The Shrinkage Characteristic of a Spherical Cavity in Three-Dimensional Piezoelectric Grain

2015 ◽  
Vol 22 (7) ◽  
pp. 530-536
Author(s):  
Y. Qin ◽  
X. Wang
2002 ◽  
Vol 37 (3) ◽  
pp. 259-264 ◽  
Author(s):  
Q. Z Wang

First, based on an approximate analysis, simple closed-form expressions of the stress concentration factor (SCF) for two- or three-dimensional models with a circular hole or a spherical cavity in a finite domain are derived. Then, an asymptotic method is adopted to improve the accuracy of the derived solutions for an extremely large circular hole or spherical cavity, when the remaining ligament approaches zero. Exact limit SCF values for these two kinds of models were given by Koiter; these values are used for the adjustment of the coefficients in the SCF expressions. Finally, simple SCF formulae for these finite domain problems are obtained, their accuracy is demonstrated to be very good by comparison with the available data from the literature, and the asymptotic validity is guaranteed.


Energies ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 926
Author(s):  
Fushou Xie ◽  
Siqi Xia ◽  
Erfeng Chen ◽  
Yanzhong Li ◽  
Hongwei Mao ◽  
...  

The hydrodynamic information of liquid oxygen in the conveying pipeline of cryogenic launch vehicles directly determines the reliability of the operation of the turbopump. A 0.09 MPa anomalous pressure fall phenomenon in the feeding system has been observed during the flight and run test of a cryogenic rocket with four parallel engines. In previous work, we set up a full-scale experimental system with liquid oxygen as media. The anomalous pressure fall was successfully reproduced. Experimental studies of this phenomenon suggest that the problem might be associated with vortices into the five-way spherical cavity structure. The objective of this study was to determine the three-dimensional instability flow by computational methods to identify and better understand the anomalous pressure fall phenomenon. A numerical model developed by the turbulent conservation equations was validated by experimental data. The generation and evolution of vortices into the five-way spherical cavity of feeding pipelines was captured. It was found that the root cause of the instability flow causing the unusual pressure fall is the formation of a spindle-like vortex into the five-way spherical cavity due to disturbance of the inlet liquid oxygen. The results showed that there is a mirror-symmetrical four-vortices structure in the absence of disturbance, in which the liquid oxygen pressure fall with the rise of the Reynolds number is in good agreement with the predicting values calculated by a set of traditional empirical correlations. In the case of the specific operating conditions, it is also consistent with the experimental results. When the disturbance occurs at the inlet of the spherical cavity, the mirror-symmetrical four-vortices structure gradually evolves into the mirror-symmetrical two-vortices structure. When the disturbance is further enhanced, the mirror-symmetrical two-vortices structure merge with each other to form a spindle-like vortex, which is similar to the Rankine vortex structure. The pressure fall on the corresponding side of the spindle-like vortex core reduces abnormally, and is about 0.07 MPa, which is consistent with the experimental data under certain disturbance conditions. Moreover, it was found that the spindle-like vortex is a stable eddy structure, and would continue to exist once it is formed, which could also not disappear with the removal of the disturbance.


2012 ◽  
Vol 39 (1) ◽  
pp. 71-97
Author(s):  
Stavros Syngellakis

The paper is concerned with a particular case of stress amplification arising from the proximity of a spherical cavity to the boundary of a loaded elastic solid. The performed approximate analysis yields distributions of stresses and displacements in the narrow region formed between a spherical cavity and the faces of a thin flat layer subjected to a far field uniform radial tension. The narrow region is modelled as a circular plate of non-uniform thickness undergoing coupled membrane and flexural deformation. Series solutions are obtained for both membrane forces and bending moments leading to estimates for the stress concentration factor at minimum thickness. These predictions are found consistent with those obtained from both the exact analytical solution and finite element modelling of the problem. Cross-validated results from the two latter methods also provide trends for the stress amplification due to the narrowness of the region.


2016 ◽  
Vol 16 (1) ◽  
pp. 61-68 ◽  
Author(s):  
S. Samavedam ◽  
S. Sundarrajan

Abstract US A356 and US 413 cast aluminium alloys shrinkage characteristic have been discussed in the present study. Specific volume reduction leads to shrinkage in castings and it can be envisaged as a casting defect. Finite difference based casting process simulation software has been used to study the shrinkage characteristic and it is quantified using mathematical formulae. The three dimensional model of the shrinkage defect has been constructed using CAD application software. Shrinkage characteristic has also been quantified through experimental validation studies and compared well with casting process simulation. Shrinkage characteristic study and control is essential for producing defect free castings. Influence of casting shape on the shrinkage characteristic has been studied in this paper.


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