Large-Deformation Theory of Shells of Revolution

1967 ◽  
Vol 34 (1) ◽  
pp. 56-58 ◽  
Author(s):  
W. Flu¨gge ◽  
S-C. Chou
Keyword(s):  
Internal Pressure ◽  
Large Deformation ◽  
Deformation Theory ◽  
Large Deflection ◽  
Small Strain ◽  
Strain Theory ◽  
Large Strains ◽  
Shells Of Revolution ◽  
Elastic Strains ◽  
Theory Of Shells

In this paper, nonlinear membrane equations are derived for a shell of revolution under the assumption that not only are the displacements and rotations large, but that, also, large strains are admitted. The equations, therefore, are aimed at shells which are not only very thin, but which are also made of a material which permits large elastic strains. The special difficulties resulting from this extension of the theory are discussed. As an example for the application of the equations, a circular toroid subjected to internal pressure is studied. Numerical results are given for a level of loading which lies clearly outside the domain of a large-deflection, small-strain theory.

Effect of Large Deformation Analysis for Site Investigation Tool - CPT in Layered Soils

2020 ◽  
Author(s):  
Qiang Xie ◽  
Yuxia Hu ◽  
Mark J. Cassidy
Keyword(s):  
Large Deformation ◽  
Strain Analysis ◽  
Small Strain ◽  
Deformation Analysis ◽  
Large Strains ◽  
Embedment Depth ◽  
Sand Layer ◽  
Clay Layer ◽  
Layered Soils ◽  
Soil Response

Abstract Cone penetration test (CPT) is regularly used during offshore site investigations to interpret soil stratification and soil characteristics due to its continuous penetration resistance profile. However, its use could be improved if better numerical methods to simulate its penetration could be developed. Finite element (FE) analysis, for instance, has the potential to provide insightful information on soil response and soil flow mechanisms. However, it is challenging to simulate CPT in layered soils, as the soil experiences extremely large strains around the cone and the simulation costs are high. In this study, the efficiency of using a partial large deformation FE (LDFE) approach was explored to examine the pre-embedment depth allowed for saving LDFE analysis cost. The LDFE analysis was conducted using the remeshing and interpolation technical with small strain (RITSS) method to model the large strain problem. Both soft-stiff-soft clays and clay-sand-clay soil were considered to study the thin stiff layer effect when it was sandwiched in soft clay. The LDFE/RITSS analysis compared a CPT penetrating from the soil surface with penetrations from a pre-embedded depth above the stiff layer. Pre-embedded small strain analysis was also conducted for comparison. The results show that the small strain analysis underestimated the resistance in both clay and sand. For the partial LDFE analysis with pre-embedment in the top clay layer, the CPT response in the middle stiff clay layer could be well captured regardless of the initial pre-embedment depth. However, for the middle medium dense sand layer (ID = 60%), the pre-embedment depth needs to have sufficient distance above it (10D, D is cone diameter) to capture the soil response in the sand layer correctly.

Analysis of the Novel Strain Responsive Actuators of Silicone Dielectric Elastomer

2008 ◽  
Vol 47-50 ◽  
pp. 298-301 ◽  
Author(s):  
Li Wu Liu ◽  
Jiu Ming Fan ◽  
Zhen Zhang ◽  
Liang Shi ◽  
Yan Ju Liu ◽  
...  
Keyword(s):  
Finite Element ◽  
Electric Field ◽  
Large Deformation ◽  
Deformation Theory ◽  
High Efficiency ◽  
High Energy ◽  
Dielectric Elastomer ◽  
Dielectric Elastomers ◽  
Large Strains ◽  
The Novel

The acrylic acid and silicone are common dielectric elastomer materials. These actuators have shown excellent activate properties including large strains up to 380% and high energy densities up to 3.4 J/g, high efficiency, high responsive speed , good reliability and durability, etc. When a voltage is applied on the compliant electrodes of the dielectric elastomers, the polymer shrinks along with the electric field and expands in the plain area which erects the orientation of the line. In this paper, we synthesize a novel silicone dielectric elastomer with high dielectric constant, large strain and high force output. Pre-strain and certain driving electric field are applied on the novel silicone film, respectively. The strain responsing to the Maxwell stress is measured. Using the large deformation theory of finite element method to simulate the deformable behavior of materials, the simulation results agree with the experiment. The coupling effect of the mechanics and electric fields applied on the electrode of the dielectric elastomers is inverstigated. The finite element simulation of large deformation theory can be used to describe the dielectric elastomers materials large deformation that induced by the static electric field.

