A semi-analytical approach based on the variational iteration method for static analysis of composite beams

Using the Variational Iteration Method (VIM) the 3D static deflection problem of composite beams subject to concentrated tip and uniformly distributed loads is analysed, resulting in a system of coupled non homogeneous ordinary differential equations. Using a general Lagrange multiplier, identified by variational theory, a special type of functional is constructed. By making an initial approximation in the form of a Maclaurin series and by using successive iterations, the solution in the form of convergent series is obtained. The results based on VIM are compared against those of the exact solution and Chebyshev Collocation Method (CCM) for different layups and boundary conditions and good agreement is observed between them. These results show the applicability and effectiveness of VIM for the static analysis of composite beams.

Automated summary

The 3D static deflection problem of composite beams subjected to loads is analyzed using the Variational Iteration Method (VIM), resulting in a system of coupled non homogeneous ordinary differential equations and a solution in the form of convergent series. Good agreement is observed between the results based on VIM and those of the exact solution and Chebyshev Collocation Method (CCM) for different layups and boundary conditions, showing the applicability and effectiveness of VIM for static analysis of composite beams.