A review on non-classical continuum mechanics with applications in marine engineering

Abstract

Marine structures are advanced material and structural assemblies that span over different length scales. The classical structural design approach is to separate these length scales. The used structural models are based on classical continuum mechanics. There are multiple situations where the classical theory breaks down. Non-classical effects tend arise when the size of the smallest repeating unit of a periodic structure is of the same order as the full structure itself. The aim of the present paper is to discuss representative problems from different length scales of ship structural design.

Keywords:

• Beam theory
• plate theory
• homogenization
• ship structures
• finite element method
• optimization

Acknowledgments

The authors would like to thank Professor JN Reddy for his seminal contributions to non-classical continuum mechanics and equivalent single-layer plate and shell theories which have had and will have a significant impact not only on our scientific careers but also to the engineering we see around us. Structural ESL models have proven to be extremely useful, and the rigorous and clear presentation of prof. Reddy has made their application easier. This paper discussed some applications for non-classical ESL models, but there is much more to follow. Rigorous treatment of these problems will keep us busy for years. Thank you JN for this. The authors would like to thank also the projects by School of Engineering of Aalto University and Business Finland (FidiPro). In addition, this work has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Action grant agreement No 745770 - SANDFECH - Micromechanics-based finite element modeling of sandwich structures.