Shock loading of fixed flexible thread and orthotropic elastic membrane

2003 ◽  
Vol 3 ◽  
pp. 52-59
Author(s):  
S.S. Komarov ◽  
N.Yu. Tsvileneva ◽  
N.I. Miskaktin
Keyword(s):  
Numerical Methods ◽  
Dynamic Loading ◽  
Elastic Deformation ◽  
Numerical Algorithm ◽  
Shock Loading ◽  
Elastic Membrane ◽  
Wave Dynamics ◽  
Elastic Membranes ◽  
Pneumatic Structures

The main problems of the wave dynamics of flexible filaments and elastic membranes are solved. The reliability of the numerical algorithm proposed by the authors for calculating the elastic deformation of pneumatic structures under dynamic loading is confirmed when compared with the results of known studies obtained by analytical and numerical methods.

Bifurcation of rotating circular cylindrical elastic membranes

1980 ◽  
Vol 87 (2) ◽  
pp. 357-376 ◽  
Author(s):  
D. M. Haughton ◽  
R. W. Ogden
Keyword(s):  
Axial Force ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Strain Energy Function ◽  
Angular Speed ◽  
Elastic Membrane ◽  
Axial Extension ◽  
End Conditions ◽  
Elastic Membranes ◽  
Realistic Choice

SummaryBifurcation from a finitely deformed circular cylindrical configuration of a rotating circular cylindrical elastic membrane is examined. It is found (for a physically realistic choice of elastic strain-energy function) that the angular speed attains a maximum followed by a minimum relative to the increasing radius of the cylinder for either a fixed axial extension or fixed axial force.At fixed axial extension (a) a prismatic mode of bifurcation (in which the cross-section of the cylinder becomes uniformly non-circular) may occur at a maximum of the angular speed provided the end conditions on the cylinder allow this; (b) axisyim-metric modes may occur before, at or after the angular speed maximum depending on the length of the cylinder and the magnitude of the axial extension; (c) an asymmetric or ‘wobble’ mode is always possible before either (a) or (b) as the angular speed increases from zero for any length of cylinder or axial extension. Moreover, ‘wobble’ occurs at lower angular speeds for longer cylinders.At fixed axial force the results are similar to (a), (b) and (c) except that an axisym-metric mode necessarily occurs between the turning points of the angular speed.

Legendre Spectral Collocation Technique for Advection Dispersion Equations Included Riesz Fractional

2021 ◽  
Vol 6 (1) ◽  
pp. 9
Author(s):  
Mohamed M. Al-Shomrani ◽  
Mohamed A. Abdelkawy
Keyword(s):  
Numerical Methods ◽  
Numerical Algorithm ◽  
Spectral Collocation ◽  
Theoretical Formulation ◽  
Numerical Examples ◽  
Dispersion Equations ◽  
Advection Dispersion ◽  
Collocation Technique ◽  
Collocation Approach

The advection–dispersion equations have gotten a lot of theoretical attention. The difficulty in dealing with these problems stems from the fact that there is no perfect answer and that tackling them using local numerical methods is tough. The Riesz fractional advection–dispersion equations are quantitatively studied in this research. The numerical methodology is based on the collocation approach and a simple numerical algorithm. To show the technique’s performance and competency, a comprehensive theoretical formulation is provided, along with numerical examples.

Stable and Unstable Axisymmetric Solutions for Membranes of Revolution

1989 ◽  
Vol 42 (11S) ◽  
pp. S289-S294 ◽  
Author(s):  
Hubertus J. Weinitschke
Keyword(s):  
Numerical Methods ◽  
Boundary Value Problems ◽  
Boundary Data ◽  
Boundary Value ◽  
Elastic Membrane ◽  
Membrane Theory ◽  
Principal Stresses ◽  
Radial Displacements ◽  
Axisymmetric Solutions ◽  
Nonlinear Elastic

Axisymmetric boundary value problems in nonlinear elastic membrane theory are studied, with prescribed tensile stresses or radial displacements at the edge(s). The membrane of revolution is subjected to a load parallel to the axis or normal to the deformed surface. Analytical and numerical methods are presented to determine the range of boundary data for which the solutions are tensile and stable in the sense that the principal stresses are nonnegative everywhere in the membrane.

Large deformation possible in every isotropic elastic membrane

1977 ◽  
Vol 287 (1341) ◽  
pp. 145-187 ◽  
Keyword(s):  
Strain Energy ◽  
Closed Surface ◽  
Elastic Membrane ◽  
Energy Response ◽  
Normal Surface ◽  
Metric Tensor ◽  
Alternative Description ◽  
Special Cases ◽  
Static Solutions ◽  
Elastic Membranes

This paper is concerned with static solutions of finitely deformed elastic membranes regarded as thin shells. It deals with deformations that can be maintained, in the absence of body force, in every isotropic elastic membrane by the application of edge loads and/or uniform normal surface loads on the major surfaces of the thin shell-like body. The solutions, which are valid for both compressible and incompressible materials, are obtained with the use of a strain energy response function which depends on the metric tensor of the membrane in its deformed configuration. The main results are summarized by several theorems and their corollaries in accordance with three mutually exclusive cases for which the initial undeformed surface of the membrane (which may be a sector of a complete or closed surface) is, respectively, developable, spherical and a surface of variable Gaussian curvature satisfying certain differential criteria. The corresponding deformed surfaces are, respectively, a plane or a right circular cylinder, a sphere and a surface of constant mean curvature. These results are exhaustive in that they represent all finite deformation solutions possible in every isotropic elastic material characterized by the strain energy response mentioned above. Also discussed are some special cases of the general results and several families of solutions in terms of an alternative description which should be useful in application and which permit easy interpretations.

