Calculation of Load Distribution in Stiffened Cylindrical ShellsThin-walled shells with strong longitudinal and transverse stiffening (for example, stressed-skin fuselages and wings) may, under certain simplifying assumptions, be treated as static systems with finite redundancies. In this report the underlying basis for this method of treatment of the problem is presented and a computation procedure for stiffened cylindrical shells with curved sheet panels indicated. A detailed discussion of the force distribution due to applied concentrated forces is given, and the discussion illustrated by numerical examples which refer to an experimentally determined circular cylindrical shell. |
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Results 1-5 of 6
Page 28
... sinh k V cos k X + C4 sinh k V sin k X ( 40 ) The arguments ↓ and X satisfy the boundary conditions : cosh cos X = 121 : Y Y z ; sinh V sin X V = D 1 1 ( 41 ) 2 whence follows : 1 cosh - 1 ( A + B ) A = 2 112 with X II 112 ( cos - 1 ) ...
... sinh k V cos k X + C4 sinh k V sin k X ( 40 ) The arguments ↓ and X satisfy the boundary conditions : cosh cos X = 121 : Y Y z ; sinh V sin X V = D 1 1 ( 41 ) 2 whence follows : 1 cosh - 1 ( A + B ) A = 2 112 with X II 112 ( cos - 1 ) ...
Page 29
... sinh k p with 1 C. + C3 sinh k cosh k p + C4 sinh k sinh k p coshcosh p = 121 ; sinh V sinh p = 712 ( 40 ) - ( 41 ' ) 112 cosh - 1 ( A + B ) ; p = 12 cosh - 1 ( A - B ) ( 42 ) ( A and B as in ( 42 ) ) ( double root of the characteristic ...
... sinh k p with 1 C. + C3 sinh k cosh k p + C4 sinh k sinh k p coshcosh p = 121 ; sinh V sinh p = 712 ( 40 ) - ( 41 ' ) 112 cosh - 1 ( A + B ) ; p = 12 cosh - 1 ( A - B ) ( 42 ) ( A and B as in ( 42 ) ) ( double root of the characteristic ...
Page 30
... sinh ( n - k + 1 ) + { sin 1 - -- sinh k ý sin ( n M k ) x ) x } sia l X sinh ( n - k ) v } ] where 1 * = sinh ( n + 1 ) ý sin X + sin ( n + 1 ) X sinh v ( For D 1 < the hyperbolic functions are to be substituted everywhere for the ...
... sinh ( n - k + 1 ) + { sin 1 - -- sinh k ý sin ( n M k ) x ) x } sia l X sinh ( n - k ) v } ] where 1 * = sinh ( n + 1 ) ý sin X + sin ( n + 1 ) X sinh v ( For D 1 < the hyperbolic functions are to be substituted everywhere for the ...
Page 31
... sinh ] Ca k❤ ] α < 0 ) with the argument ♡ = cosh1 | al the solution is : Xx = ( ± 1 ) 1 = [ C1 + C2 k ] ( 47 ) There are thus obtained for the above boundary values the solutions : and = ( +1 ) k sinh ( n - sinh n n ( +1 ) k ( 1 - 1 ...
... sinh ] Ca k❤ ] α < 0 ) with the argument ♡ = cosh1 | al the solution is : Xx = ( ± 1 ) 1 = [ C1 + C2 k ] ( 47 ) There are thus obtained for the above boundary values the solutions : and = ( +1 ) k sinh ( n - sinh n n ( +1 ) k ( 1 - 1 ...
Page 31
... sinh ( n + 1 ) = sin kỵ sinh ( n - k ) ( k + 1 ) sinh ( n + 1 - kh k sinh ( n - kh D = 1 9k ( A - B - 1 ) F D < 1 J = sinh ( k + 1 ) sinh ( n + 1 - k ) ( A - B > 1 ) 7 sinh kế Sinh ( n - k ) rigid 9x = sin ( k + 1 ) x sinh ( n + 1 - k ) ...
... sinh ( n + 1 ) = sin kỵ sinh ( n - k ) ( k + 1 ) sinh ( n + 1 - kh k sinh ( n - kh D = 1 9k ( A - B - 1 ) F D < 1 J = sinh ( k + 1 ) sinh ( n + 1 - k ) ( A - B > 1 ) 7 sinh kế Sinh ( n - k ) rigid 9x = sin ( k + 1 ) x sinh ( n + 1 - k ) ...
Common terms and phrases
12-stringer shell according ak+1 applied approximately arbitrary assumed assumption axial force axis bending force group bending moment bulkhead rings characteristic force groups circumference cm² component forces concentrated forces convexing force group corresponding cosh cross section cutaway portion cyclical symmetry determined difference equations dimensions effect elasticity equations elementary stress end bulkhead equal bays F₁ F₂ flexurally stiff force distribution infinitely long shell Krümling Ks,k kth bay kth bulkhead linear linearly independent longitudinal forces main spars monocoque normal forces numerical example obtained orthogonal peripheral principal system radial load rigid bulkheads Schapitz shear flows shear stress shell length shell model shell shapes shown in figure simply symmetrical sinh solution static redundancies statically indeterminate computation stress condition stress distribution stringers symmetrical force group symmetrical relations table of formulas tion torsion transverse forces transverse stiffener walls transverse walls values Xu,k ак