Elasticity solutions for nano-plane structures under body forces using lattice elasticity, continualised nonlocal model and Eringen nonlocal model

2021 ◽  
Author(s):  
Y. P. Zhang ◽  
N. Challamel ◽  
C. M. Wang
Keyword(s):  
Nonlocal Model ◽  
Body Forces ◽  
Elasticity Solutions

Proper Inclusion of Interiorly Applied Loads With Beam Theory

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
Jimmy C. Ho ◽  
Wenbin Yu ◽  
Dewey H. Hodges
Keyword(s):  
Asymptotic Method ◽  
Beam Theory ◽  
Elliptic Cylinder ◽  
Conventional Approach ◽  
Body Forces ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Elasticity Solutions ◽  
Precise Distribution

An error is introduced by the conventional approach of applying beam theory in the presence of interiorly applied loads. This error arises from neglecting the influence of the precise distribution of surface tractions and body forces on the warping displacements. This paper intends to show that beam theory is capable of accounting for this influence on warping and accomplishes this by the variational asymptotic method. Correlations between elasticity solutions and beam solutions provide not only validations of beam solutions, but also illustrate the resulting errors from the conventional approach. Correlations are provided here for an isotropic parallelepiped undergoing pure extensional deformations and for an isotropic elliptic cylinder undergoing pure torsional deformations.

Elasticity Solutions for Thick-Wall Submersible Spheres

1974 ◽  
Vol 96 (4) ◽  
pp. 1136-1140
Author(s):  
F. J. Dzialo
Keyword(s):  
Hydrostatic Pressure ◽  
Infinite Series ◽  
Legendre Polynomials ◽  
Buoyancy Force ◽  
Potential Functions ◽  
Thick Wall ◽  
Arbitrary Boundary ◽  
Numerical Example ◽  
Body Forces ◽  
Elasticity Solutions

Elasticity solutions utilizing the classical Boussinesq potential functions for thick-wall submersible spheres are developed. The solutions provide field stresses and strains, which consider the effect of gravity body forces, and arbitrary boundary loadings. The boundary loadings may be due to a nonuniform hydrostatic pressure, hull equipment, ballast, and can be expressed as an infinite series of Legendre polynomials. A numerical example which considers a nonuniform hydrostatic pressure and an arbitrary counter-buoyancy force applied at the inner boundary is given. Field stresses and strains are presented for various shell thicknesses and hydrostatic pressures.

Large eddy simulation in complex geometric configurations using boundary body forces

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 427-433 ◽  
Author(s):  
Roberto Verzicco ◽  
Jamaludin Mohd-Yusof ◽  
Paolo Orlandi ◽  
Daniel Haworth
Keyword(s):  
Large Eddy Simulation ◽  
Eddy Simulation ◽  
Geometric Configurations ◽  
Body Forces ◽  
Large Eddy

scholarly journals Nonlocal elastodynamics and fracture

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Robert P. Lipton ◽  
Prashant K. Jha
Keyword(s):  
Field Theory ◽  
Brittle Fracture ◽  
A Priori ◽  
Nonlocal Model ◽  
Elastic Fields ◽  
Nonlocal Field Theory ◽  
Nonlocal Field ◽  
Increasing Function ◽  
Non Locality

AbstractA nonlocal field theory of peridynamic type is applied to model the brittle fracture problem. The elastic fields obtained from the nonlocal model are shown to converge in the limit of vanishing non-locality to solutions of classic plane elastodynamics associated with a running crack. We carry out our analysis for a plate subject to mode one loading. The length of the crack is prescribed a priori and is an increasing function of time.

scholarly journals Structure, dynamics, and reconnection of vortices in a nonlocal model of superfluids

2018 ◽  
Vol 3 (11) ◽  
Author(s):  
Jason Reneuve ◽  
Julien Salort ◽  
Laurent Chevillard
Keyword(s):  
Nonlocal Model ◽  
Structure Dynamics
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