A comparison between the dynamic stability of three types of nonlinear orthotropic functionally graded plates under random lateral loads

2015 ◽  
Vol 23 (15) ◽  
pp. 2520-2537 ◽  
Author(s):  
A Asnafi ◽  
M Abedi
Keyword(s):  
Dynamic Stability ◽  
Three Dimensional ◽  
Mean Value ◽  
Functionally Graded ◽  
Kolmogorov Equation ◽  
Lateral Loads ◽  
Functionally Graded Plates ◽  
The Mean ◽  
Stochastic Loads ◽  
Stable Zone

In this manuscript, the dynamic stability and bifurcation occurrence for three famous types of plates including orthotropic sigmoid, power-law and exponential functionally graded plates under lateral stochastic loads are studied. Due to randomness, the behavior and analysis are not conventional deterministic investigation. So, the dynamic stability zone and border curves of bifurcation are evaluated using probability density function of the response. The latter is computed from a completely exact solution of the Fokker Planck Kolmogorov equation. The three dimensional dynamic stable zone and the border surfaces of bifurcation are obtained as a function of material parameter, in-plane forces and the mean value of lateral load. To generalize the results, all the parameters are transformed to some proper non-dimensional variables and then the effects of all prescribed parameters on the dynamic stability are completely discussed and compared. The comparison is done between the plates with themselves and also the corresponding homogenous plate. Finally the results are validated by the bifurcation diagrams of non dimensional deflection of plates that are obtained directly and numerically from the governing equations of plates.

scholarly journals On the zeroth law of turbulence for the stochastically forced Navier-Stokes equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yat Tin Chow ◽  
Ali Pakzad
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Mean Value ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Additional Hypothesis ◽  
The Mean ◽  
Deterministic Force ◽  
Martingale Solutions

<p style='text-indent:20px;'>We consider the three-dimensional stochastically forced Navier–Stokes equations subjected to white-in-time (colored-in-space) forcing in the absence of boundaries. Upper bounds of the mean value of the time-averaged energy dissipation rate are derived directly from the equations for weak (martingale) solutions. This estimate is consistent with the Kolmogorov dissipation law. Moreover, an additional hypothesis of energy balance implies the zeroth law of turbulence in the absence of a deterministic force.</p>

scholarly journals Wits Appraisal of a Qatari Male Population: A Comparative Study. Part II

2020 ◽  
Vol 2 (6) ◽  
Author(s):  
Hayder A. Hashim ◽  
Najat Al-Sayed ◽  
Ayah AL-Qaisi
Keyword(s):  
Three Dimensional ◽  
Mean Value ◽  
Cone Beam ◽  
Facial Appearance ◽  
Male Population ◽  
Significant Difference ◽  
The Mean ◽  
Age Range ◽  
Relationship Of ◽  
Gender Specific

Introduction: Cephalometric analysis aims to determine skeletal and dental relationships. The ANB angle, initially suggested by Rediel and applied by Steiner. is the most used angle in establishing the anteroposterior relationship of the mandible to the maxilla. However, limitations to the accuracy of the ANB angle for this purpose have been reported. To avoid these potential sources of inaccuracy a diagnostic tool was introduced by Jenkins and later modified by Jacobson and became known as the “Wits appraisal”. Aims: The aim of this study was to establish the Wits appraisal value in a sample of Qatari males, a group which had not previously been studied in this context, and to compare the findings with those from racially and ethnically differing groups as reported in the literature. Materials and Methods: The sample consisted of 28 lateral cephalometric radiographs of Qatari males with an age range of 15 to 32 years, presenting with a well-balanced facial appearance and an acceptable profile. Results: The mean value of the Wits appraisal for Qatari males in the present study was 0.50 ± 2.96. This differed at a statistically significant level from the mean value in the Jacobson study with no gender significant difference noted. On the other hand, significant differences were found when compared with previous reports on different races. Conclusion: The Wits appraisal value for the Qatari male population studied was 0.5±2.96, a result which is significantly higher than that reported in Jacobson’s study. This study revealed that the Wits appraisal is not ethnicity or gender-specific, and therefore cannot be used to differentiate between different ethnic groups. However, it can find application as an alternative to the ANB angle in the treatment of borderline cases. The application of cone beam computed tomography (CBCT) will enhance the diagnosis and treatment of cases by yielding three-dimensional views.