scholarly journals Elastic membranes in confinement

2016 ◽  
Vol 13 (120) ◽  
pp. 20160408 ◽  
Author(s):  
J. B. Bostwick ◽  
M. J. Miksis ◽  
S. H. Davis
Keyword(s):  
Internal Structure ◽  
Parameter Space ◽  
Continuation Methods ◽  
Elastic Membrane ◽  
Two Dimensional ◽  
Membrane Mechanics ◽  
Confinement Pressure ◽  
Elastic Membranes ◽  
Dimensional Shape ◽  
Secondary Bifurcations

An elastic membrane stretched between two walls takes a shape defined by its length and the volume of fluid it encloses. Many biological structures, such as cells, mitochondria and coiled DNA, have fine internal structure in which a membrane (or elastic member) is geometrically ‘confined’ by another object. Here, the two-dimensional shape of an elastic membrane in a ‘confining’ box is studied by introducing a repulsive confinement pressure that prevents the membrane from intersecting the wall. The stage is set by contrasting confined and unconfined solutions. Continuation methods are then used to compute response diagrams, from which we identify the particular membrane mechanics that generate mitochondria-like shapes. Large confinement pressures yield complex response diagrams with secondary bifurcations and multiple turning points where modal identities may change. Regions in parameter space where such behaviour occurs are then mapped.

Numerical Simulation Study of Quasi-Static Loading and Dynamic Loading for Micro Bending Forming of Copper Foil

2016 ◽  
Vol 723 ◽  
pp. 503-511
Author(s):  
Wen Hao Zhang ◽  
Qing Qian ◽  
Zong Bao Shen ◽  
You Juan Ma ◽  
Hui Xia Liu
Keyword(s):  
Numerical Simulation ◽  
Plastic Strain ◽  
Strain Rate ◽  
Dynamic Loading ◽  
Static Loading ◽  
Shock Loading ◽  
Equivalent Plastic Strain ◽  
Plastic Strain Rate ◽  
Laser Shock ◽  
Feature Size

A variety of micro forming processes has been invented, and the size effects have become a research hotspot at home and abroad. Micro bending molds with different feature sizes were designed. Quasi-static tester loading and dynamic laser shock loading with soft punch for micro bending forming was studied by numerical simulation respectively based on ANSYS implicit analysis and LS-DYNA explicit analysis. The constitutive models of workpiece are bilinear kinematic hardening model and Johnson-cook model respectively. The effects of different loading conditions and feature sizes of the die on the forming depth, equivalent plastic strain and equivalent plastic strain rate were studied. The results of numerical simulation show that, with the increasing of feature size of the mold, the forming depth under two kinds of loading conditions shows a tendency to increase. In dynamic laser shock loading, the equivalent plastic strain and equivalent plastic strain rate of the key position of the bent part would decrease with the increasing of the feature size of the die. While in quasi-static loading, the opposite law is shown. The research shows that, the flexible micro-bending processes with different loading models showed similar size effect. However, compared with quasi-static loading, in dynamic loading, the strain of forming parts is more centralized, and there is a high strain rate and better formability of the workpiece.

scholarly journals Displacement flows under elastic membranes. Part 1. Experiments and direct numerical simulations

2015 ◽  
Vol 784 ◽  
pp. 487-511 ◽  
Author(s):  
Draga Pihler-Puzović ◽  
Anne Juel ◽  
Gunnar G. Peng ◽  
John R. Lister ◽  
Matthias Heil
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Theoretical Models ◽  
Navier Stokes ◽  
Elastic Membrane ◽  
Two Phase ◽  
Constant Flow Rate ◽  
Viscous Forces ◽  
Elastic Membranes ◽  
Set Up

The injection of fluid into the narrow liquid-filled gap between a rigid plate and an elastic membrane drives a displacement flow that is controlled by the competition between elastic and viscous forces. We study such flows using the canonical set-up of an elastic-walled Hele-Shaw cell whose upper boundary is formed by an elastic sheet. We investigate both single- and two-phase displacement flows in which the localised injection of fluid at a constant flow rate is accommodated by the inflation of the sheet and the outward propagation of an axisymmetric front beyond which the cell remains approximately undeformed. We perform a direct comparison between quantitative experiments and numerical simulations of two theoretical models. The models couple the Föppl–von Kármán equations, which describe the deformation of the thin elastic membrane, to the equations describing the flow, which we model by (i) the Navier–Stokes equations or (ii) lubrication theory. We identify the dominant physical effects that control the behaviour of the system and critically assess modelling assumptions that were made in previous studies. The insight gained from these studies is then used in Part 2 of this work, where we formulate an improved lubrication model and develop an asymptotic description of the key phenomena.

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