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.

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.

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.

Aman deep@ on — Edited @ onDear Team

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.

Wenbin Yu@ onThe 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.

Aman deep@ onThank 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.

Wenbin Yu@ onThe whole purpose is to make phi vanish along the boundary similarly like what has been done in elasticity about Saint Venant problems.