Axisymmetric Elastoplasticity of a Temperature-Sensitive Functionally Graded Cylindrical Vessel

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Mojtaba Sadeghian ◽  
Hamid Ekhteraei Toussi
Keyword(s):  
Plastic Material ◽  
Yield Criterion ◽  
Small Deformation ◽  
Functionally Graded ◽  
Cylindrical Vessel ◽  
Linear Functions ◽  
Temperature Sensitive ◽  
Power Functions ◽  
Closed Form Solutions ◽  
Perfectly Plastic

Based on the small deformation theory and Tresca's yield criterion an axisymmetric, plane strain, elastoplastic, thermal stress analysis for a cylindrical vessel made of functionally graded elastic, perfectly plastic material is offered. Elastic modulus and yield strength coefficients are assumed to be power functions of radius and linear functions of temperature. A cylindrical vessel is taken to be composed of two or more nested fully elastic and perfectly plastic cylinders. By comparing the values of the deformation or stress components in the interfaces of the neighboring cylinders, a system of equations is formed. The interfacial boundary values of the fully elastic or perfectly plastic regions are obtained by simultaneous solution of the resulting interfacial consistency conditions. Having prepared the closed form solutions for the stress fields in purely elastic and purely plastic regions, the distribution of stress throughout the vessel can be obtained. Using this model, in some sample problems, the influences of temperature and pressure on the stress, strain, and plastic zone patterns are studied. The location of plastic zones is obtained for a class of material property compositions.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

Dynamic Plastic Response of Circular Plates With Transverse Shear and Rotatory Inertia

1980 ◽  
Vol 47 (1) ◽  
pp. 27-34 ◽  
Author(s):  
Norman Jones ◽  
J. Gomes de Oliveira
Keyword(s):  
Transverse Shear ◽  
Plastic Material ◽  
Yield Criterion ◽  
Circular Plates ◽  
Plastic Response ◽  
Governing Equations ◽  
Rotatory Inertia ◽  
Perfectly Plastic ◽  
Shear Effects ◽  
Transverse Shear Effects

The response of a simply supported circular plate made from a rigid perfectly plastic material and subjected to a uniformly distributed impulsive velocity is developed herein. Plastic yielding of the material is controlled by a yield criterion which retains the transverse shear force as well as bending moments and the influence of rotatory inertia is included in the governing equations. Various equations and numerical results are presented which may be used to assess the importance of transverse shear effects and rotatory inertia for this particular problem.

Limit Design of a Full Reinforcement for a Circular Cutout in a Uniform Slab

1952 ◽  
Vol 19 (3) ◽  
pp. 397-401
Author(s):  
H. J. Weiss ◽  
W. Prager ◽  
P. G. Hodge
Keyword(s):  
Upper Bound ◽  
Plastic Material ◽  
Yield Criterion ◽  
Curved Beam ◽  
Shearing Stress ◽  
Concentric Ring ◽  
Perfectly Plastic ◽  
Circular Cutout

Abstract A thin square slab with a central circular cutout reinforced by a concentric ring is subjected to uniform tensions Tx and Ty on the exterior edges. It is desired to determine the dimensions of the reinforcement if the slab is not to collapse under any load which could be supported by a similar slab without any cutout or reinforcement. It is assumed that the slab and reinforcement are made of a perfectly plastic material which satisfies the Tresca yield criterion of maximum shearing stress, and that the dimensions of the reinforcement are such that it may reasonably be approximated by a curved beam. Under these assumptions, an upper bound on the necessary thickness of the reinforcement for any given radius is obtained. Certain practical limitations of the theory are discussed.

