tailieunhanh - Bruhn - Analysis And Design Of Flight Vehicles Structures Episode 2 Part 6

Tham khảo tài liệu 'bruhn - analysis and design of flight vehicles structures episode 2 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | ANALYSIS AND DESIGN OF PLIGHT VEHICLE STRUCTURES plate this approximation becomes Umax - - for V tt D Eh3 which Is by 2-1 2 is error with the exact solution. The expressions for bending and twisting moments are not so quickly convergent. To Improve the solution another series solution can be developed as follows b Levy alternate single series solution The method will be developed for uniform load q0 const. Levy suggested a solution in the form w z Ym y ------------- 16 m l where Ym Is a function of y only. Each term of the series satisfies the boundary conditions _ - ă3W _ w ơ à 0 a t X a. It remains to Ca where for symmetry m 1 3 5 . . . This equation can be satisfied for all values of X If Ym32- y aX. Ym 0------------------------ 19b a a The general solution of 19b is Ym y - a cos h . Ba SL sin h . ạ sin h as. . Da S os h -2 S. 1 Q CL J determine Ym so as to satisfy the remaining two w 0 aaw ay 0 at y b A further simplification can be made If we take the solution In the form w a wx Wa 17a where w Qo x - 2axa aax 17b 13 the deflection of a very long strip with the long side in the x-dlrectlon loaded by a uniform load q0 supported at the short sides X 0 X a and free at the two long sides. Since 17b satisfies the differential equation and the boundary conditions at X 0 X s a the problem is solved if we find the solution of Since the deflection is symmetric with respect to the x-axis It follows that Cm Dm - 0. Thus w s pan x - 23x3 a x - n 2 240 D m l 3 5 z. 1. nmy u. n w u TOtyA mnx Ạn cos h Bm sin h d L sin or ID 1. nny. -A-sin h dd_ sin - a a a w3 ax a w ax3 3ya a w3 ------- 18 where m 1 3 5 . . Substituting this expression Into the boundary conditions with wa m the form of 16 and satisfying together with wx of eq. a w conditions w 0 ay Fig. 7 . 17b the boundary 0 at y - Ỷ see w 0 0 for g - Ặ we find ay 2 4 Am cos h Oja Offi Bm sin h dm 0 _ _ - - 21a An 2Bm cos h dm Om Bffl slnhQm 0 Substituting 16 Into 18 we obtain m l aa a .