Elastic-Plastic Analysis of Pressurized Cylindrical Shells

1987 ◽  
Vol 54 (3) ◽  
pp. 597-603 ◽  
Author(s):  
G. N. Brooks
Keyword(s):  
Shell Theory ◽  
Plastic Region ◽  
Yield Condition ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Axisymmetric Shell ◽  
Bending Stresses ◽  
Principal Directions ◽  
The Moment ◽  
Thin Shell Theory

Plasticity in shells is often contained near the ends of a segment where the bending stresses are significant. Outside of this local neighborhood the behavior is elastic. Thus, an axisymmetric shell can be divided along its axis into a purely elastic region away from an end and the local region where plasticity is present. The moment-curvature relation in the elastic-plastic region is calculated using the Tresca yield condition. Use of the Tresca yield condition greatly simplifies this derivation because the principal directions are known. This moment-curvature relationship is “exact” in the sense that only the standard assumptions of thin shell theory are made. The solutions of the elastic and plastic regions are matched at their intersection for an efficient numerical solution. The technique is used here to study the semi-infinite clamped cylindrical shell with an internal pressure loading.

Elastic-Plastic Ring-Loaded Cylindrical Shells

1988 ◽  
Vol 55 (4) ◽  
pp. 761-766 ◽  
Author(s):  
Gregory N. Brooks
Keyword(s):  
Axisymmetric Problem ◽  
Shell Theory ◽  
Complete Solution ◽  
Yield Condition ◽  
Plastic Ring ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Small Deflection ◽  
Principal Directions ◽  
Long Cylindrical Shell

The elastic-plastic solution for an infinitely long cylindrical shell with an axisymmetric ring load is presented. Except for the material nonlinearity, the standard assumptions of small deflection shell theory were made. Because the principal directions are known for the axisymmetric problem, the Tresca yield condition wasused. This made it possible to obtain closed-form expressions for the elastic-plastic, moment-curvature relations, greatly simplfying the computational task. The actual stress distribution through the thickness was used, making these relations exact. Yielding was contained near the load. Thus, for the analysis the cylinder was divided along its axis into elastic-plastic and purely elastic regions. Solutions were obtained for each region which were then matched at their intersection to give the complete solution. All results are given in dimensionless form so that they may be applied to any shell.

Finite Elastic-Plastic Expansion of a Cylindrical Tube

1973 ◽  
Vol 2 (4) ◽  
pp. 216-222
Author(s):  
B. Slevinsky ◽  
J. B. Haddow
Keyword(s):  
Plastic Deformation ◽  
Yield Condition ◽  
Cylindrical Tube ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
End Conditions ◽  
Cylindrical Tubes ◽  
Limiting Case ◽  
Plastic Flow Rule

A numerical method for the analysis of the isothermal elastic-plastic expansion, by internal pressure, of cylindrical tubes with various end conditions is presented. The Tresca yield condition and associated plastic flow rule are assumed and both non-hardening and work-hardening tubes are considered with account being taken of finite plastic deformation. Tubes which undergo further plastic deformation on unloading are also considered. Expansion of a cylindrical cavity from zero radius in an infinite medium is considered as a limiting case.

A Piezothermoelastic Thin Shell Theory Applied to Active Structures

1994 ◽  
Vol 116 (3) ◽  
pp. 295-302 ◽  
Author(s):  
H. S. Tzou ◽  
R. V. Howard
Keyword(s):  
High Performance ◽  
Shell Theory ◽  
Piezoelectric Materials ◽  
Electromechanical Properties ◽  
Mechanical Loads ◽  
Active Structures ◽  
Control Electronics ◽  
Principal Directions ◽  
And Control ◽  
Thin Shell Theory

“Smart” structures with integrated sensors, actuators, and control electronics are of importance to the next-generation high-performance structural systems. Piezoelectric materials possess unique electromechanical properties, the direct and converse effects, which, respectively, can be used in sensor and actuator applications. In this study, piezothermoelastic characteristics of piezoelectric shell continua are studied and applications of the theory to active structures in sensing and control are discussed. A generic piezothermoelastic shell theory for thin piezoelectric shells is derived, using the linear piezoelectric theory and Kirchhoff-Love assumptions. It shows that the piezothermoelastic equations, in three principal directions, include thermal induced loads, as well as conventional electric and mechanical loads. The electric membrane forces and moments induced by the converse effect can be used to control the thermal and mechanical loads. A simplification procedure, based on the Lame´ parameters and radii of curvatures, is proposed and applications of the theory to (1) a piezoelectric cylindrical shell, (2) a piezoelectric ring, and (3) a piezoelectric beam are demonstrated.

