Elastoplastic analytical solution of circular ring expansion problem for bi-modulus material based on SMP yield criterion

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Tianmin Wang ◽  
Jianhong Ye
Keyword(s):  
Analytical Solution ◽  
Yield Criterion ◽  
Ring Expansion ◽  
Circular Ring

scholarly journals Analytical solution for torsion of cylindrical orthotropic annular wedge-shaped bars reinforced by thin shells

2021 ◽  
Author(s):  
István Ecsedi ◽  
Attila Baksa
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Analytical Method ◽  
Torsional Rigidity ◽  
Circular Ring ◽  
Thin Shells ◽  
Elastic Wedge ◽  
Curved Boundary ◽  
Cylindrically Orthotropic ◽  
Boundary Surfaces

AbstractThis paper deals with the Saint-Venant torsion of elastic, cylindrically orthotropic bar whose cross section is a sector of a circular ring shaped bar. The cylindrically orthotropic homogeneous elastic wedge-shaped bar strengthened by on its curved boundary surfaces by thin isotropic elastic shells. An analytical method is presented to obtain the Prandtl’s stress function, torsion function, torsional rigidity and shearing stresses. A numerical example illustrates the application of the developed analytical method.

An Analytical Solution to Metal Plane Problem in Terms of Orthotropic Anisotropy and Strain Hardening

2010 ◽  
Vol 97-101 ◽  
pp. 348-356
Author(s):  
Yao He Liu ◽  
Guo Feng Yi ◽  
Jian Ming Xiong
Keyword(s):  
Stress State ◽  
Analytical Solution ◽  
Plane Stress ◽  
Yield Criterion ◽  
Research Result ◽  
Yield Condition ◽  
Plane Stress State ◽  
Yield Function ◽  
Anisotropic Parameter ◽  
Symmetric Plane

In this paper, the yield condition of Hill’s orthotropic yield criterion under axial symmetric plane stress state was discussed. The yield function of orthotropic material was proposed and the analytical solution to meet the condition of equations of equilibrium and compatibility under axial symmetric plane stress state is obtained, in which the conditions of power hardening materials was considered. The research result indicates that hardening coefficient and anisotropic parameter have substantial influence over stress and strain. However, in the presence of the coefficient R90=H/F，the influence appears to be quite weak.

Limit Load Solutions of the Orthotropic Thick-Walled Pipe Subjected to Internal Pressure, Bending Moment and Torsion Moment

2019 ◽  
Author(s):  
Min Xu ◽  
Yujie Zhao ◽  
Binbin Zhou ◽  
Xiaohua He ◽  
Changyu Zhou
Keyword(s):  
Analytical Solution ◽  
Yield Strength ◽  
Internal Pressure ◽  
Yield Criterion ◽  
Bending Moment ◽  
Limit Load ◽  
Pure Bending ◽  
Pure Torsion ◽  
Torsion Moment ◽  
The Difference

Abstract Based on the Hill yield criterion, the analytical solutions of the limit load of orthotropic thick-walled pipes under pure internal pressure, bending moment and torsion are given respectively. The simplified Mises analytical solution and finite element results of limit load for isotropic thick-walled pipe are obtained. The solution verifies the reliability of the analytical solution. The paper discusses the difference of limit load of isotropic and orthotropic pipes under the conditions of pure internal pressure, pure bending moment and pure torsion moment. It is concluded that the influence of material anisotropy on the limit load is significant. The limit load of pipe under pure internal pressure is mainly determined by circumferential yield strength, pure bending is only related to axial yield strength and pure torsion moment is related to the yield strength in the 45° direction and radial yield strength.

Analytical Solution for Strain Gradient Plasticity of Rotating Functionally Graded Thick Cylinders

2020 ◽  
Vol 12 (07) ◽  
pp. 2050082
Author(s):  
Saeid Varmazyari ◽  
Hassan Shokrollahi
Keyword(s):  
Analytical Solution ◽  
Strain Gradient ◽  
Yield Criterion ◽  
External Pressure ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Gradient Plasticity ◽  
Elastic Plastic ◽  
Von Mises

The elastic-plastic deformation of rotating functionally graded (FG) cylinders is investigated based on strain gradient theory. The governing equations are obtained based on the modified von Mises yield criterion, linear work hardening and plane strain assumptions. An analytical solution for the obtained equations is presented by which the deformation, strain and stress components for any point of the cylinder can be obtained. After verification of the formulation by comparing the obtained results with the reported results in the literature, some studies are presented to investigate the effects of cylinder size on the stress distribution and elastic-plastic interface radius of the rotating FG cylinder under internal and external pressure. The effects of the strain gradient coefficient, angular velocity, and the heterogeneity constant of the material are investigated. The results show that increasing the heterogeneity constant of the material and decreasing the cylinder radius lead to increasing the strength of material and decreasing the elastic-plastic interface radius. Moreover, classical theory is compared with this study and the range of the sizes in which both the theories leading to the same results, are defined.

The Triple-Shear Unified Analytical Solution of Stress and Displacement of Softening Material Thick Walled Cylinder

2012 ◽  
Vol 204-208 ◽  
pp. 4437-4442
Author(s):  
Jing Huai Ma
Keyword(s):  
Analytical Solution ◽  
Internal Pressure ◽  
Yield Criterion ◽  
Lode Parameter ◽  
Reasonable Solution ◽  
Softening Material ◽  
Walled Cylinder

Based on the further analysis to triple-shear unified yield criterion, the Lode parameter expression of the triple-shear unified yield criterion were given. This paper performs the analysis computation to softening material thick-walled cylinder under internal pressure based on triple-shear unified yield criterion. The analytical solution of stress and displacement is obtained. By using triple-shear unified yield criterion, more reasonable solution for different softening material can be derived.

