Mathematical model of the problem of analyzing an elastic?Plastic system at shakedown

1985 ◽  
Vol 21 (6) ◽  
pp. 596-600
Author(s):  
Yu. Yu. Atkochyunas
Keyword(s):  
Mathematical Model ◽  
Elastic Plastic

A Method for Calculating the Amount of the Deflection and Force-Energy Parameters for Copper-Clad Steel Tube in the Process of Straightening

2013 ◽  
Vol 477-478 ◽  
pp. 137-140
Author(s):  
Liang Yu Xia ◽  
Dong Ming Sun ◽  
Gui Rong Kang ◽  
Jian Sun
Keyword(s):  
Mathematical Model ◽  
Engineering Application ◽  
Bending Moment ◽  
Scientific Basis ◽  
Steel Tube ◽  
Elastic Plastic ◽  
Energy Parameters ◽  
Continuous Bending ◽  
Clad Steel ◽  
The Relationship

Based on Roller Straightening Theory and Elastic-Plastic Beam Research, A Appropriate Mathematical Model of Straightening has Set up.The Author Regards the Tube as a Continuous Bending Beam and Discuss in Detail the Relationship between the Straightening Force and the Bending Moment. Calculating the Amount of Deflection for Tube. in this way ,it Provided a Scientific Basis for the Copper-Clad Steel Tube Straightening Parameter Set and Engineering Application.

A Mathematical Model for Frictional Elastic-Plastic Sphere-on-Flat Contacts at Sliding Incipient

2005 ◽  
Vol 74 (1) ◽  
pp. 100-106 ◽  
Author(s):  
L. Chang ◽  
H. Zhang
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Shear Strength ◽  
Contact Pressure ◽  
Interfacial Shear Strength ◽  
Interfacial Shear ◽  
Contact Model ◽  
Elastic Plastic ◽  
Plastic Sphere ◽  
Flat Contact

This paper presents a mathematical model for frictional elastic-plastic sphere-on-flat contacts at sliding incipient. The model is developed based on theoretical work on contact mechanics in conjunction with finite-element results. It incorporates the effects of friction loading on the contact pressure, the mode of deformation, and the area of contact. The shear strength of the contact interface is, in this paper, assumed to be proportional to the contact pressure with a limiting value that is below the bulk shear strength of the sphere. Other plausible interfacial-shear-strength characteristics may also be implemented into the contact model in a similar manner. The model is used to analyze the frictional behavior of a sphere-on-flat contact where the experimental data suggest that the interfacial shear strength is similar in nature to the one implemented in the model. The theoretical results are consistent with the experimental data in all key aspects. This sphere-on-flat contact model may be used as a building block to develop an asperity-based contact model of rough surfaces with friction loading. It may also serve in the modeling of boundary-lubricated sliding contacts where the interfacial shear strength in each micro-contact is coupled with its flash temperature and related to the lubricant/surface physical-chemical behavior.

Mathematical Modeling and Modifying of Turntable’s Angle for 5/12 Automatic Numerical Controlling Bending Hoop Machine

2011 ◽  
Vol 189-193 ◽  
pp. 1955-1959
Author(s):  
Xiao Hong Zhang ◽  
Guo Fu Yin
Keyword(s):  
Mathematical Model ◽  
Rotation Angle ◽  
Bending Moment ◽  
Numerical Control ◽  
Bending Test ◽  
Spring Back ◽  
Plastic Bending ◽  
Elastic Plastic ◽  
The Mathematical Model ◽  
Nc Bending

Aiming at 5/12 full-automatic numerical control (NC) bending hoop machine, the paper analyzed the elastic-plastic bending deformation with the knowledge of elastic-plastic bending principle, theoretically mechanics and spring-back, and deduced the relationship of bending moment and curvature ratio, and built the mathematical model between bending hoop turntable’s rotation angle and stirrups angle considering the spring-back deformation. Then the different spring-back angles under two types of stirrups diameter, Φ=8 mm and Φ=10 mm, are measured. The mathematical model of turntable’s rotation angle and stirrup’s angle for 5/12 automatic NC bending hoop machine is modified according to the analysis of bending test data.

