On an Extremum Principle for Mode Form Solutions in Plastic Structural Dynamics

1975 ◽  
Vol 42 (3) ◽  
pp. 630-640 ◽  
Author(s):  
P. S. Symonds ◽  
T. Wierzbicki
Keyword(s):  
Structural Dynamics ◽  
Yield Function ◽  
Velocity Fields ◽  
Extremum Principle ◽  
Material Behavior ◽  
Structure Model ◽  
Discrete Structure ◽  
First Variation ◽  
Admissible Velocity ◽  
Perfectly Plastic

An extremum principle of Lee and Martin [2], for mode form solutions of a structure deforming plastically as result of dynamic loading, is discussed with special reference to conditions for the extrema to be stationary, with vanishing first variation of a functional of kinematically admissible velocity fields. Three classes of material behavior are treated: rigid-perfectly plastic, rigid-viscoplastic, and viscous, the last having no yield function. We illustrate various forms of these which are realistic as well as convenient in problems of plastic dynamics of structures. For all three classes of material, we show that stationary extrema occur under certain conditions, but may be regarded as exceptional. The properties of the extrema for structures are illustrated by means of a simple discrete structure model with two masses.

A General Solution for the Pressurized Elastoplastic Tube

1992 ◽  
Vol 59 (1) ◽  
pp. 20-26 ◽  
Author(s):  
David Durban ◽  
Michael Kubi
Keyword(s):  
General Solution ◽  
Finite Strain ◽  
Cylindrical Tube ◽  
Yield Function ◽  
Material Behavior ◽  
Deformation Pattern ◽  
Perfectly Plastic ◽  
Plastic Phase ◽  
Thin Walled ◽  
Elastic Perfectly Plastic

The problem of a thick-walled cylindrical tube subjected to internal pressure is investigated within the framework of continuum plasticity. Material behavior is modeled by a finite strain elastoplastic flow theory based on the Tresca yield function. The deformation pattern is restricted by the plane-strain condition but arbitrary hardening and elastic compressibility are accounted for. A general solution is given in terms of quadratures. The analysis also includes treatment of a second plastic phase, characterized by corner relations, that may develop at the inner boundary. It is shown that the interface between the two plastic regions moves initially outwards and then, beyond a certain strain level, it moves back inwards. Some useful and simple results are given for thin-walled tubes of hardening materials and for thick-walled elastic/perfectly plastic tubes.

Shakedown Limit Load Determination for a Kinematically Hardening 90-Degree Pipe Bend Subjected to Constant Internal Pressure and Cyclic Bending

2007 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Plastic Material ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Material Behavior ◽  
Pipe Bend ◽  
Cyclic Bending ◽  
Perfectly Plastic ◽  
Shakedown Limit

A simplified technique for determining the shakedown limit load of a structure employing an elastic-perfectly-plastic material behavior was previously developed and successfully applied to a long radius 90-degree pipe bend. The pipe bend is subjected to constant internal pressure and cyclic bending. The cyclic bending includes three different loading patterns namely; in-plane closing, in-plane opening, and out-of-plane bending moment loadings. The simplified technique utilizes the finite element method and employs small displacement formulation to determine the shakedown limit load without performing lengthy time consuming full cyclic loading finite element simulations or conventional iterative elastic techniques. In the present paper, the simplified technique is further modified to handle structures employing elastic-plastic material behavior following the kinematic hardening rule. The shakedown limit load is determined through the calculation of residual stresses developed within the pipe bend structure accounting for the back stresses, determined from the kinematic hardening shift tensor, responsible for the translation of the yield surface. The outcomes of the simplified technique showed very good correlation with the results of full elastic-plastic cyclic loading finite element simulations. The shakedown limit moments output by the simplified technique are used to generate shakedown diagrams of the pipe bend for a spectrum of constant internal pressure magnitudes. The generated shakedown diagrams are compared with the ones previously generated employing an elastic-perfectly-plastic material behavior. These indicated conservative shakedown limit moments compared to the ones employing the kinematic hardening rule.

