Causes and Consequences of Nonuniqueness in an Elastic/Perfectly-Plastic Truss

1986 ◽  
Vol 53 (2) ◽  
pp. 235-241 ◽  
Author(s):  
P. G. Hodge ◽  
K.-J. Bathe ◽  
E. N. Dvorkin
Keyword(s):  
Plastic Deformation ◽  
Plastic Material ◽  
Complete Solution ◽  
Physical Modelling ◽  
Equilibrium Equations ◽  
First Order ◽  
Perfectly Plastic ◽  
Points Of View ◽  
Elastic Perfectly Plastic

A complete solution to collapse is given for a three-bar symmetric truss made of an elastic/perfectly-plastic material, using linear statics and kinematics, and the solution is found to be partially nonunique in the range of contained plastic deformation. The introduction of a first-order deviation from symmetry and/or the inclusion of first-order nonlinear terms in the equilibrium equations is found to restore uniqueness. The significance of these effects is analyzed and discussed from mathematical, physical, modelling, computational, and engineering points of view.

scholarly journals GBT-Based Elastic-Plastic Analysis of Cold-Formed Steel Members

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Nuno Silvestre
Keyword(s):  
Plastic Material ◽  
Beam Theory ◽  
Mapping Algorithm ◽  
First Order ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Return Mapping ◽  
Steel Members ◽  
Shell Finite Element ◽  
Elastic Perfectly Plastic

This paper presents a formulation of Generalised Beam Theory (GBT) intended to perform thorough first-order elastic-plastic analyses of thin-walled members subjected to arbitrary deformations and made of an isotropic non-linear material. The J2-flow theory is used to model plasticity in conjunction with the Euler-Backward return-mapping algorithm. After presenting the formulation, its application is illustrated by means of the first order analysis of a simply supported Z-section beam made of an elastic-perfectly plastic material (e.g., carbon steel) and acted by a load uniformly distributed along the flanges. The set of GBT-based results comprises the load-deflection curves (equilibrium paths), displacement profiles, stress distributions (diagrams and 3D contours), and deformed shapes (modal amplitude functions and 3D configurations). These results are compared with the ones obtained from shell finite element analyses (SFEA) using ABAQUS. It is seen that the GBT results display a very good agreement with the SFEA values.

scholarly journals First order elastoplastic GBT analysis of tubular beams

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Nuno Silvestre
Keyword(s):  
Plastic Material ◽  
Beam Theory ◽  
Hollow Section ◽  
Mapping Algorithm ◽  
First Order ◽  
Perfectly Plastic ◽  
Return Mapping ◽  
Return Mapping Algorithm ◽  
Elastic Perfectly Plastic ◽  
Abaqus Code

This paper aims to present an original formulation of Generalised Beam Theory (GBT) intended to perform first order elastoplastic analysis of thin-walled members, made of isotropic non-linear material and subjected to arbitrary deformation. The J2-flow theory is used to model plasticity in conjunction with the Euler-Backward return-mapping algorithm. After presenting the formulation, its application is illustrated by means of the first order analysis of beams with (i) rectangular hollow section (RHS) and (ii) LiteSteel section, made of an elastic-perfectly plastic material and subjected to distributed and point loading, respectively. The GBT results, which include equilibrium paths, displacement profiles, stress diagrams, 3D stress/displacement con-tours and deformed shapes, are compared with the ones obtained by ABAQUS code using a shell finite ele-ment model. GBT and ABAQUS results display a very good agreement.

Elastic-Plastic State of Inhomogeneous Soil Array with a Spherical Cavity

2013 ◽  
Vol 842 ◽  
pp. 462-465 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Anatoliy S. Avershyev ◽  
Stanislaw Jemiolo
Keyword(s):  
Plastic Deformation ◽  
Outer Surface ◽  
Spherical Cavity ◽  
Plastic Material ◽  
Plastic State ◽  
Cavity Model ◽  
Limit Loads ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The article deals with the elastic-plastic state of inhomogeneous array with a spherical cavity. Model is used thick-walled ball of an elastic-perfectly plastic material (Prandtl diagram). It is shown that in the inhomogeneous material, depending on the inhomogeneity functions describing the change of the modulus of elasticity and yield stress of soil plastic deformation may appear on both the inner and outer surface of the ball and inside it. Are found values of the limit loads, displacement diagrams are constructed in an array.