Limit Analysis of Ice Sheet Indentation

1983 ◽  
Vol 105 (3) ◽  
pp. 352-355 ◽  
Author(s):  
D. G. Karr ◽  
S. C. Das
Keyword(s):  
Limit Analysis ◽  
Plastic Material ◽  
Yield Criterion ◽  
Ice Sheet ◽  
Yield Function ◽  
Infinite Layer ◽  
Perfectly Plastic ◽  
Aspect Ratios ◽  
Yield Functions ◽  
Stress Ratios

The methods of plastic limit analysis are used to determine the indentation pressures of a flat rectangular punch on an ice sheet. The ice sheet is idealized as a semi-infinite layer of elastic-perfectly plastic material. Lower bounds are computed by application of the lower bound limit theorem. The suitability of basic yield functions are assessed based on their ability to predict failure at demonstrated ice failure stress ratios. The particular yield functions that are employed include the generalized Mohr-Coulomb (or Drucker-Prager) criterion, a modified Drucker-Prager criterion, as well as a parabolic yield criterion used previously in literature on this topic. A study of the effects on indentation pressure of varying ice strength parameters is presented. Limit analysis solutions are obtained for plane stress conditions, and thus the applicability of a particular yield function can be evaluated for a range of ice strengths for indentation problems involving high aspect ratios.

Numerical Simulation of the Installation and Extraction Process of Spudcan Foundations in Clay

2009 ◽  
Author(s):  
Jun Liu ◽  
Yuxia Hu
Keyword(s):  
Plastic Material ◽  
Yield Criterion ◽  
Strain Analysis ◽  
Small Strain ◽  
Extraction Process ◽  
Interface Roughness ◽  
Large Displacement ◽  
Centrifuge Model Test ◽  
Element Analysis ◽  
Perfectly Plastic

This paper presents results from large displacement finite element analysis for spudcan foundation penetrating into and extracting from normally consolidated (NC) clay. The soil was idealized as an elastic-perfectly plastic material obeying a Mohr-Coulomb yield criterion and the large displacement analysis was carried out using Remeshing and Interpolating Technique with Small Strain (RITSS) model to simulate the full installation and extraction process. The numerical results were compared with centrifuge model test data and existing analytical solutions. A full parametric study was undertaken to quantify the influence on spudcan extraction process from soil strength profile, foundation interface roughness and penetration depth. The extraction results showed that the normalized uplift resistance after spudcan installation was much lower than that from small strain analysis, and it was also lower than that of pre-embedded case. Thus it is necessary to apply RITSS method in spudcan extraction simulation after installation.

Elastic-Plastic Analysis for Functionally Graded Thick-Walled Tube Subjected to Internal Pressure

2016 ◽  
Vol 8 (2) ◽  
pp. 331-352 ◽  
Author(s):  
Libiao Xin ◽  
Guansuo Dui ◽  
Shengyou Yang ◽  
Ying Liu
Keyword(s):  
Internal Pressure ◽  
Yield Criterion ◽  
Functionally Graded ◽  
Power Functions ◽  
Unknown Parameters ◽  
Volume Fractions ◽  
Elastic Plastic ◽  
Graded Material ◽  
Two Phases ◽  
Elastic Plastic Materials

AbstractThe elastic-plastic response of the functionally graded thick-walled tube subjected to internal pressure is investigated by using the relation of the volume average stresses of constituents and the macroscopic stress of composite material in micromechanics. The tube consists of two idealized isotropic elastic-plastic materials whose volume fractions are power functions of the radius. As the internal pressure increases, the deformations of one phase and two phases from elastic to plastic are analyzed. In order to simplify the calculations we assume both materials with the same Poisson's ratio. By using the assumption of a uniform strain field within the representative volume element and the Tresca yield criterion, the theoretical solutions are obtained for the case of two elastic phases and the case of two plastic phases, and the function of the radial displacement is presented for the case with both elastic and plastic phases. The yield criterion of functionally graded material is given in terms of the yield stresses and volume fractions of constituents rather than Young's modulus and yield stress with different unknown parameters of the whole material in the existing papers. Finally we also discuss the position where the plastic deformation first occurs and the conditions for which material first yields in the tube.

