Optimization of dynamic mechanical response of a composite plate using multi-field coupling with thermal constraints

We consider the problem of optimizing the dynamic response of a mechanically loaded, rectangular, electrically conductive anisotropic composite plate by applying an electromagnetic field, which exploits the electro-magneto-mechanical field coupling phenomenon. An important aspect of the formulated nonlinear partial differential equation (PDE)-constrained optimization model is the presence of a thermal constraint that prevents polymer matrix degradation in the composite material due to Joule heating produced by the electromagnetic field. A black-box optimization approach based on the active set algorithm is employed. A system of governing PDEs is solved using a series of sequential numerical procedures that includes the method of lines, Newmark time-stepping scheme, quasilinearization, integration of two-point boundary-value problems, and a superposition method followed by orthonormalization. Implementation in hyper-dual arithmetics facilitated automatic differentiation and computation of the gradient. Optimization results show that application of an electromagnetic field with optimal characteristics enables one to significantly reduce the amplitude of the plate vibrations while controlling for Joule heating.