Application of an Eigenfunction Expansion Method in Plasticity

1974 ◽  
Vol 41 (2) ◽  
pp. 448-452 ◽  
Author(s):  
T. Wierzbicki
Keyword(s):  
Plastic Material ◽  
Expansion Method ◽  
Plastic Behavior ◽  
Sensitive Material ◽  
Rigid Plastic ◽  
Simple Method ◽  
Elastic Mode ◽  
Perfectly Plastic ◽  
Eigenfunction Expansion Method ◽  
Expansion Technique

Possibilities of extending the eigenvalue expansion method to dynamic problems for plastic continua and structures are examined. A model of a pseudo strain rate sensitive material is introduced as an approximation to the concept of rigid-perfectly plastic material. A simple method is then developed which parallels the familiar elastic mode expansion technique but yet retains the main features of rigid-plastic behavior. The accuracy of the method is discussed and comparison with previous theories is made. An illustrative example is presented.

The Estimation of Large Deflections of a Portal Frame Under Asymmetric Pulse Loading

1984 ◽  
Vol 51 (3) ◽  
pp. 494-500 ◽  
Author(s):  
J. L. Raphanel ◽  
P. S. Symonds
Keyword(s):  
Local Deformation ◽  
Elastic Response ◽  
Sensitive Material ◽  
Rigid Plastic ◽  
Finite Element Program ◽  
Perfectly Plastic ◽  
Portal Frame ◽  
Element Program ◽  
Loaded Column ◽  
Asymmetric Pulse

Modifications of a simple elastic-plastic technique [1-4] are shown which allow estimation of local deformation in the loaded column of a portal frame as well as the side-sway deflections of the frame. A wholly elastic response stage provides input to a simplified rigid-plastic solution, in which velocity patterns first of local and then of modal (side-sway) type occur, and which furnishes estimates of final plastic deflections. Maximum (elastic plus plastic) deflections are estimated by adding displacements corresponding to the elastic strain field defined by the stresses of the closing rigid-plastic mode. The method is described for perfectly plastic and for strain-rate sensitive material, and comparisons are shown here with values computed3 for both types of material by a finite element program. Emphasis in this paper is put on the inclusion of elastic and vicoplastic effects.

scholarly journals Rigid plastic plates at large deformations

1985 ◽  
Vol 7 (3) ◽  
pp. 18-23
Author(s):  
Vu Van The
Keyword(s):  
Large Deformations ◽  
Plastic Material ◽  
Plastic Hinge ◽  
Yield Condition ◽  
Rectangular Plates ◽  
Rigid Plastic ◽  
Hinge Line ◽  
Perfectly Plastic ◽  
Relationship Of ◽  
Line Patterns

The method developed in [8] is applied herein in order to obtain estimations of the load-deflection relationship of the hinge supported rectangular plates acted on by a uniformly distributed loading. The plate is made from rigid perfectly plastic material which yields according to the square yield condition and maximum normal yield condition. the plastic hinge line patterns shown  in figs. 1. 2. are chosen. The obtained results are presented in figs. 4, 5, 6, 8.

Mathematical Modeling of Large-Amplitude Dynamic-Plastic Behavior of Circular Plates Subjected to Impulsive Loads

2010 ◽  
Vol 26 (4) ◽  
pp. 533-546 ◽  
Author(s):  
Asghar Zajkani ◽  
Hamidreza Sefidi Shirkoohi ◽  
Abolfazl Darvizeh ◽  
Mansour Darvizeh ◽  
Hashem Ghareh Babaei
Keyword(s):  
Large Amplitude ◽  
Plastic Material ◽  
Mathematical Formulation ◽  
Energy Functional ◽  
Plastic Behavior ◽  
Transverse Displacement ◽  
Circular Plates ◽  
Displacement Fields ◽  
Perfectly Plastic ◽  
Short Time

ABSTRACTIn this paper, an analysis of the large-amplitude dynamic-plastic behavior of the circular plates with a rigid perfectly plastic material is presented. The plate is subjected to a short-time high-intensity impulsive load uniformly distributed over the surface. Modeling is complemented by using specific convex yield criteria. Corresponding to boundary conditions of the plate, it can be deformed through more than one mechanism, so, the mathematical formulation is based on the principle of calculus of variations in which the transverse displacement fields are assumed as a combination of appropriate paths. Based on the upper bound approach, the different terms of kinetic and consumed plastic energies likewise the applied impulse energy derived to produce an energy functional with unknown coefficients which is minimized through the displacement path. Finally, calculating the constants maximum residual deflection and strain distribution are obtained. Results of present model show satisfactory correlation with the empirical data for the different levels of the pulsed loads.

