Eq. ) Finally, from equilibrium: [fes] = [ Ä ] [ / ] - i [ Ä ] r With the foregoing definitions of the component stiffnesses in terms of the flexibility coefficients, Eq.

12). 0. Identical to Model 1 except that all spanwise dimensions were halved. This halving of spanwise dimensions provides a measure of aspect ratio effects without the introduction of complicating effects such as sweep. Model 5 (Fig. 13). A 30 degrees swept planform obtained by sweeping the spars of Model 1 through 30 degrees. Past experience has indicated that among the seven original models this wing provides the severest test with respect to the prediction of sweep behavior. Since fabricational details have been described elsewhere*5» 6* 7> they will merely be outlined here.

24a) for {a} ; (8U [ da = [ ^ [DY [E] [D] «Li] [B] -i {Δ} (41a) Hence, with Eqs. (40) and (41a), Eq. (34b) becomes: {F} = [B-^Y [^ [Dy [E] [D] idj] [£]-i {A} (34c) iW [E] [D] tdA~\ [B]-i (33) that is, [k] = [^Yl^ which is the same result obtained in the preceding section. 29 M E T H O D S OF MATRIX S T R U C T U R A L ANALYSIS Reference 22 has shown that an alternative relationship for deriving an element stiffness coefficient is : d2U *« = *n* w When formalized as a sequence of operations leading to the complete stiffness matrix, Eq.

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