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.

Multiscale Nonlocal Elasticity: A Distributed Order Fractional Formulation

“…These novel materials find important applications in the most diverse fields of engineering, nanotechnology, biotechnology, and even medicine. Specific examples of the different applications of complex architectured materials include, but are not limited to, biological implants [1,2], lightweight aerospace, automobile and naval structures [3,4], metamaterials designed for wave-guiding and vibration control [5][6][7], and even micro/nano-electromechanical devices [8,9]. In all these applications, the ability to achieve accurate predictions is paramount to deliver optimal designs and performance once these complex systems are deployed in the field.…”

“…The most well-known and studied included long-range interatomic and intermolecular interactions as well as material heterogeneity at micro-and nano-scales [10][11][12]. However, nonlocal interactions can also be generated at the macroscale by means of intentionally nonlocal designs [6] and medium heterogeneity [4,[13][14][15]. Since the source of the nonlocal effects are typically specific to a material scale, the corresponding effects were often assumed to be localized at the respective scale while becoming negligible once integrated over the larger scales.…”

Displacement-Driven Approach to Nonlocal Elasticity

“…Experimental and theoretical investigations have shown that, irrespective of the spatial scale, size-dependent or nonlocal effects can become prominent in the response of several structures in the most diverse fields of engineering, nanotechnology, biotechnology, and even medicine [1][2][3][4][5][6][7][8]. The study and analysis of nonlocal effects has increasingly become an important component of structural design and analysis.…”

“…The study and analysis of nonlocal effects has increasingly become an important component of structural design and analysis. Specific examples of size-dependent structures include sensors, biological implants, micro/nano-electromechanical devices and even macroscale structures such as stiffened panels in naval and aerospace applications [4][5][6][7][8]. In the case of microand nano-structures, for example those involving carbon nanotubes or graphene sheets, nonlocal effects can be traced back to interatomic interactions, and even medium heterogeneity [8][9][10][11][12][13].…”

“…For these reasons, nonlocal effects have long been considered negligible at the macro scales. However, at the macro scales, nonlocal effects can originate from material heterogeneities [2][3][4][5][14][15][16][17] or even from intentionally nonlocal designs [6,7]. While long-range interactions occur naturally in heterogeneous materials (e.g.…”