Upper Bound Solutions to Plane-Strain Extrusion Problems

1970 ◽  
Vol 92 (1) ◽  
pp. 158-164 ◽  
Author(s):  
P. C. T. Chen
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Material Properties ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Deformation Pattern ◽  
Upper Bound Theorem ◽  
Admissible Velocity ◽  
Die Geometry ◽  
Bound Theorem

A method for selecting admissible velocity fields is presented for incompressible material. As illustrations, extrusion processes through three basic types of curved dies have been treated: cosine, elliptic, and hyperbolic. Upper-bound theorem is used in obtaining mean extrusion pressures and also in choosing the most suitable deformation pattern for extrusion through square dies. Effects of die geometry, friction, and material properties are discussed.

Anisotropy: Benefits for UOE Line Pipe

2012 ◽  
Author(s):  
Oliver Hilgert ◽  
Steffen Zimmermann ◽  
Christoph Kalwa
Keyword(s):  
Anisotropic Material ◽  
Isotropic Material ◽  
Three Dimensional ◽  
Structural Response ◽  
Bending Moment ◽  
Yield Function ◽  
Material Behavior ◽  
Load Case ◽  
Line Pipe ◽  
Anisotropic Plastic

Plastic anisotropic material behavior of UOE line pipe is investigated in view of its structural response. Common load cases are considered and their resultant strain capacity concerning Strain Based Design demands are discussed. Hill’s yield function is used to analyze steel line pipe under internal pressure and bending moment. Here, a three-dimensional anisotropic plastic strain evolution is considered. It was shown, that underlying anisotropic material behavior can be beneficial for the structural response of line pipe, although it depends on the load case and the directional anisotropy. That is in some way contrary to the demands in specifications, where isotropic material behavior is desired.

A New Upper-Bound Method for Analysis of Some Steady-State Plastic Deformation Processes

1969 ◽  
Vol 91 (3) ◽  
pp. 731-741 ◽  
Author(s):  
E. R. Lambert ◽  
H. S. Mehta ◽  
S. Kobayashi
Keyword(s):  
Plastic Deformation ◽  
Steady State ◽  
Plane Strain ◽  
Velocity Component ◽  
Velocity Fields ◽  
Flow Lines ◽  
Upper Bound Method ◽  
Admissible Velocity ◽  
Tube Extrusion ◽  
Deformation Processes

A method of obtaining admissible velocity fields without velocity discontinuities is described, and applied to plane-strain extrusion, tube extrusion, and axisymmetric piercing. In plane-strain extrusion, the flow lines, grid distortions, and extrusion pressures were obtained and the values were compared with those found in previous solutions. For tube extrusion and axisymmetric piercing, the solutions are presented as examples in terms of flow lines and velocity component distributions; these solutions await experimental confirmation.

A Cross Weighted-Residual Time Integration Scheme for Structural Dynamics

2014 ◽  
Vol 14 (06) ◽  
pp. 1450023 ◽  
Author(s):  
Wooram Kim ◽  
Sang-Shin Park ◽  
J. N. Reddy
Keyword(s):  
Structural Dynamics ◽  
Linear Time ◽  
Time Integration ◽  
Velocity Fields ◽  
Inner Product ◽  
Integration Scheme ◽  
Time Interval ◽  
Element Discretization ◽  
Integration Schemes ◽  
Time Integration Scheme

In this article, we develop a novel stable time integration scheme for the transient analysis of structural dynamics problems. A second-order (in time) differential operator equation (e.g. obtained after finite element discretization in space) is written as a pair of first-order equations in terms of displacements and velocities. Then the solution is sought by minimizing the inner product of the residuals in the two equations (an unconventional approach) over typical time interval to obtain a symmetric set of algebraic equations involving displacements and velocities at two subsequent intervals. The new time integration scheme is termed the cross weighted-residual (CWR) time integration scheme because each of the two residuals takes the other one as a weight function in the minimization. The CWR time integration scheme is developed by using a uniform linear time approximation of the displacement and velocity fields to yield only a single step time integration scheme, which is comparable to the Newmark family of time integration scheme. A reduced integration technique is used to prevent velocity locking, which is caused by linear approximation of both the displacement and velocity fields. For the verification of the consistency and the stability, the CWR time integration scheme is tested with single-degree as well as multi-degree of freedom problems. The scheme performs extremely well compared with those of the well-known Newmark family of time integration schemes.