On the Conditions to Prevent Plastic Shakedown of Structures: Part I—Theory

1993 ◽  
Vol 60 (1) ◽  
pp. 15-19 ◽  
Author(s):  
Castrenze Polizzotto
Keyword(s):  
Mechanical Load ◽  
Plastic Material ◽  
Perfectly Plastic ◽  
Shakedown Theory ◽  
Elastic Perfectly Plastic ◽  
Plastic Shakedown ◽  
Steady Load

For a structure of elastic perfectly plastic material subjected to a given cyclic (mechanical and/or kinematical) load and to a steady (mechanical) load, the conditions are established in which plastic shakedown cannot occur whatever the steady load, and thus the structure is safe against the alternating plasticity collapse. Static and kinematic theorems, analogous to those of classical shakedown theory, are presented.

Elasto-Plastic Coupled Temperature-Displacement Finite Element Analysis of Two-Dimensional Rolling-Sliding Contact With a Translating Heat Source

1991 ◽  
Vol 113 (1) ◽  
pp. 93-101 ◽  
Author(s):  
S. M. Kulkarni ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Plastic Material ◽  
Element Model ◽  
Rolling Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Element Mesh ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper, describes a transient translating elasto-plastic thermo-mechanical finite element model to study 2-D frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a non-uniform thermo-mechanical distribution across the surface of an elasto-plastic half space. The half space is represented by a two dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermo-physical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on 1) the temperature gradients and 2) the magnitudes of the normal and tangential tractions.

Crushing of an Elastic-Perfectly Plastic Ring or Tube Between Two Planes

1987 ◽  
Vol 54 (1) ◽  
pp. 159-164 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Plastic Deformation ◽  
Numerical Integration ◽  
Mathematical Problem ◽  
Plastic Ring ◽  
Perfectly Plastic ◽  
Analytical Approximations ◽  
Original Shape ◽  
Thin Ring ◽  
Elastic Perfectly Plastic

A thin ring is crushed between two rigid planes. Due to plastic deformation the ring does not recover its original shape when the compression is removed. For an elastic-perfectly plastic flexural material, the ring undergoes two to five different stages. The mathematical problem is formulated and solved by exact numerical integration and accurate analytical approximations.

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.

Effect of Core Plasticity on the Post-Buckling Behavior of Debonded Sandwich Beams

2000 ◽  
Author(s):  
Bhavani V. Sankar ◽  
Manickam Narayanan ◽  
Abhinav Sharma
Keyword(s):  
Plastic Material ◽  
Maximum Load ◽  
Face Sheet ◽  
Compression Tests ◽  
Element Analysis ◽  
The Core ◽  
Perfectly Plastic ◽  
The Face ◽  
Post Buckling ◽  
Elastic Perfectly Plastic

Abstract Nonlinear finite element analysis was used to simulate compression tests on sandwich composites containing debonded face sheets. The core was modeled as an elastic-perfectly-plastic material, and the face-sheet as elastic isotropic. The effects of core plasticity, face-sheet and core thickness, and debond length on the maximum load the beam can carry were studied. The results indicate that the core plasticity is an important factor that determines the maximum load.

Stresses and Displacements in an Elastic-Plastic Wedge

1957 ◽  
Vol 24 (1) ◽  
pp. 98-104
Author(s):  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Isotropic Material ◽  
Complete Solution ◽  
Normal Pressure ◽  
Stress Strain ◽  
Included Angle ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Domain ◽  
Elastic Perfectly Plastic

Abstract An elastic, perfectly plastic wedge of an incompressible isotropic material in the state of plane strain is considered, where the stress-strain relations of Prandtl-Reuss are employed in the plastic domain. For a wedge (with an included angle β) subjected to a uniform normal pressure on one boundary, the complete solution is obtained which is valid in the range 0 < β < π/2; this latter limitation is due to the character of the initial yield which depends on the magnitude of β. Numerical results for stresses and displacements are given in one case (β = π/4) for various positions of the elastic-plastic boundary.

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