Curve Fitting an equation

Hi, I was wondering if someone could help me in developing a code to curve fit equaion 16. The estimate expression obtained is equation 17. I wanted to verify this by coding. Any help is appreciated. Thanks!

[William Rose]

• @Arjun Siddharth, Please provide the full paper rather than just a small fragment.
• Is equation 17 supposed to be an approximation for equation 16, under certain conditions? If so, then what values of x were used to compute ? And what were the values of , and E, and I, and L? What is the funciton ?
• Equation 17 includes four constants: 2.7E-5, 99, 0.01, and 1.207E-5. Were all of those constants obtained by curve-fitting, or were some of them set in advance, based on other knowledge?
• Equation 17 is for . Does the bar over μ mean it is an average? If so, then an average over what variable, and over what range of values?

[William Rose]

@Arjun Siddharth, I inspected the full paper. It is not at all clear to me what the authors are doing. For example, it is not clear whethere the "length" in the top row of table 1 is L or x. And if we knew that, then we would still not know the value for the other quantity (x or L). I also note that Table 1 contains only five (x,) pairs (or five (L,pairs). As I noted earlier, equation 17 has four constants. It is not reasonable to fit four parameters if you only have five data points. Since the authors have not explained their method clearly, I would not spend time trying to reproduce their results.

[Arjun Siddharth]

Oh okay. Actually, in my code the value of EI, and L has changed. Any idea how I can modify mew_bar expression to incorporate this change?

Answer 1

[William Rose]

@Arjun Siddharth, EI appears as a constant factor in the denominator of eq. 16 for . Therefore if you use a different value of EI than the authors, then multiply by the factor .

For different vaues of L, just plug in L into equation 17.

[Arjun Siddharth]

Thanks a bunch!