相关论文: Shells without drilling rotations: a representatio…

In this tutorial, we provide a coordinate-free derivation of the system of equations that govern equilibrium of a thin shell that can undergo shear. This system involves tensorial fields representing the internal force and couple per unit…

In this paper we study analytically the viscous `sabra' shell model of energy turbulent cascade. We prove the global regularity of solutions and show that the shell model has finitely many asymptotic degrees of freedom, specifically: a…

We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described…

The paper considers the general case of incompressible non-classical elasticity with small deformations and rotations. The thermodynamic stability is analysed for free energy density with three rotational degrees of freedom. Although the…

The geometrically rigorous nonlinear analysis of elastic shells is considered in the context of finite, but small, strain theory. The research is focused on the introduction of the full shell metric and examination of its influence on the…

Starting from a three-dimensional model based on the Ciarlet-Geymonat energy, we derive nonlinear shell models within the classical elasticity theory of compressible isotropic materials. The Neo-Hookean term involving the norm of the…

Stretching, drilling, and bending are the independent deformation modes of a thin shell, each of which has an individual energy content. When the energy content of a mode vanishes, that mode is neutral. We characterize all neutral modes of…

Budiansky's nonlinear shell theory is particularized to a 2D setting, and thereupon generalized to a fully nonlinear, statically and kinematically exact, theory of strain-gradient elasticity of beams. The governing equations are displayed…

The structural analysis of ultra-lightweight flexible shells and membranes may require the adoption of complex nonlinear strain-displacement relations. These may be approximated and simplified in some circumstances, e.g., in the case of…

We study theoretically the low-energy phonons and the static strain in cylindrical core/shell nanowires (NWs). Assuming pseudomorphic growth, isotropic media, and a force-free wire surface, we derive algebraic expressions for the dispersion…

Thin shells are characterized by a high cost of stretching compared to bending. As a result isometries of the midsurface of a shell play a crucial role in their mechanics. In turn, curves with zero normal curvature play a critical role in…

In the theory of weakly non-linear elasticity, Hamilton et al. [J. Acoust. Soc. Am. \textbf{116} (2004) 41] identified $W = \mu I_2 + (A/3)I_3 + D I_2^2$ as the fourth-order expansion of the strain-energy density for incompressible…

Shells are ubiquitous thin structures that can undergo large nonlinear elastic deformations while exhibiting combined modes of bending and stretching, and have profound modern applications. In this paper, we have proposed a new Isogeometric…

A 3D fluid-structure interaction solver based on an improved weakly-compressible moving particle simulation (WC-MPS) method and a geometrically nonlinear shell structural model is developed and applied to hydro-elastic free-surface flows.…

This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this…

In the direct approach to continua in reduced space dimensions, a thin shell is described as a mathematical surface in three-dimensional space. An exploratory kinematic study of such surfaces could be very valuable, especially if conducted…

We perform numerical simulations of the dynamical equations for free water surface in finite basin in presence of gravity. Wave Turbulence (WT) is a theory derived for describing statistics of weakly nonlinear waves in the infinite basin…

The aim of this study is three-fold: (i) to present a general higher-order shell theory to analyze large deformations of thin or thick shell structures made of general compressible hyperelastic materials; (ii) to utilize the orthonormal or…

In this paper, we study the problem of shape-programming of incompressible hyperelastic shells through differential growth. The aim of the current work is to determine the growth tensor (or growth functions) that can produce the deformation…

The formulation of a new prism finite element is presented for the nonlinear analysis of solid shells subject to large strains and large displacements. The element is based on hierarchical, heterogeneous, and anisotropic shape functions. As…