Numerical Study of Defect Free Elbows Subjected to In-Plane Bending Moment

2011 ◽  
Vol 189-193 ◽  
pp. 1494-1497
Author(s):  
Wang Chen ◽  
Yin Pei Wang ◽  
Pei Ning Li ◽  
Chen Jin ◽  
Xiao Ming Sun
Keyword(s):  
Numerical Study ◽  
Plastic Material ◽  
Three Dimensional ◽  
Bending Moment ◽  
Plastic Behavior ◽  
Piping System ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Bending Radius ◽  
Elastic Perfectly Plastic

Elbow is a type of components widely used in a piping system, and so it is very important to know the plastic carrying capacity of elbow. In this study, the elastic-plastic behavior of elbows with various ratios of t/rm and relative bending radius R/rm were investigated in detail by using of three-dimensional (3D) non-linear finite element (FE) analyses, assuming elastic-perfectly-plastic material behaviour and taking geometric nonlinearity into account. The analyses indicated that elbow exhibited different behavior obviously at the elastic-plastic states subjected to In-Plane opening bending moment and closing bending moment. The closed form equations of elbow involving effect of tangent pipes were established.

Analytical Modeling of Hydraulically Expanded Tube-to-Tubesheet Joints

2007 ◽  
Author(s):  
Nor Eddine Laghzale ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Contact Pressure ◽  
Analytical Modeling ◽  
Plastic Material ◽  
Material Behavior ◽  
Plastic Behavior ◽  
Initial Contact ◽  
Expansion Process ◽  
Perfectly Plastic ◽  
Reliable Assessment ◽  
Elastic Perfectly Plastic

The loss of the initial tightness during service is one of the major causes of failure of tube-to-tubesheet joints. The initial residual contact pressure and its variation during the lifetime of the joint is among the parameters to blame. A reliable assessment of the initial contact pressure value requires accurate and rigorous modeling of the elasto-plastic behavior of the tube and the tubesheet during the expansion process. This paper deals with the development of a new analytical model used to accurately predict the residual contact pressure resulting from a hydraulic expansion process. It is based on the elastic perfectly plastic material behavior of the tube and the tubesheet and the interaction between them. The model results have been compared and validated with those of the more accurate numerical FEA models. Additional comparisons have been made with existing methods.

Interaction of Pressure, End Load, and Twisting Moment for a Rigid-Plastic Circular Tube

1963 ◽  
Vol 30 (3) ◽  
pp. 396-400 ◽  
Author(s):  
Joseph E. Panarelli ◽  
Philip G. Hodge
Keyword(s):  
Circular Cylinder ◽  
Shell Theory ◽  
Circular Tube ◽  
Plastic Material ◽  
Rigid Plastic ◽  
End Effects ◽  
Perfectly Plastic ◽  
Special Cases ◽  
Interaction Surface

A thick-walled circular cylinder acted on by pressure, axial end load, and twisting moment is analyzed under the assumption that end effects are negligible. The locus of all load points (interaction surface) for which unaccelerated flow of a perfectly plastic material can occur is found parametrically. Certain special cases are considered and the results compared with those of shell theory.

scholarly journals Rigid-Plastic Approximations for Predicting Plastic Deformation of Cylindrical Shells Subject to Dynamic Loading

1996 ◽  
Vol 3 (3) ◽  
pp. 169-181 ◽  
Author(s):  
Michelle S. Hoo Fatt ◽  
Tomasz Wierzbicki ◽  
Minos Moussouros ◽  
John Koenig
Keyword(s):  
Plastic Deformation ◽  
Tensile Force ◽  
Bending Moment ◽  
Expansion Method ◽  
Rigid Plastic ◽  
Closed Form Solutions ◽  
Eigenfunction Expansion Method ◽  
Longitudinal Bending ◽  
Final Deformation ◽  
String State

