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 beam

Lipschitz stability at the boundary for time-harmonic diffuse optical tomography

We study the inverse problem in Optical Tomography of determining the optical properties of a medium ⊂ Rn, with n ≥ 3, under the so-called diffusion approximation. We consider the time-harmonic case where is probed with an input field that is modulated with a fixed harmonic frequency ω = k/c, where c is the speed of light and k is the wave number