Structural Similitude and Scaling Laws for Plates and Shells: A Review

Abstract

IntroductionThis paper deals with the development and use of scaled-down models in order to predict the structural behavior of large prototypes. The concept is fully described and examples are presented which demonstrate its appficability to beam-plates, plates and cylindrical shells of laminated cons_ction. The concept is based on the use of field equations, which govern the response behavior of both the small model as well as the large prototype. The conditions under which the experimental data of a small model can be used to predict the behavior of a large prototype are called scaling laws or similarity conditions and the term that best describes the process is structural similitude. Moreover, since the term scaling is used to describe the effect of size on strength characteristics of materials, a discussion is included which should clarify the difference between "scaling law" and "size effect".Finally, a historical review of all published work in the broad area of stnmtural similitude is presented for completeness.• Aircraft and spacecraft comprise the class of aerospace structures that require efficiency and wisdom in design, sophistication and accuracy in analysis and numerous and careful experimental evaluations of components and prototype, in order to achieve the necessary system reliability, performance and safety.Preliminary and/or concept design entails the assemblage of system mission requirements, system expected performance and identification of components and their connections as well as of manufacturing and system assembly techniques. This is accomplished through experience based on previous similar designs, and through the possible use of models to simulate the entire system characteristics.Detail design is heavily dependent on information and concepts derived from the previous step. This information identifies critical design areas 'which need sophisticated analyses, and design and redesign procedures to achieve the expected component performance.This step may require several independent analysis models, which, in many instances, require component testing.The last step in the design process, before going to production, is the verification of the design. This step necessitates the production of large components and prototypes in order to test component and system analytical predictions and verify strength and peffom3ance requirements under the worst loading conditions that the system is expected to encounter in service.

Similitude and Physical Modeling for Buckling and Vibration of Symmetric Cross-Ply Laminated Circular Cylindrical Shells

“…Authors in [2][3][4][5] published several papers on symmetrically laminated plates and in [6,7] on symmetrically laminated shells that deal with the establishment of the similarity conditions between the model and the prototype. However, they have applied the similitude theory to the solutions of the governing differential equations instead of to the governing differential equations directly.…”

“…The main objective of this study is to derive the similitude invariants and propose physical modeling for the buckling and vibration response of the symmetric cross-ply laminated circular cylindrical shells by applying the similitude transformation to the governing differential equations directly. The method is much easier and more direct than that was done in [2][3][4][5][6][7]. The resulting scaling laws are unique because they are forced by the governing differential equations.…”

Complex network analysis for early detection of failure mechanisms in resilient bio-structures

“…Their work also made use of finite element analysis to validate the similitude relationships between the model and the prototype. Simitses et al [79][80][81][82] carried out several research efforts focused on symmetrically laminated plates to identify the similarity conditions between the model and the prototype. Their research makes use of scaling laws to design scaled models and uses theoretical methods to compute the model data to predict the behavior of the prototype.…”

Dimensional analysis of structural response in complex biological structures

“…Their work made use of finite element analysis software for validating the similitude relationships between the model and the prototype. Simitses et al [16,[21][22][23] carried out several research efforts focused on symmetrically laminated plates to identify the similarity conditions between the model and the prototype. Their research makes use of scaling laws for designing scaled models and uses theoretical methods to compute the model data to predict the behavior of the prototype.…”