State-Space Approaches to Complex Structures in Aerospace

Abstract

The state-space approach (SSA), traditionally utilized in modern control theory, has been successfully adopted over the last three decades to investigate the mechanical behaviors of complex structures composed of composite or smart materials. This is largely due to their increasing application across various fields, including aerospace, civil and marine engineering, and transportation vehicles. This paper provides a comprehensive review of the establishment of state-space formulations for structures of typical configurations, such as beams, plates, shells, and trusses, with a particular focus on their applications in the mechanical analyses of various complex aerospace or smart structures using the transfer matrix method. The paper first summarizes the three-dimensional SSAs applied to laminated structures without any assumptions on physical fields. By employing structural theories such as various beam, plate, and shell theories, simplified one-dimensional and two-dimensional SSAs for laminated structures are developed. The paper then outlines the advances in generating analytical solutions for the mechanical behaviors of laminated structures. For the sake of completeness, the paper also provides an account of SSAs applied to complex periodic structures, particularly in beam and truss forms. To overcome the limitations of conventional SSAs related to structures with specialized geometric configuration or under arbitrary boundary conditions, state-space based numerical methods have been proposed, for example, the state-space based differential quadrature method and state-space based finite-element method. The applications of these methods in the analyses of static and dynamic responses of complex structures are extensively reviewed. It is observed that there are still intriguing and potential research topics for the development of advanced SSAs with enhanced versatility and the studies on practical complex structures used in modern engineering, particularly in aerospace industry. Therefore, this review is expected to be beneficial for researchers in the fields of analytical and numerical methods, composite structures, aerospace, structural engineering, and more.