scholarly journals A problem of non – linear deformation of five–layer conical shells with allowance for discrete ribs

2021 ◽  
Author(s):  
N. V. Arnauta ◽  
Keyword(s):  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Shells Of Revolution ◽  
Linear Deformation ◽  
Conical Shells ◽  
Non Linear ◽  
Stationary Loading ◽  
Discrete Ribs ◽  
Linear Differential ◽  
Wave Problems

A problem of non – linear deformation of multiplayer conical shells with allowance for discrete ribs under non – stationary loading is considered. The system of non – linear differential equations is based on the Timoshenko type theory of rods and shells. The Reissner’s variational principle is used for deductions of the motion equations. An efficient numerical method with using Richardson type finite difference approximation for solution of problems on nonstationary behaviour of multiplayer shells of revolution with allowance distcrete ribs which permit to realize solution of the investigated wave problems with the use of personal computers. As a numerical example, the problem of dynamic deformation of a five-layer conical shell with rigidly clamped ends under the action of an internal distributed load was considered.

scholarly journals Forced vibrations of multilayered cylindrical shells taking into account the discresibility of the ribs with non-steady loads

2020 ◽  
Author(s):  
N. Arnauta ◽  
Keyword(s):  
Cylindrical Shells ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Technology ◽  
Nonstationary Vibrations ◽  
Shells Of Revolution ◽  
Motion Equations ◽  
Discrete Ribs ◽  
Wave Problems ◽  
Theory Of Shells

This work considers the problem of nonstationary behavior of multilayered discretely reinforced cylindrical shells.By the way the problem is very important. Multiplayed shells with allowance for discrete ribs are widely used in engineering, industrial and public building, aviation and space technology, shipbuilding. In the framework of the Timoshenko type non – linear theory of shells and ribs nonstationary vibrations multilayered shells of revolution with allowance for discrete ribs are investigated. Reissner’s variational principle for dynamical processes is used for deduction of the motion equations. An efficient numerical method with using Richardson type finite difference approximation for solution of problems on nonstationary behaviour of multiplayer shells of revolution with allowance for discrete ribs which permit to realize solution of the investigated wave problems with the use of personal computers, as well as bringing their solutions to receiving concrete numerical results in wide diapason of geometrical, physico–mechanical parameters of structures are elaborated. In particular three-layer discretely reinforced cylindrical shells were investigated.

Springback Analysis of Rectangular Sectioned Bar of Non Linear Work-Hardening Materials under Torsional Loading

2013 ◽  
Vol 393 ◽  
pp. 422-434 ◽  
Author(s):  
Radha Krishna Lal ◽  
Vikas Kumar Choubey ◽  
J.P. Dwivedi ◽  
V.P. Singh ◽  
Sandeep Kumar
Keyword(s):  
Work Hardening ◽  
Deformation Theory ◽  
Rectangular Cross Section ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Torsional Loading ◽  
Rectangular Section ◽  
Steel Bars ◽  
Non Linear ◽  
Theoretical Results

This paper deals with the springback problems of rectangular section bars of non-linear work-hardening materials under the torsional loading. Using the deformation theory of plasticity, a numerical scheme based on the finite difference approximation has been proposed. The growth of the elastic-plastic boundary and the resulting stresses while loading, and the springback and the residual stresses after unloading are calculated. The results are verified experimentally with mild steel bars having a rectangular cross-section and the experimental results have been found to agree well with the theoretical results obtained numerically.

scholarly journals Displacement convexity for the entropy in semi-discrete non-linear Fokker–Planck equations

2018 ◽  
Vol 30 (6) ◽  
pp. 1103-1122 ◽  
Author(s):  
JOSÉ A. CARRILLO ◽  
ANSGAR JÜNGEL ◽  
MATHEUS C. SANTOS
Keyword(s):  
A Priori ◽  
Gradient Flow ◽  
Planck Equation ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Standard Entropy ◽  
Non Linear ◽  
Finite State ◽  
Mean Function ◽  
Fokker Planck

The displacement λ-convexity of a non-standard entropy with respect to a non-local transportation metric in finite state spaces is shown using a gradient flow approach. The constant λ is computed explicitly in terms ofa prioriestimates of the solution to a finite-difference approximation of a non-linear Fokker–Planck equation. The key idea is to employ a new mean function, which defines the Onsager operator in the gradient flow formulation.

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

scholarly journals Steady Motion of Ice Sheets

1980 ◽  
Vol 25 (92) ◽  
pp. 229-246 ◽  
Author(s):  
L. W. Morland ◽  
I. R. Johnson
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Power Law ◽  
Perturbation Expansion ◽  
Ice Sheet ◽  
Leading Order ◽  
Plane Flow ◽  
General Law ◽  
Non Linear ◽  
Linear Differential

AbstractSteady plane flow under gravity of a symmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding according to a shear-traction-velocity power law, is treated. The surface accumulation is taken to depend on height, and the drainage and sliding coefficient also depend on the height of overlying ice. The ice is described as a general non-linearly viscous incompressible fluid, with illustrations presented for Glen’s power law, the polynomial law of Colbeck and Evans, and a Newtonian fluid. Uniform temperature is assumed so that effects of a realistic temperature distribution on the ice response are not taken into account. In dimensionless variables a small paramter ν occurs, but the ν = 0 solution corresponds to an unbounded sheet of uniform depth. To obtain a bounded sheet, a horizontal coordinate scaling by a small factor ε(ν) is required, so that the aspect ratio ε of a steady ice sheet is determined by the ice properties, accumulation magnitude, and the magnitude of the central thickness. A perturbation expansion in ε gives simple leading-order terms for the stress and velocity components, and generates a first order non-linear differential equation for the free-surface slope, which is then integrated to determine the profile. The non-linear differential equation can be solved explicitly for a linear sliding law in the Newtonian case. For the general law it is shown that the leading-order approximation is valid both at the margin and in the central zone provided that the power and coefficient in the sliding law satisfy certain restrictions.

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