Search results for "Linear elasticity"

Isotropic Chiral Acoustic Phonons in 3D Quasicrystalline Metamaterials.

2020

International audience; The elastic properties of three-dimensional (3D) crystalline mechanical metamaterials, unlike those of amorphous structures, are generally strongly anisotropic—even in the long-wavelength limit and for highly symmetric crystals. Aiming at isotropic linear elastic wave propagation, we therefore study 3D periodic approximants of 3D icosahedral quasicrystalline mechanical metamaterials consisting of uniaxial chiral metarods. Considering the increasing order of the approximants, we approach nearly isotropic effective speeds of sound and isotropic acoustical activity. The latter is directly connected to circularly polarized 3D metamaterial chiral acoustic phonons—for all …

Guaranteed Error Bounds I

2014

In Chap. 3, we discussed the main ideas of fully reliable error control methods and the corresponding numerical algorithms with the paradigm of simple elliptic type problems. This chapter is intended to show a deep connection between a posteriori estimates of the functional type and physical relations generating the problem. Also, the goal of this chapter is to consider a wider set of problems arising in various applications and explain things in terms of computational mechanics. For this purpose, we begin with a simple class of mechanical problems (straight beams) and after that consider curvilinear beams and more complicated models of continuum mechanics (linear elasticity, viscous fluids…

Probabilistic analysis of truss structures with uncertain parameters (virtual distortion method approach)

2004

A new approach for probabilistic characterization of linear elastic redundant trusses with uncertainty on the various members subjected to deterministic loads acting on the nodes of the structure is presented. The method is based on the simple observation that variations of structural parameters are equivalent to superimposed strains on a reference structure depending on the axial forces on the elastic modulus of the original structure as well as on the uncertainty (virtual distortion method approach). Superposition principle may be applied to separate contribution to mechanical response due to external loads and parameter variations. Statically determinate trusses dealt with the proposed m…

Fatigue Design of Roller Bearing for Large FPSO Turrets

2012

The present report presents the fatigue design and a fatigue life prediction method for large roller bearings applied in the turret turn table for large Floating Production Storage and Offloading (FPSO) units. The contact point between wheel and rail in these bearings is subjected to a multi-axial stress situation and both surface wear and fatigue cracking may occur. Stress analyses with contact elements are carried out and a methodology based on the Dang Van fatigue criterion is adopted. The criterion is based on an equivalent stress defined as a combination of the fluctuation of the shear stress from its mean value and the associated hydrostatic stress at a critical plane at any time. The…

A unifying variational framework for stress gradient and strain gradient elasticity theories

2015

Abstract Stress gradient elasticity and strain gradient elasticity do constitute distinct continuum theories exhibiting mutual complementary features. This is probed by a few variational principles herein presented and discussed, which include: i) For stress gradient elasticity, a (novel) principle of minimum complementary energy and an (improved-form) principle of stationarity of the Hellinger–Reissner type; ii) For strain gradient elasticity, a (known) principle of minimum total potential energy and a (novel) principle of stationarity of the Hu–Washizu type. Additionally, the higher order boundary conditions for stress gradient elasticity, previously derived by the author (Polizzotto, Int…

An efficient framework for the elasto-plastic reliability assessment of uncertain wind excited systems

2016

Abstract In this paper a method to efficiently evaluate the reliability of elastic-perfectly plastic structures is proposed. The method is based on combining dynamic shakedown theory with Subset Simulation. In particular, focus is on describing the shakedown behavior of uncertain elasto-plastic systems driven by stochastic wind loads. The ability of the structure to shakedown is assumed as a limit state separating plastic collapse from a safe, if not elastic, state of the structure. The limit state is therefore evaluated in terms of a probabilistic load multiplier estimated through solving a series of linear programming problems posed in terms of the responses of the underlying linear elast…

Analysis of errors caused by incomplete knowledge of material data in mathematical models of elastic media

2011

Revisited mixed-value method via symmetric BEM in the substructuring approach

2012

Abstract Within the Symmetric Boundary Element Method, the mixed-value analysis is re-formulated. This analysis method contemplates the subdivision of the body into substructures having interface kinematical and mechanical quantities. For each substructure an elasticity equation, connecting weighted displacements and tractions to nodal displacements and forces of the same interface boundary and to external action vector, is introduced. The assembly of the substructures is performed through both the strong and weak regularity conditions of the displacements and tractions. We obtain the solving equations where the compatibility and the equilibrium are guaranteed in the domain Ω for the use of…

Disentangling the Role of Chain Conformation on the Mechanics of Polymer Tethered Particle Materials

2019

[Image: see text] The linear elastic properties of isotropic materials of polymer tethered nanoparticles (NPs) are evaluated using noncontact Brillouin light spectroscopy. While the mechanical properties of dense brush materials follow predicted trends with NP composition, a surprising increase in elastic moduli is observed in the case of sparsely grafted particle systems at approximately equal NP filling ratio. Complementary molecular dynamics simulations reveal that the stiffening is caused by the coil-like conformations of the grafted chains, which lead to stronger polymer–polymer interactions compared to densely grafted NPs with short chains. Our results point to novel opportunities to …

Approximation of pre-twisted Achilles sub-tendons with continuum beam elements

2022

Achilles sub-tendons are materially and geometrically challenging structures that can nearly undergo around 15% elongation from their pre-twisted initial states during physical activities. Sub-tendons' cross-sectional shapes are subject-specific, varying from simple to complicated. Therefore, the Achilles sub-tendons are often described by three-dimensional elements that lead to a remarkable number of degrees of freedom. On the other hand, the continuum-based beam elements in the framework of the absolute nodal coordinate formulation have already been shown to be a reliable and efficient replacement for the three-dimensional continuum elements in some special problems. So far, that element …