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Aircraft Stability and Control - download pdf or read online

By A. W. Babister

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3. 4. PSEUDOTHERMAL INPUTS 4–12 EXERCISES . . . . . . . . . . . 1 PRESCRIBED NONZERO DISPLACEMENTS Chapters 2 and 3 presented the “core” steps of the Direct Stiffness Method (DSM). These steps were illustrated with the hand analysis of a plane truss structure. This Chapter covers some additional topics that were left out from Chapters 2–3 for clarity. These include: the imposition of prescribed nonzero displacements, and the treatment of thermal effects.

1. 7). 4(a) we get  f (1)   x1 1 (1)  f y1   0    f (1)  = 10  −1 x2 (1) 0 f y2 0 0 0 0    u (1) x1 0  u (1) 0 y1  . 8)    u (2) x2 0  u (2) −1   y2  . 5   y1  . 3. Assembly Rules The key operation of the assembly process is the “placement” of the contribution of each member to the master stiffness equations. The process is technically called merging of individual members. The merge operation can be physically interpreted as reconnecting that member in the process of fabricating the complete structure.

16) Chapter 3: THE DIRECT STIFFNESS METHOD: ASSEMBLY AND SOLUTION          (3)  f x1  10 (3)  f y1   10 (3)   f x2   0 =   (3)   0 f y2   (3)  −10 f x3 −10 (3) f y3 10 10 0 0 −10 −10 0 0 0 0 0 0 0 0 0 0 0 0   −10 u x1 −10   u y1    0   u x2  . 17) These three equations can be represented in direct matrix notation as f(1) = K(1) u, f(2) = K(2) u, f(3) = K(3) u. 19) so all we have to do is add the three stiffness matrices that appear above, and we arrive at the master stiffness equations:          20 f x1 f y1   10   f x2   −10 = f y2   0   f x3 −10 f y3 −10 10 10 0 0 −10 −10 −10 0 10 0 0 0 0 0 0 5 0 −5 −10 −10 0 0 10 10   −10 u x1 −10   u y1    0   u x2   .

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Aircraft Stability and Control by A. W. Babister


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