Elastic-Plastic Analysis of a Spherical Shell Loaded Radially Through a Flexible Cylindrical Nozzle

1990 ◽  
Vol 112 (3) ◽  
pp. 296-302 ◽  
Author(s):  
C.-P. Leung ◽  
G. N. Brooks
Keyword(s):  
Spherical Shell ◽  
Efficient Solution ◽  
Yield Condition ◽  
Geometric Parameters ◽  
Plastic Behavior ◽  
Elastic Plastic ◽  
Cylindrical Nozzle ◽  
Tresca Yield Condition ◽  
Failure Loads ◽  
Range Of Values

This study investigates the elastic-plastic behavior of a shallow spherical shell loaded radially through a flexible cylindrical nozzle. Both the sphere and the cylinder can yield and exhibit plastic deformation. The Tresca yield condition is employed to derive elastic-plastic moment-curvature relationship in a simple form which is implemented in an efficient solution scheme. Three geometric parameters represent the relative dimensions of the structure. Numerical results are obtained for a range of values of these parameters. Various situations involving the failure of the sphere and/or the cylinder are studied. The ultimate or failure loads of the structure are plotted as functions of the geometric parameters.

The Elastic, Plastic Bending of a Simply Supported Plate

1961 ◽  
Vol 28 (3) ◽  
pp. 395-401 ◽  
Author(s):  
G. Eason
Keyword(s):  
Yield Condition ◽  
Constant Load ◽  
Flow Rule ◽  
Plastic Bending ◽  
Simply Supported ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this paper the problem of the elastic, plastic bending of a circular plate which is simply supported at its edge and carries a constant load over a central circular area is considered. The von Mises yield condition and the associated flow rule are assumed and the material of the plate is assumed to be nonhardening, elastic, perfectly plastic, and compressible. Stress fields are obtained in all cases and a velocity field is presented for the case of point loading. Some numerical results are given comparing the results obtained here with those obtained when the Tresca yield condition is assumed.

Elastic-Plastic Analysis of a Radially Loaded Spherical Shell

1989 ◽  
Vol 111 (1) ◽  
pp. 39-46 ◽  
Author(s):  
G. N. Brooks ◽  
C.-P. Leung
Keyword(s):  
Spherical Shell ◽  
Shallow Shell ◽  
Efficient Solution ◽  
Solution Method ◽  
Yield Condition ◽  
Computationally Efficient ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Plastic Analysis ◽  
Infinite Extent

An elastic-plastic analysis of a spherical shell loaded radially through a rigid inclusion is performed. The sphere is modeled as a shallow shell of infinite extent. The Tresca yield condition is used to derive the elastic-plastic moment-curvature relationship in a simple form. This is used to develop a computationally efficient solution method.

The Elastic-Plastic Stress Distribution Within a Wide Curved Bar Subjected to Pure Bending

1955 ◽  
Vol 22 (3) ◽  
pp. 305-310
Author(s):  
Bernard W. Shaffer ◽  
Raymond N. House
Keyword(s):  
Stress Distribution ◽  
Convex Surface ◽  
Plastic Material ◽  
Circumferential Stress ◽  
Yield Condition ◽  
Bending Moment ◽  
Stress Distributions ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Plastic Stress

Abstract Analytical expressions are obtained for the radial and circumferential stress distributions within a wide curved bar made of a perfectly plastic material when it is subjected to a uniformly distributed bending moment. The elastic stress distributions are based on the use of the Airy stress function, whereas the plastic stress distributions in this problem of plane strain are based on the use of the Tresca yield condition. It is found that as the bending moment increases in the direction which tends to straighten the initially curved bar, an elastic-plastic boundary develops first around the concave surface. It meets a second boundary, which starts sometime later around the convex surface, when the bar is completely plastic. The elastic region within the bar decreases at a fairly uniform rate as the bending moment increases to within approximately 90 per cent of the fully plastic bending moment but then it degenerates very much more rapidly until it no longer exists when the bar is completely plastic. The position of the neutral surface is independent of the applied bending moment when the stress distribution is within the completely elastic and the completely plastic ranges. Within the elastic-plastic range, however, it moves away from and then toward the center of curvature as the bending moment increases.

scholarly journals Elastic Simulation of Joints with Particle-Based Fluid

2021 ◽  
Vol 11 (15) ◽  
pp. 6900
Author(s):  
Su-Kyung Sung ◽  
Sang-Won Han ◽  
Byeong-Seok Shin
Keyword(s):  
Principal Stress ◽  
Human Body ◽  
Yield Condition ◽  
Maximum Principal Stress ◽  
Human Motion ◽  
The Difference ◽  
The Moment ◽  
External Forces ◽  
Physical Changes ◽  
Elastic Simulation

Skinning, which is used in skeletal simulations to express the human body, has been weighted between bones to enable muscle-like motions. Weighting is not a form of calculating the pressure and density of muscle fibers in the human body. Therefore, it is not possible to express physical changes when external forces are applied. To express a similar behavior, an animator arbitrarily customizes the weight values. In this study, we apply the kernel and pressure-dependent density variations used in particle-based fluid simulations to skinning simulations. As a result, surface tension and elasticity between particles are applied to muscles, indicating realistic human motion. We also propose a tension yield condition that reflects Tresca’s yield condition, which can be easily approximated using the difference between the maximum and minimum values of the principal stress to simulate the tension limit of the muscle fiber. The density received by particles in the kernel is assumed to be the principal stress. The difference is calculated by approximating the moment of greatest force to the maximum principal stress and the moment of least force to the minimum principal stress. When the density of a particle increases beyond the yield condition, the object is no longer subjected to force. As a result, one can express realistic muscles.

Sign in / Sign up

Export Citation Format

Share Document