scholarly journals Three-Dimensional Stochastic Seepage Field Analysis of Multimedia Embankment

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Xiaoming Zhao ◽  
Shiyu Shang ◽  
Yuanlin Yang ◽  
Mingming Hu
Keyword(s):  
Hydraulic Conductivity ◽  
Random Field ◽  
Three Dimensional ◽  
Mean Value ◽  
Field Analysis ◽  
Anisotropy Ratio ◽  
Seepage Field ◽  
The Monte Carlo Method ◽  
Total Head ◽  
The Mean

The soil hydraulic conductivity of an embankment has strong spatial variability due to the spatiotemporal variation, both natural and artificial. The strong randomness of the hydraulic conductivity can be expressed by the coefficient of variation (COV) and the fluctuation scale θ. Moreover, different coefficients of variation and fluctuation scales correspond to different random field structures. To study the characteristics of the three-dimensional stochastic seepage field in an embankment under different COVs and fluctuation scales, we generate a three-dimensional random field of the hydraulic conductivity of multimedia embankment based on the local average subdivision technique. In particular, a calculation method for a three-dimensional random seepage field based on the Monte Carlo method combined with a three-dimensional multimedia random field and a deterministic analysis is proposed. The results showed that after three thousand realizations and considering the randomness of the hydraulic conductivity, the position of the free surface of each section in the embankment differed. The mean value of the total head decreased when the COV increased. Furthermore, when the COV was small, the change in the total head with anisotropy ratio was not evident, while the COV was large. The mean value of the total head increased with the anisotropy ratio. When the anisotropy ratio increased, the mean value of the standard deviation of the total head increased first and then decreased.

scholarly journals Comparison of Valgus Correction Angle between Patients with Developmental Dysplasia Hip and Normal Volunteers Measured by Three-Dimensional Reconstruction and X-Ray

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Aobo Zhang ◽  
Qing Han ◽  
Bingpeng Chen ◽  
Chenyu Wang ◽  
Xue Zhao ◽  
...  
Keyword(s):  
3D Reconstruction ◽  
Three Dimensional ◽  
Mean Value ◽  
Normal Group ◽  
Correction Angle ◽  
X Ray ◽  
Normal Volunteers ◽  
Significant Difference ◽  
The Mean ◽  
Valgus Correction Angle

Background and purpose. A new method of three-dimensional (3D) reconstruction technology was used to take place of X-ray in measuring valgus correction angle (VCA) of both DDH patients and normal volunteers to improve precision. Two different ways to define VCA according to the various conditions of patients were compared and analyzed. Methods. Bilateral VCA of 50 DDH patients and 56 normal volunteers were measured by Mimics software in the 3D method and X-ray in 2D. Two VCA (the upper VCA and the lower VCA) were measured in both two methods. Every VCA was measured by observer A and observer B for twice separately. The statistical analyses of the differences were calculated among the measurements of the VCA. Results. The mean value of the upper VCA measured in 3D was 4.95°±0.76° in DDH group and 5.56°±0.62° in the normal group with significant difference (t=−6.457, p<0.01). The VCA of DDH group and normal group measured by 3D was larger than 2D, both the upper VCA and the lower VCA. The differences indicated statistically significant. The mean value of lower VCA was 0.60° smaller than the mean value of upper VCA in normal volunteers. The mean value of the lower VCA was 0.58° larger than the mean value of the upper VCA in DDH patients. Conclusions. Compared to X-ray, 3D reconstruction technology is more accurate without conventional limitations. The lower VCA of DDH patients should be regarded as the femoral intramedullary guide angle in TKA, especially for patients with femoral deformities.

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