A novel Linear Complementarity Problem implementation for elastic–plastic structural optimisation of cable–rib satellite antennas

In the growing field of deployable aerospace structures, cable–rib satellite antennas are nowadays a target of increasing interest [1], fostering the need of consistent mechanical modelling and structural optimisation. The present work adopts Limit Analysis (LA) computational methods, as specific tools for structural modelling (see, e.g., [2, 3, 4]), accounting for material non–linearity, up to structural collapse, and possibly getting coupled to optimisation loops, toward maximisation of structural performance. In the contribution, a consistent mechanical formulation is proposed, accounting for rib elements with non–linear joints (exhibiting concentrated plastic deformations) and for linear tensioning cables, modelled by a common, wholly original, Linear Complementarity Problem (LCP) formulation. Such a computational approach is implemented within a self–made feasible procedure and validated on first specific antenna application examples. Moreover, optimisation scenarios of various, mechanical and geometrical, structural properties are investigated, within a coupled LA–optimisation framework, toward optimal automated design. The proposed computational modelling platform, both from a general standpoint in (Computational) Mechanics and from a specific viewpoint on such structures, allows for an innovative systematic structural description of satellite antennas, toward computationally efficient modelling and design.