tailieunhanh - Designing Capable and Reliable Products Episode 2 Part 10

Tham khảo tài liệu 'designing capable and reliable products episode 2 part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Appendix XI 365 The stress can be approximated by a Normal distribution with parameters L A MPa Determining the second order terms in the variance equation will provide more accurate values for the mean and standard deviation of the function under certain circumstances. B. Finite difference method Substituting y x2 xri into the variance equation for the output of the function and expanding for n variables gives 2 ơy 4 i 1 uxi - . 2 dy Ấ ỠX J ơx ỡx2 2 dy 2 2 I0 5 dxj i 1 2 The finite difference method can be used to approximate each term in this equation by using the difference equation for the first partial derivative see Figure 2 . The values of the function at two points either side of the point of interest k are determined yk and yk _J which are equally spaced by an increment Av. The finite difference equation approximates the value of the partial derivative by taking the difference of these values and dividing by the increment range. The terms subscripted by i indicate that only Xị is incremented by Av for calculating yk J and yk _ holding the other independent variables constant at their k value points. dy ừk 1 - yk-1 Figure 2 The finite difference principle 366 Appendix XI 2 2 -1 2 ơb The expanded variance equation to determine the standard deviation of the stress in the rectangular bar problem above was ỀỊ 2. oa ob ƠL The variables F a and b were are all assumed to be random in nature following the Normal distribution with parameters F N 100 10 kN a A m b A m Consider the point xk to be the mean value of a variable and xk J and xk _J the extremes of the variable. The extremes can be determined for each variable by assuming they exist 4x away from the mean which covers of situations. For each variable in the problem above the extremes become Fk 100000 4 10000 140 000 MPa Fk_ 100 000 - 4 10 000 60 000 MPa AT 4 10 000 40 000 MPa ak 4 ak_ - 4 m Aứ 4 bk .

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