Shiyi Bao

A derivative-free algorithm for nonlinear equations and its applications in multibody dynamics

Local floating coordinate system is used to represent the deployment motion of each rigid and flexible body of multibody system dynamics. Normal substructure modes are employed to describe the flexibility of a flexible body. Constraint equations establish the linkage between different bodies, part of them to specify positions and the others to specify orientations. Systems governing equations are then derived using generalized coordinates by Lagrange methods. The resulting differential-algebraic equations are transformed to algebraic equations using backward differential formula corrector method, thus highly coupled nonlinear equations are obtained. However, Jacobian matrix of the nonlinear equations is hard to calculate, and then a quasi-Newton method based on Broyden–Fletcher–Goldfarb–Shanno update approach for the solution of the nonlinear equations is proposed. And a suitable line search approach is combined with the Broyden–Fletcher–Goldfarb–Shanno method to improve its efficiency. Some numerical results are reported to show efficiency of the proposed method. Afterwards, the Broyden–Fletcher–Goldfarb–Shanno method is integrated into multibody dynamics method. A rigid multibody case and a rigid-flex multibody case are further studied to show the efficiency of the proposed multibody solver.

Creep Analysis of Hemisphere Shell Structure Under High Temperature Gradient

The In-Vessel Retention (IVR) of molten core debris has been part of the severe accident management strategy for advanced pressurized water reactor (PWR) plant. Generally, the pressure is supposed to successfully be released, and the externally cooled lower head wall mainly experiences the temperature difference which may be more than 1000°C. However, the Fukushima accident shows that a certain pressure (up to 8.0MPa) still exists inside the reactor pressure vessel (RPV). Therefore, in order to make the IVR succeed, it is necessary to investigate the structural integrity of the RPV under the combined internal pressure and the thermal load on the lower head.Therefore, it is supposed that the lower head of RPV is a Hemisphere Shell Structure (HSS) with 2150mm external radius and 25mm wall thickness. Similarly, the outer wall temperature is supposed to be 127°C, the wall temperature difference 1200°C, and the material properties (i.e., thermal conductivity, specific heat capacity, yield strength, and so on) are dependent on the temperature. In this paper, the main subjects discussed are as below.First, the heat transfer analysis is carried out to obtain the temperature distribution of the HSS wall. Due to the high temperature gradient, there may present different failure modes along the HSS wall thickness, i.e., plastic failure and creep failure. Then, the stress and strain distributions along the wall thickness are analyzed by ANSYS finite element method where the Norton-Bailey type creep law is adopted. The result shows that the stress in the lower temperature part (LTP) whose temperature is lower than 405°C is lower than the yield stress of the material with the corresponding temperature. That is to say, the LTP still can bear a certain internal pressure. At last, to consider the combined impact of internal pressure and temperature difference on the HSS, the finite element analysis is carried out by adopting the isochronous stress-strain curves of the Chinese RPV material. The relationship between the stress in the LTP at 100 hours and the internal pressure is discussed, and the limit internal pressure is determined. It is concluded that HSS still can maintain its integrity under IVR, even if there exists a certain internal pressure.Copyright

Analysis on Ultimate Load Capacity of Cylinder With Local Discontinuity Under High Temperature Gradient

A severe accident management concept, known as ‘in-vessel retention (IVR)’, is widely used in advanced pressurized water reactor, such as AP600, AP1000, and so on. The severe accident management strategy is to flood the reactor cavity, submerging the reactor pressure vessel (RPV). In such condition, the temperature on the inside of RPV may exceed the melting point (about 1327 °C) of RPV material, and results in the localized wall thinning. On the outside, the temperature is remained at about 127 °C, by assuming the flow regime is kept to be nucleate boiling. So it will form a high temperature gradient on the wall, and caused high thermal stress.It will bring about the local discontinuity on the PRV wall because of the wall molten under the elevated temperature. A cylinder model is established to simulate the local discontinuity. The model is composed of the cylinder with the same external radius, but different wall thickness in the local discontinuity zone. Two elastic perfectly plastic models are used to analyze the stress and strain distributions on the wall and ultimate load capacity, based on the hot tensile curves and isochronous stress-strain curves at 100 hour with the change of temperature. The effect of local discontinuity is discussed, under the case of high temperature gradient and internal pressure. The results show that the Mises stress on the whole wall-thickness in the region of local discontinuity will achieve yield stress, under the high thermal stress. Appling internal pressure, the stress decreases in the zone of local discontinuity. The weakest link takes place in the thin segment of the cylinder model, and the ultimate pressure is obtained.Copyright

Reliability Analysis of Spring Operated Pressure Relief Valve

Pressure relief valve (PRV) is an important automatic overpressure protection system in the process industry. Because of the operating characteristics, the performance of PRV is supposed to be proved by the proof test. However, it’s difficult to determine the proof test intervals and the availability of the PRV between two proof tests. Based on stochastic Petri nets (SPN), the reliability modeling and analysis procedure of spring operated full lift pressure relief valve which is the most widely used PRV is depicted in this paper.Firstly, the FMECA method is used to analyze the causes and effects of the typical six failure modes of the PRV, such as vibration, leakage, frequency hopping, unable to open, open before the settings and the low back seat pressure. Second, the corresponding fault tree (FT) models of the PRV are built through the multi-component failure analysis. Third, the SPN models of the PRV are established by employing the logical relations in the FT models. Based on the collected failure data of the PRVs, the steady state and transient reliability index are calculated by Monte Carlo simulation based on the SPN software SPN@. Last, the idea about PRV reliability data collection in domestic process industries is proposed.The result of the reliability analysis can provide the basis for determination the proof test intervals of the PRV, and the proposed procedure also bears significance in its application in the reliability analysis of general system in process industry.Copyright