scholarly journals Thermo-Mechanical Modeling of Distortions Promoted during Cooling of Ti-6Al-4V Part Produced by Superplastic Forming

2016 ◽  
Vol 838-839 ◽  
pp. 196-201
Author(s):  
Maxime Rollin ◽  
Vincent Velay ◽  
Luc Penazzi ◽  
Thomas Pottier ◽  
Thierry Sentenac ◽  
...  
Keyword(s):  
Finite Element ◽  
Thermal Stresses ◽  
Superplastic Forming ◽  
Model Material ◽  
Material Behavior ◽  
Mechanical Modeling ◽  
Temperature Dependent ◽  
Finite Element Software ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

In AIRBUS, most of the complex shaped titanium fairing parts of pylon and air inlets are produced by superplastic forming (SPF). These parts are cooled down after forming to ease their extraction and increase the production rate, but AIRBUS wastes a lot of time to go back over the geometric defects generated by the cooling step. This paper investigates the simulations of the SPF, cooling and clipping operations of a part on Abaqus® Finite element software. The different steps of the global process impact the final distortions. SPF impacts the thickness and the microstructure/behavior of material, cooling impacts also the microstructure/behavior of material and promotes distortions through thermal stresses and finally, clipping relaxes the residual stresses of the cut part. An elastic-viscoplastic power law is used to model material behavior during SPF and a temperature dependent elastic perfectly plastic model for the cooling and clipping operations.

Direct Upper Bound Solution to Rectangular-to-Polygonal Extrusion Through Square Die

1999 ◽  
Vol 121 (2) ◽  
pp. 195-201 ◽  
Author(s):  
S. K. Sahoo ◽  
P. K. Kar ◽  
K. C. Singh
Keyword(s):  
Steady State ◽  
Velocity Field ◽  
Upper Bound ◽  
Velocity Fields ◽  
Extrusion Pressure ◽  
Admissible Velocity ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Aspect Ratios

This paper is concerned with an attempt to find an upper bound solution for the problems of steady-state extrusion of asymmetric polygonal section bars through rough square dies. A class of kinematically admissible velocity fields is examined, reformulating the SERR technique, to get the velocity field that gives the lowest upper bound. This velocity field is utilized to compute the non-dimensional average extrusion pressure at various area reductions for different billet aspect ratios.

scholarly journals Simulation of three-dimensional rapid free-surface granular flow past different types of obstructions using the SPH method

2016 ◽  
Vol 62 (232) ◽  
pp. 335-347 ◽  
Author(s):  
AHMED M. ABDELRAZEK ◽  
ICHIRO KIMURA ◽  
YASUYUKI SHIMIZU
Keyword(s):  
Granular Flow ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Material Behavior ◽  
Sph Method ◽  
Perfectly Plastic ◽  
Depth Direction ◽  
Aspect Ratios ◽  
Flow Past ◽  
Different Types

ABSTRACTIn nature, when hazardous geophysical granular flows (e.g. a snow avalanche) impact on an obstacle as they stream down a slope, rapid changes in flow depth, direction and velocity will occur. It is important to understand how granular material flows around such obstacles in order to enhance the design of defense structures. In this study, a three dimensional (3-D) Smoothed Particle Hydrodynamics (SPH) model is developed to simulate granular flow past different types of obstacles. The elastic–perfectly plastic model with implementation of the Mohr–Coulomb failure criterion is applied to simulate the material behavior, which describes the stress states of soil in the plastic flow regime. The model was validated by simulating the collapse of a 3-D column of sand with two different aspect ratios; the results showed that the SPH method is capable of simulating granular flow. The model is then applied to simulate the gravity-driven granular flow down an inclined surface obstructed by a group of columns with different spacing, a circular cylinder and a tetrahedral wedge. The numerical results are then compared with experimental results and two different numerical solutions. The good agreements obtained from these comparisons demonstrate that the SPH method may be a powerful method for simulating granular flow and can be extended to design protective structures.

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