Dynamic tailoring of beam-like structures. Application to High Aspect Ratio unitized box-beam and internal resonant structures

This work is a journey into the dynamic tailoring of beam-like structures which aims to exploit unconventional couplings and nonlinearities to enlarge the design space and improving the performances of engineering systems. Particularly, two examples pertaining dynamic tailoring of aerospace and mechanical systems are investigated in depth. In the first case, the work aims to attain a desired structural performance exploiting typical nonlinear structural phenomena and unconventional couplings offered by the unitized structures. As for the unitized structures, the present work, derives two equivalent plate models of curvilinear stiffened panels namely, constant (or homogenized) stiffness model and variable stiffness model. The models are assessed through finite element analysis. In the spirit of CAS (Circumferentially Asymmetric Stiffness), the equivalent plate stiffness’s are used to determine the cross- sectional beam stiffness’s. The governing equations for the Euler-Bernoulli, anisotropic beam with variable stiffness are derived and then used to address the optimization problem. The objective of the optimization is to attain a desired static or dynamic performance of the unitized beam exploiting the enlarged design space which arises from the stiffness variability and the unconventional couplings. In the second type of system analyzed, the aim is synthesize meaningful topologies for planar resonators. The topology optimization is addressed using as initial guess a ground structure. Motivated by the results of the optimization, a generalized reduced order model is derived for multi-members beam structures. The generalized model have been then specialized for three cases namely, V- Y- and Z-shaped resonators. The analytical solution for the V-shaped resonator is also derived along with the electro-mechanical equations of motion. Different solutions are studied aiming at investigating the effect of the folding angle on to the performances of a V-shaped harvester. Beside the study of the static and dynamic behavior of the systems, the thesis presents two novel optimization algorithms namely, the Stud^P GA and the GERM. The Stud^P GA, is a population based algorithm conceived to enhance the exploration capabilities, and hence the convergence rate, of classical GA. The Stud^P GA has been preliminary assessed through benchmark problems for composite layered structure and then used for the optimization of the stiffeners' path aiming at attaining a desired static or dynamic performances. The GERM (Graph-based Element Removal Method), is a double filtering technique conceived for the topology synthesis of planar ground structures. The GERM has been used, in combination with a standard GA, to address the topology optimization problem of the two types of system namely, planar resonator and compliant structures. The work introduces also the concept of trace-based scaling for predicting the behavior of anisotropic structures. The effectiveness of the trace-based scaling is assessed through comparison between scaled and analytical performances of anisotropic structures.