Good day everyone,
I am building a Hertzian stress calculator and got stuck at the step where I calculate the k value for a particular B/A reationship.
Any help will be appriciated
contact stress calc.sm (22 KiB) downloaded 44 time(s).

We also know than K will always be in the range (0,1)
The equations presented above is obtained from the book Advanced Mechanics of Materials by Boresi Et al

In case of these functions, al_nleqsolve() can be the answer.
No other solver is capable other than al_nleqsolve().
k' should be under line, otherwise not solveable.
Here is your function solved.

Regards

contact stress calc_1.sm (28 KiB) downloaded 45 time(s).

I'm super impressed !!!

Wrote

Your original document is circular and indigestible.
From un-sourced [K,E] and arbitrary datum ... solve.

This sample is not appropriate.
As you have said, it is only solvable when K and E already given.
roots() can't solve without K and E given or calculated separately.
And you can't calculate K and E while not knowing what k is.

Your sample is not what OP wants.
He means to solve that complicated Q function.
Without any parameter or variable of K and E are pre-given.

With elliptic integrals from GSL and Cephes library.

Wrote

Good day everyone,
I am building a Hertzian stress calculator and got stuck at the step where I calculate the k value for a particular B/A reationship.
Any help will be appriciated
contact stress calc.sm (22 KiB) downloaded 44 time(s).

Solving by the old bisection method:


contact stress calc_by_bisection.sm (26 KiB) downloaded 21 time(s).

Solving with a custom algorithm.

Regards

contact stress calc_2.sm (21 KiB) downloaded 26 time(s).

Wrote

Solving with a custom algorithm.

Very elegant!

... slightly refreshed/augmented
Absent of comments from Originator !
Cheers ... Jean.

Solve Circular Elliptic Datum Native Copy.sm (68 KiB) downloaded 37 time(s).