11 Oct 2020
I was trying to reproduce the work of book titled "Nonlinear Composite Beam Theory". I am getting problem in the equation 7.48 of this book. How did one get the idea of converting the equation in this way. I am not able to find out the specific reason for using (1+nu)x2^2 k3'+f [x3] and -(1+nu)x3^2 k2' in equation 7.48.
12 Oct 2020
The insight comes from the flexure solution of a cantilever beam under transverse force. Such assumptions not in terms of k3' but in terms of transverse force P can be found in any elasticity textbook.
14 Oct 2020
Thank you sir for the response. Further to this question, Technically why cannot we simply write it as a derivative of phi with respect to x3. The ultimate aim is to solve the governing differential equation for a defined boundary condition. Why we are making a complicated boundary condition instead of simply using derivative of phi wrt x3.
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