Extended rotation-free plate and beam elements with shear deformation effects

2010 ◽  
Vol 83 (2) ◽  
pp. 196-227 ◽  
Author(s):  
Eugenio Oñate ◽  
Francisco Zárate
Keyword(s):  
Shear Deformation ◽  
Beam Elements

Application Of Electron Probe Analyses Of Minerals In Discussing The Relationship Between Ductile Deformation And Metamorphism

1990 ◽  
Vol 48 (2) ◽  
pp. 250-251
Author(s):  
Fan Guochuan ◽  
Sun Zhongshi
Keyword(s):  
Chemical Composition ◽  
Shear Deformation ◽  
Electron Probe ◽  
General Rule ◽  
Granulite Facies ◽  
Ductile Deformation ◽  
Higher Temperature ◽  
Ductile Shear ◽  
The Relationship ◽  
Ductile Shear Deformation

Under influence of ductile shear deformation, granulite facies mineral paragenesis underwent metamorphism and changes in chemical composition. The present paper discusses some changes in chemical composition of garnet in hypers thene_absent felsic gnesiss and of hypersthene in rock in early and late granulite facies undergone increasing ductile shear deformation .In garnet fetsic geniss, band structures were formed because of partial melting and resulted in zoning from massive⟶transitional⟶melanocrate zones in increasing deformed sequence. The electron-probe analyses for garnet in these zones are listed in table 1 . The Table shows that Mno, Cao contents in garnet decrease swiftly from slightly to intensely deformed zones.In slightly and moderately deformed zones, Mgo contents keep unchanged and Feo is slightly lower. In intensely deformed zone, Mgo contents increase, indicating a higher temperature. This is in accord with the general rule that Mgo contents in garnet increase with rising temperature.

In-Plane Bending and Shear Deformation of Belt Contributions on Tire Cornering Stiffness Characteristics

2020 ◽  
Author(s):  
Gibin Gil ◽  
Sujin Lee
Keyword(s):  
Mathematical Model ◽  
Shear Deformation ◽  
Beam Theory ◽  
Slip Angle ◽  
Wear Properties ◽  
Angle Change ◽  
Foundation Model ◽  
Plane Bending ◽  
Stiffness Characteristics ◽  
Brush Model

ABSTRACT In radial tires, belt structure plays a role of minimizing the lateral deflection of carcass, which has a significant influence on the cornering and wear properties of a tire. The deflection of carcass affects the magnitude of tread block deformation when the tire is under the slip angle. As a result, it can change the cornering stiffness characteristics of the tire, especially when the vertical load is high. During tire development, a tire design engineer tries to find the optimal belt ply angle that satisfies the various performance requirements simultaneously, but it is not an easy task because the effect of belt angle change is different depending on the size of the tire. There have been many attempts to construct a mathematical model that represents the structural properties of the belt package, including the string-based model and the beam on elastic foundation model. But, in many cases, only the in-plane bending of belt is considered and the shear deformation is not taken into consideration. In this study, the effect of belt angle change on belt stiffness is analyzed using a mathematical model based on the Timoshenko beam theory. This model can account for the in-plane bending and shear deformation of the belt structure at the same time. The results of the analysis show how the contribution of bending and shear is changed depending on a tire design parameter, herein the belt cord angle. The effect of belt ply angle change on cornering stiffness is investigated by means of the brush model including belt flexibility. The prediction by the brush model is compared with the measurement using a Flat-trac machine, and the validity of the model is discussed.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

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