Non Linear Composite Beam Theory

  1. Aman deep

    Dear 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.

  2. Wenbin Yu

    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. 

  3. Aman deep

    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.

  4. Wenbin Yu

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