In order to obtain any probability of survival for crack growth life, a randomization method of deterministic equation for probability fracture mechanics is presented. According to this method, the deterministic equat...In order to obtain any probability of survival for crack growth life, a randomization method of deterministic equation for probability fracture mechanics is presented. According to this method, the deterministic equation of fracture mechanics is randomized to stochastic equation, and the parameters of the stochastic equation are estimated by means of the statistics. Three new kinds of random models to gain the p d a/ d N Δ K curve and the γ p d a/ d N Δ K curve (confidence level probability of survival fatigue crack growth rate stress intensity factor range curve) are proposed by using this randomization method. And the p d a/ d N Δ K curves and the γ p d a/ d N Δ K curves determined by these three models are discussed and compared according to the treatment result of the experimental data from CT specimens. From examples, it is found that the three deterministic fatigue crack growth rate equations determined by these models are very near and in agreement with the traditional deterministic fatigue crack growth rate equation, and these models are effectively and easily used to treat fatigue crack growth rate data.展开更多
The average-passage equation system （APES） provides a rigorous mathematical framework for account- ing for the unsteady blade row interaction through multi- stage compressors in steady state environment by introduc-...The average-passage equation system （APES） provides a rigorous mathematical framework for account- ing for the unsteady blade row interaction through multi- stage compressors in steady state environment by introduc- ing deterministic correlations （DC） that need to be modeled to close the equation system. The primary purpose of this study is to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES. In Part 1 of this two-part paper, firstly a 3D viscous unsteady and time-averaging flow CFD solver is developed to investi- gate the APES technique. Then steady and unsteady simu- lations are conducted in a transonic compressor stage. The results from both simulations are compared to highlight the significance of the unsteady interactions. Furthermore, the distribution characteristics of DC are studied and the DC at the rotor/stator interface are compared with their spatial cor- relations （SC）. Lastly, steady and time-averaging （employing APES with DC） simulations for the downstream stator alone are conducted employing DC derived from the unsteady re- suits. The results from steady and time-averaging simula- tions are compared with the time-averaged unsteady results. The comparisons demonstrate that the simulation employing APES with DC can reproduce the time-averaged field and the 3D viscous time-averaging flow solver is validated.展开更多
In this article,a brief biological structure and some basic properties of COVID-19 are described.A classical integer order model is modified and converted into a fractional order model withξas order of the fractional...In this article,a brief biological structure and some basic properties of COVID-19 are described.A classical integer order model is modified and converted into a fractional order model withξas order of the fractional derivative.Moreover,a valued structure preserving the numerical design,coined as Grunwald–Letnikov non-standard finite difference scheme,is developed for the fractional COVID-19 model.Taking into account the importance of the positivity and boundedness of the state variables,some productive results have been proved to ensure these essential features.Stability of the model at a corona free and a corona existing equilibrium points is investigated on the basis of Eigen values.The Routh–Hurwitz criterion is applied for the local stability analysis.An appropriate example with fitted and estimated set of parametric values is presented for the simulations.Graphical solutions are displayed for the chosen values ofξ(fractional order of the derivatives).The role of quarantined policy is also determined gradually to highlight its significance and relevancy in controlling infectious diseases.In the end,outcomes of the study are presented.展开更多
文摘In order to obtain any probability of survival for crack growth life, a randomization method of deterministic equation for probability fracture mechanics is presented. According to this method, the deterministic equation of fracture mechanics is randomized to stochastic equation, and the parameters of the stochastic equation are estimated by means of the statistics. Three new kinds of random models to gain the p d a/ d N Δ K curve and the γ p d a/ d N Δ K curve (confidence level probability of survival fatigue crack growth rate stress intensity factor range curve) are proposed by using this randomization method. And the p d a/ d N Δ K curves and the γ p d a/ d N Δ K curves determined by these three models are discussed and compared according to the treatment result of the experimental data from CT specimens. From examples, it is found that the three deterministic fatigue crack growth rate equations determined by these models are very near and in agreement with the traditional deterministic fatigue crack growth rate equation, and these models are effectively and easily used to treat fatigue crack growth rate data.
基金supported by the National Natural Science Foundation of China (51006006,51136003,50976010,50976009)the National Basic Research Program of China (2012CB720205)+2 种基金the Aeronautical Science Foundation of China (2010ZB51)the 111 Project (B08009)the National Science Special Foundation for Post-doctoral Scientists of China (201104049)
文摘The average-passage equation system （APES） provides a rigorous mathematical framework for account- ing for the unsteady blade row interaction through multi- stage compressors in steady state environment by introduc- ing deterministic correlations （DC） that need to be modeled to close the equation system. The primary purpose of this study is to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES. In Part 1 of this two-part paper, firstly a 3D viscous unsteady and time-averaging flow CFD solver is developed to investi- gate the APES technique. Then steady and unsteady simu- lations are conducted in a transonic compressor stage. The results from both simulations are compared to highlight the significance of the unsteady interactions. Furthermore, the distribution characteristics of DC are studied and the DC at the rotor/stator interface are compared with their spatial cor- relations （SC）. Lastly, steady and time-averaging （employing APES with DC） simulations for the downstream stator alone are conducted employing DC derived from the unsteady re- suits. The results from steady and time-averaging simula- tions are compared with the time-averaged unsteady results. The comparisons demonstrate that the simulation employing APES with DC can reproduce the time-averaged field and the 3D viscous time-averaging flow solver is validated.
文摘In this article,a brief biological structure and some basic properties of COVID-19 are described.A classical integer order model is modified and converted into a fractional order model withξas order of the fractional derivative.Moreover,a valued structure preserving the numerical design,coined as Grunwald–Letnikov non-standard finite difference scheme,is developed for the fractional COVID-19 model.Taking into account the importance of the positivity and boundedness of the state variables,some productive results have been proved to ensure these essential features.Stability of the model at a corona free and a corona existing equilibrium points is investigated on the basis of Eigen values.The Routh–Hurwitz criterion is applied for the local stability analysis.An appropriate example with fitted and estimated set of parametric values is presented for the simulations.Graphical solutions are displayed for the chosen values ofξ(fractional order of the derivatives).The role of quarantined policy is also determined gradually to highlight its significance and relevancy in controlling infectious diseases.In the end,outcomes of the study are presented.