Analysis of Large Deformation Wound Roll Models

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
C. Mollamahmutoglu ◽  
J. K. Good
Keyword(s):  
Large Deformation ◽  
Deformation Theory ◽  
Computation Time ◽  
Small Deformation ◽  
Linear Analysis ◽  
Strain Theory ◽  
Metal Foil ◽  
Linear Strain ◽  
Almost All ◽  
Deformation Models

Almost all winding models incorporate the assumption of small linear deformations and strain in their development. These models treat the addition of a layer of web to a winding roll with linear analysis using linear strain theory. Very few winding models have been developed that incorporate large deformation theory although many models treat material nonlinearity. Tissue and nonwoven webs are highly extensible in-plane and highly compressible in the thickness dimension when compared to paper, plastic film, and metal foil webs. Winding models that embody large deformation theory should apply to all web materials. Such models may be wasteful in computation time for web materials such as paper, film, and foils where models that employ small deformation theory may provide sufficient accuracy. This would appear deterministic based upon the extensibility and compressibility of a web material, but the issue becomes more complex due to limitations in tension that can be exerted on the webs. Herein, a large deformation winding model will be developed. Results from this model will be used to benchmark results from other small and large deformation models, and with laboratory test data, a review of all results will be used to determine when or if large deformation winding models are required.

scholarly journals The theory of combined plastic and elastic deformation with particular reference to a thick tube under internal pressure

1947 ◽  
Vol 191 (1026) ◽  
pp. 278-303 ◽  
Keyword(s):  
Stress Distribution ◽  
Internal Pressure ◽  
Plastic Flow ◽  
Plastic Region ◽  
Strain Diagram ◽  
Combined Stresses ◽  
Usual Theory ◽  
Plastic Components ◽  
Longitudinal Extension ◽  
Elastic Strains

In certain problems of plastic flow, for example, a thick tube expanded by internal pressure, it is important to consider changes in the elastic strain of material which is flowing plastically in order to deduce the correct stress distribution and deformation. The usual plastic theory which neglects elastic strains in the plastic region may lead to considerable errors in certain cases. In this paper we review the theory of the deformation of a material under combined stresses which involves both elastic and plastic components of strain. The relationship between stress and strain is represented on a plane diagram, the reduced stress-strain diagram, which facilitates discrimination between the elastic and plastic components of strain and aids considerably the solution of certain problems. The diagram can also be used to express the relationships governing the dissipation of energy during plastic flow under combined stresses. The theory is applied to the deformation of a long thick tube under internal pressure with zero longitudinal extension. The solution is compared with that based on the usual theory which neglects elastic strains in the plastic region, revealing an error which reaches a maxi­mum of over 60% in the longitudinal stress distribution. The significance of the differences between the two solutions is discussed in detail.

The Axisymmetric Deformation of Linearly and Nonlinearly Elastic Spinning Tubes Under End Thrusts and Torques

1998 ◽  
Vol 65 (1) ◽  
pp. 99-106
Author(s):  
T. J. McDevitt ◽  
J. G. Simmonds
Keyword(s):  
Anisotropic Material ◽  
Large Strain ◽  
Axisymmetric Deformation ◽  
Large Strains ◽  
Shells Of Revolution ◽  
Large Rotation ◽  
Elastic Tubes ◽  
Axisymmetric Bending ◽  
Combined Parameters ◽  
Nonlinearly Elastic

We consider the steady-state deformations of elastic tubes spinning steadily and attached in various ways to rigid end plates to which end thrusts and torques are applied. We assume that the tubes are made of homogeneous linearly or nonlinearly anisotropic material and use Simmonds” (1996) simplified dynamic displacement-rotation equations for shells of revolution undergoing large-strain large-rotation axisymmetric bending and torsion. To exploit analytical methods, we confine attention to the nonlinear theory of membranes undergoing small or large strains and the theory of strongly anisotropic tubes suffering small strains. Of particular interest are the boundary layers that appear at each end of the tube, their membrane and bending components, and the penetration of these layers into the tube which, for certain anisotropic materials, may be considerably different from isotropic materials. Remarkably, we find that the behavior of a tube made of a linearly elastic, anisotropic material (having nine elastic parameters) can be described, to a first approximation, by just two combined parameters. The results of the present paper lay the necessary groundwork for a subsequent analysis of the whirling of spinning elastic tubes under end thrusts and torques.

On Stresses in Pipeline Expansion Bellows

1988 ◽  
Vol 110 (2) ◽  
pp. 215-217 ◽  
Author(s):  
A. V. Singh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Procedure ◽  
Circumferential Stress ◽  
Shell Element ◽  
Shells Of Revolution ◽  
Axisymmetric Shell ◽  
Stress Components ◽  
Stress Patterns ◽  
Theory Of Shells

An analytical procedure employing the general theory of shells of revolution and finite element method is presented to examine the stress patterns along the convolution of the pipeline expansion bellows under axial compression. A simple three-node axisymmetric shell element is used to compute axial and circumferential stress components. Three example problems which include two corrugated-pipe-type and one U-type bellows, have been analyzed. Comparison of the present numerical results with the experimentally procured data from the open literature illustrates the reliability, accuracy, elaborateness and versatility of this approach.

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