A theoretical approach was developed for predicting the plastic deformation of a cylindrical shell subject to asymmetric dynamic loads. The plastic deformation of the leading generator of the shell is found by solving for the transverse deflections of a rigid-plastic beam/string-on-foundation. The axial bending moment and tensile force in the beam/string are equivalent to the longitudinal bending moments and membrane forces of the shell, while the plastic foundation force is equivalent to the shell circumferential bending moment and membrane resistances. Closed-form solutions for the transient and final deformation profile of an impulsive loaded shell when it is in a “string” state were derived using the eigenfunction expansion method. These results were compared to DYNA 3D predictions. The analytical predictions of the transient shell and final centerline deflections were within 25% of the DYNA 3D results.

scholarly journals A new displacement bound technique for rigid plastic continua subjectet to strong dynamic loading at large deflections II.

1987 ◽  
Vol 9 (3) ◽  
pp. 23-30
Author(s):  
Vu Van The ◽  
Tran Ba Tinh
Keyword(s):  
Space Variable ◽  
Shape Function ◽  
Plastic Material ◽  
Yield Condition ◽  
Time Function ◽  
Rigid Plastic ◽  
Perfectly Plastic ◽  
Previous Solution ◽  
Admissible Displacement ◽  
Strong Dynamic

The method developed in [ 1] is applied herein in order to obtain lower hound to large displacements of the hinge supported circular plate acted on by impulsively, uniformly distributed loading. The plate is made from rigid and perfectly plastic material which yields according to the yield condition shown in fig- 1· The lower bound (1.21) is obtained when the dynamically admissible displacement and velocity are chosen in separated variable form which is a scalar time function multiplied by a vector shape function of space variable (1.13). In the case when W, Ẇ * are chosen in form (1.22). [comparison of the obtained estimate Eq (1.24) with previous solution of the same problem [1], upper bound [2] and experimental date [3] are presented in fig. 2

scholarly journals Plastic forming processes of transverse non-homogeneous composite metallic sheets

2021 ◽  
Vol 11 (1) ◽  
pp. 294-302
Author(s):  
Gal Davidi
Keyword(s):  
Inner Core ◽  
Plastic Material ◽  
Radial Solution ◽  
Algebraic Differential Equation ◽  
Forming Process ◽  
Perfectly Plastic ◽  
Plastic Forming ◽  
Validity Limit ◽  
Significant Achievement

Abstract In this work an analysis of the radial stress and velocity fields is performed according to the J 2 flow theory for a rigid/perfectly plastic material. The flow field is used to simulate the forming processes of sheets. The significant achievement of this paper is the generalization of the work by Nadai & Hill for homogenous material in the sense of its yield stress, to a material with general transverse non-homogeneity. In Addition, a special un-coupled form of the system of equations is obtained where the task of solving it reduces to the solution of a single non-linear algebraic differential equation for the shear stress. A semi-analytical solution is attained solving numerically this equation and the rest of the stresses term together with the velocity field is calculated analytically. As a case study a tri-layered symmetrical sheet is chosen for two configurations: soft inner core and hard coating, hard inner core and soft coating. The main practical outcome of this work is the derivation of the validity limit for radial solution by mapping the “state space” that encompasses all possible configurations of the forming process. This configuration mapping defines the “safe” range of configurations parameters in which flawless processes can be achieved. Several aspects are researched: the ratio of material's properties of two adjacent layers, the location of layers interface and friction coefficient with the walls of the dies.

The Quasi-Static Analysis for Two-Dimensional Thin Plates

2011 ◽  
Vol 255-260 ◽  
pp. 166-169
Author(s):  
Li Chen ◽  
Yang Bai
Keyword(s):  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Solution Space ◽  
Expansion Method ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Elastic Plates ◽  
Various Boundary Conditions ◽  
Eigenfunction Expansion Method ◽  
Concentration Phenomena

The eigenfunction expansion method is introduced into the numerical calculations of elastic plates. Based on the variational method, all the fundamental solutions of the governing equations are obtained directly. Using eigenfunction expansion method, various boundary conditions can be conveniently described by the combination of the eigenfunctions due to the completeness of the solution space. The coefficients of the combination are determined by the boundary conditions. In the numerical example, the stress concentration phenomena produced by the restriction of displacement conditions is discussed in detail.

Sign in / Sign up

Export Citation Format

Share Document