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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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27). Since the idealization of displacements predominates one would anticipate that this approach will produce a suffer representation than is actually the case. Hence, Eq. (33a) would yield suffer force-displacement relationships than Eq. (27) when the two differ. The direct determination of element flexibility through virtual work concepts can be achieved by application of Eq. (47f), which has the more general form: [8] = [ΜΕ-ψ[νΕ][ΜΕ]-ι (59) The matrix [VE] is the same as [V] in Eq. (33a), except the for absence of rows and columns in the former that correspond to the element supports in the latter.

S] = ν-^τ (4°) Consider now the development of {dU/da}. e. the differentiation of U with respect to ai) when applied to Eq. (39b) result in : S} = [L [ i ) ] T [ £ ] [ i ) ] H { a } (41) and, substituting Eq. (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.

Thus, an additional connection point on the internal members is required. The internal members are assumed to behave as conventional flexural elements, but since the basic 55 M E T H O D S OF M A T R I X S T R U C T U R A L ANALYSIS relationships must account for the additional connection point, they are referred to as "compound" flexural elements. f. Equivalent plate-Grzedzielski approach. The idealization of a multiweb wing as a thin plate in flexure requires no sketch to implement its description.

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