scholarly journals ANALYSIS OF GEOMETRICALLY NON-LINEAR ELASTIC-PLASTIC FRAMED STRUCTURES/TAMPRIAI PLASTINŲ GEOMETRIŠKAI NETIESINIŲ STRYPINIŲ KONSTRUKCIJŲ ANALIZĖ

1998 ◽  
Vol 4 (1) ◽  
pp. 36-42 ◽  
Author(s):  
Romualdas Karkauskas
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Extremum Principle ◽  
Complementary Energy ◽  
Analysis Problem ◽  
Framed Structures ◽  
Elastic Plastic ◽  
Non Linear ◽  
Residual Strains ◽  
Energy Increment

A stress-strain field (SSF) evaluation of elastic-plastic structures under the action of a completely specified external loading that doesn't exceed its limiting value, but produces plastic deformation, is under consideration. An assumption of the discrete structure, possesing the small bar strains and large displacements assumptions, is applied. It is known that for disipative structures SSF depends on the loading history. When solving the analysis extremum problems on the basis of extreme energetical principles [1]-[8] for global external loads (final load magnitudes) one cannot fix directly the unloading phenomenon in cross-sections. Therefore, the possibilities to evaluate the SSF change of the structure, as well as the possibility to take into account various plastic deformation stages, finishing prior to the stage when the final magnitudes of loads are achieved, are lost. Therefore, the residual displacement magnitudes, obtained by solving the problem for global loads only, can be determined only very approximately. The proposed in the manuscript complementary load method to investigate the SSF for geometrically non-linear structure enables to avoid the above-mentioned negative aspects. Applying the method, design process of a structure is iterative step-by-step procedure. A load step ΔF is introduced. Monotonically increasing the load by step ΔF, increments of SSF are obtained. The analysis problem in static and kinematic formulations is stated for this purpose. Formulations are based on the dual extreme energetic principles formulated for residual strains and residual displacements increments for any structure deformation stage. The actual field of residual forces proceeding the plastic failure is obtained by using the extreme principle of the minimum of complementary energy increment—the ststic formulation (8). Applying the Lagrange function of this formulation, the dual problem is formulated to determine the displacements of the structure. Thus the mathematical model (11) corresponds to the extremum principle of a maximum of complementary work increment. Changing the sign of the objective function the problem (11) corresponds to the extremum principle of a minimum of total complementary energy increment. Finally, we conclude that increments of residual forces (15) and displacements (14) are the linear functions only one of plastic multipliers Δλv. By substituting that functions into problem (11) the elastic-plastic geometrically non-linear framed structures SSF analysis problem can be transformed to modified problem (16). Then applying formulae (14) and (15) the SSF increments for the V—th step are determined. The actual SSF is obtained applying the relationships (1) and (2). The SSF analysis problem for a two-storey frame made of reinforcement concrete at the stage prior to plastic collapse is presented for the numerical example. Numerical experiments show that proposed mathematical model (16) allows to determine the actual forces and displacements for real structures and to achieve sufficient results for practical design needs.

Large Axisymmetric Deformations of Elastic/Plastic Perforated Circular Plates

2003 ◽  
Vol 125 (4) ◽  
pp. 357-364 ◽  
Author(s):  
D. Wu ◽  
J. Peddieson ◽  
G. R. Buchanan ◽  
S. G. Rochelle
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Circular Plate ◽  
Numerical Solutions ◽  
Outer Edge ◽  
Plate Bending ◽  
Large Deflections ◽  
Circular Plates ◽  
Elastic Plastic ◽  
Thickness Variations

A mathematical model of axisymmetric elastic/plastic perforated circular plate bending and stretching is developed which accounts for through thickness yielding, through thickness variations in perforation geometry, elastic outer edge restraint, and moderately large deflections. Selected numerical solutions of the resulting differential equations are presented graphically and used to illustrate interesting trends.

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