A New Analytical Solution for Optimum Design of Shrink-Fit Multi-Layer Compound Cylinders

2012 ◽  
Author(s):  
Mojtaba Sharifi ◽  
M. R. Hematiyan ◽  
Roshanak Banan
Keyword(s):  
Analytical Solution ◽  
Optimum Design ◽  
Analytical Method ◽  
Yield Criterion ◽  
Optimization Method ◽  
Shear Stresses ◽  
Layer Compound ◽  
Shrink Fitting ◽  
Shrink Fit ◽  
Contact Pressures

In this paper, by using an analytical optimization method, formulas for general optimum design of multi-layer compound cylinders are presented. For this purpose, considering the Tresca’s yield criterion, the maximum shear stresses occurred simultaneously in inner radiuses of all layers, are minimized. The formulas for obtaining optimum values of layers radiuses, contact pressures, and radial interferences are derived. A technique for shrink-fitting of cylinders is also described and relationships for radial interferences and required temperature differences between cylinders for each step of the shrink-fitting process are derived using an analytical method. It is indicated that compound cylinders with more layers have higher internal pressure capacity for a specified weight. Three different examples are presented to show the effectiveness of the method.

scholarly journals ANALYZING THE SPHERICAL CAVITY EXPANSION PROBLEM IN A MEDIUM WITH MOHR − COULOMB − TRESCA'S PLASTICITY CONDITION

2019 ◽  
Vol 81 (3) ◽  
pp. 292-304 ◽  
Author(s):  
V.L. Kotov ◽  
D.B. Timofeev
Keyword(s):  
Plastic Deformation ◽  
Analytical Solution ◽  
Spherical Cavity ◽  
Yield Criterion ◽  
Closed Form Solution ◽  
Cavity Expansion ◽  
Plasticity Condition ◽  
Rigid Plastic ◽  
Tangential Stresses ◽  
Shockwave Front

An analytical solution of the one-dimensional problem of a spherical cavity expanding at a constant velocity from a point in a space occupied by a plastic medium has been obtained. Impact compressibility of the medium is described using linear Hugoniot's adiabat. Plastic deformation obeys the Mohr - Coulomb yield criterion with constraints on the value of maximum tangential stresses according to Tresca's criterion. In the assumption of rigid-plastic deformation (the elastic precursor being neglected), incompressibility behind the shockwave front and the equality of the propagation velocities of the fronts of the plastic wave and the plane shockwave defined by linear Hugoniot's adiabat, a boundary-value problem for a system of two first-order ordinary differential equations for the dimensionless velocity and stress depending on the self-similar variable is formulated. A closed-form solution of this problem has been obtained in the form of a stationary running wave - a plastic shockwave propagating in an unperturbed half-space. This solution is a generalization of the earlier obtained analytical solution for a medium with the Mohr - Coulomb plasticity condition. The effect of constraining the limiting value of maximal tangential stresses on the distribution of dimensionless stresses behind the shockwave front has been examined. Formulas for determining the range of cavity expansion velocities, within which a simple solution for a medium with Tresca's plasticity condition is applicable, have been derived. The obtained solution can be used for evaluating resistance to high-velocity penetration of rigid strikers into low-strength soil media.

Analytical Solution for Elastic and Elastoplastic Bending of a Curved Beam Composed of Inhomogeneous Materials

2013 ◽  
Vol 535-536 ◽  
pp. 353-356 ◽  
Author(s):  
Guo Jun Nie ◽  
Zheng Zhong
Keyword(s):  
Stress State ◽  
Analytical Solution ◽  
Numerical Solutions ◽  
Yield Criterion ◽  
Flow Rule ◽  
Curved Beam ◽  
Power Functions ◽  
Inhomogeneous Materials ◽  
Elastoplastic Behavior ◽  
Elastoplastic Bending

We present an analytical solution for elastic and elastoplastic bending problem of a curved beam composed of inhomogeneous materials. Suppose the material is isotropic, ideally elastoplastic and it obeys Tresca’s yield criterion and the corresponding associated flow rule. And the elastic modulus and yield limit of the material vary radially according to general power functions. The expressions of stresses and displacements of a curved beam in both purely elastic stress state and partially plastic stress state are derived. The influence of material inhomogeneity on the elastoplastic behavior of a curved beam is demonstrated in numerical examples. Analytical solutions presented here can serve as benchmark results for evaluating numerical solutions.

Analytical Solution for the Large Deflection of Fully Clamped Metallic Foam Sandwich Beam

2008 ◽  
Vol 33-37 ◽  
pp. 559-566 ◽  
Author(s):  
Qing Hua Qin ◽  
Tie Jun Wang
Keyword(s):  
Analytical Solution ◽  
Large Deflection ◽  
Yield Criterion ◽  
Sandwich Beam ◽  
Metallic Foam ◽  
Concentrated Load ◽  
Core Strength ◽  
Load Carrying ◽  
Axial Stretching ◽  
Geometrical Dimensions

A unified yield criterion is proposed in this paper, which is valid for the metallic sandwich sections with various core strength and geometrical dimensions and can reduce to the classical yield criteria for solid monolithic section and sandwich section with weak core, respectively. Then, the unified yield criterion is used to derive the analytical solution for the large deflection of fully clamped metallic sandwich beam subject to a transversely concentrated load, in which the interaction of bending and stretching is considered. Comparisons of the present solutions with experimental results are carried out and good agreements are found. It is seen that the axial stretching induced by large deflection has a significant effect on the deflection of sandwich structure in the post-yield regime, and the load carrying capacity of metallic foam core sandwich beam may be underestimated as the core strength is neglected in analysis.

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