The Application of Limit Analysis to Punch-Indentation Problems

1953 ◽  
Vol 20 (4) ◽  
pp. 453-460
Author(s):  
R. T. Shield ◽  
D. C. Drucker
Keyword(s):  
Limit Analysis ◽  
Plane Surface ◽  
Plastic Material ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Flat Punch ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract Limit analysis is applied to obtain upper and lower bounds for the punch pressure in the indentation of the plane surface of an elastic-perfectly plastic material by a flat rigid punch. The two-dimensional flat punch and the three-dimensional flat square and rectangular punch problems are considered. The analysis assumes Tresca’s yield criterion of constant maximum shearing stress k, during plastic deformation. It is shown that the pressure required to produce indentation in the two-dimensional problem lies between 5k and (2 + π)k. The lower bound obtained for any rectangular punch is again 5k while the upper bound for a smooth punch lies between 5.71k for a square and (2 + π)k for a very long rectangle. A value of 5.36k is found for a ratio of length to breadth of 3. The limit pressure for a uniformly loaded area, as distinguished from an area loaded by a punch, is bracketed by 5k and (2 + π)k when the area is convex.

scholarly journals Probability of Exceeding Damage States in Plates Using BEM

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Ernesto Pineda-León ◽  
José Manuel Rosales-Juárez ◽  
Dante Tolentino ◽  
Orlando Susarrey-Huerta
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Plate Theory ◽  
Plastic Material ◽  
Yield Criterion ◽  
Fragility Curves ◽  
Structural Response ◽  
Boundary Integral ◽  
Damage State ◽  
Perfectly Plastic

An approach to obtain fragility curves taking into account the formulation for shear deformable plate theory with combined geometric and material nonlinearities and the boundary element method is proposed. It is assumed that the material undergoes large deflection with small strains. The von Mises yield criterion is used to evaluate the plastic zone and is supposed to have elastic-perfectly plastic material behaviour. An initial stress formulation is used to formulate the boundary integral equations. The domain integrals are evaluated using a cell discretization technique. A total incremental method is applied to solve the nonlinear boundary integral equations. The approach is illustrated in a plate subjected to incremental load. The uncertainties in both geometric and mechanical properties are considered in order to obtain the structural response. Results show that there are high probabilities of exceeding the damage state, d, equal to 0.05 while for the rest of the values of d, these probabilities are low.

Interaction Curves for Circular Cylindrical Shells According to the Mises or Tresca Yield Criterion

1962 ◽  
Vol 29 (2) ◽  
pp. 375-380 ◽  
Author(s):  
P. G. Hodge ◽  
Joseph Panarelli
Keyword(s):  
Cylindrical Shell ◽  
Circular Cylindrical Shell ◽  
Plastic Material ◽  
Yield Criterion ◽  
External Pressure ◽  
Shell Material ◽  
Perfectly Plastic ◽  
Axial Tensile ◽  
Circular Cylindrical Shells ◽  
Interaction Curves

A circular cylindrical shell is subjected to uniform internal or external pressure and a constant axial tensile or compressive stress. The interaction curve constituting load combinations which just cause plastic flow of a rigid/perfectly plastic material depends upon the assumed yield criterion of the shell material. Close bounds on the interaction curve are found when the material yields according to either the Tresca or Mises criterion.

Plane-Strain Compression of a Three Layer Strip Containing Viscoplastic Material with Saturation Stress

2009 ◽  
Vol 623 ◽  
pp. 89-103 ◽  
Author(s):  
Wiktoria Miszuris
Keyword(s):  
Plane Strain ◽  
Plastic Material ◽  
Plane Strain Compression ◽  
Material Structure ◽  
Saturation Stress ◽  
Viscoplastic Material ◽  
Closed Form Solutions ◽  
Layer Material ◽  
Perfectly Plastic ◽  
Friction Surfaces

The plane strain compression of a long symmetric strip consisted of a three layer material between rigid, parallel, rough plates is under consideration. Two possible geometrical configurations of the layers are examined (a) a viscoplastic material is situated between two layers consisting of a rigid/perfectly plastic material, (b) a rigid/perfectly plastic material lies between two viscoplastic layers. It is assumed throughout the paper that the viscoplastic law is bounded in that sense that it reaches its critical value (saturation stress) as the strain rate tends to infinity. Exploiting closed form solutions obtained, qualitative differences between them and the known from literature solutions for three layer material structure with classic viscoplastic material are discussed. Asymptotic behaviour of solutions in the vicinity of maximum friction surfaces is analysed for any configuration.

Sign in / Sign up

Export Citation Format

Share Document