In this paper, the response of sharp-notched circular tubes with notch depths of 0.2, 0.4, 0.6, 0.8 and 1.0 mm subjected to bending creep and relaxation are investigated. The bending creep or relaxation is to bend the tube to a desired moment or curvature and hold that moment or curvature constant for a period of time. From the experimental result of bending creep, the creep curvature and ovalization increase with time. In addition, higher held moment leads to the higher creep curvature and ovalization of the tube's cross-section. From the experimental result for bending relaxation, the bending moment rapidly decreases with time and becomes a steady value. As for the ovalization, the amount increases a little with time and gradually becomes a steady value. Due to the constant ovalization caused by the constant curvature under bending relaxation, the tube does not buckle. Finally, the formulation proposed by Lee and Pan (2002) is modified for simulating both the creep curvature–time relationship in the first stage under bending creep and the relaxation moment-time relationship under bending relaxation for sharp-notched circular tubes with different notch depths. Through comparing with the experimental finding, the theoretical analysis can reasonably describe the experimental result.
Thermal fatigue cracking may initiate at a T-junction pipe where high and low temperature fluids flow in from different directions and mix. Thermal stress is caused by a temperature gradient in a structure and by its variation. In this study, an experimental method was developed to estimate stress distributions at a T-junction pipe. FEM analysis and experiments to measure wall temperatures at the inner surface of the pipe with thermocouples were used in this method. The numerical simulations were performed to decide the optimum measuring points in the axial and circumferential directions for thermocouples. The numerical simulation results also showed that the attenuation of temperature amplitude and phase delay from the inner surface to the thermocouple measurement points was not negligible for 0.5 mm diameter sheathed thermocouples. A transfer function was calculated to obtain wall temperatures at the inner surface from measured data. In addition, the numerical simulation results showed that the amplitude and the phase of temperature fluctuations differed depending on existence of voids around thermocouples. These results showed that thermocouples should be installed in pipes without voids to measure accurate temperature fluctuations. It was confirmed that the voids disappeared when thermocouples were brazed in a vacuum atmosphere. Such thermocouples are expected to provide reliable experimental data from which the proper thermal stress distributions can be estimated by this method.
Machine condition monitoring and diagnosis have become increasingly important. It is generally considered that larger numbers of sensors will supply useful information for diagnosis, although the number of sensors is limited in actual applications. In this study, therefore, a method of virtual measurement at many points of the structure, i.e., an approximation method of responses at non-measured points, is proposed, and the diagnostic accuracy is checked. To this end, two methods are proposed. A method is based on the modal analysis using the measured displacements, in which the displacement of the overall structure is approximated using natural vibration modes whose number is the same as that of sensors. The other method is also based on the modal analysis, though the displacements used for the approximation are modified by the displacement ratio between the actual measurement and the simulated one. The validity of each method is checked using the experimental data. From the results, it was recognized that the proposed method based on the displacement ratio is useful for virtual measurements.
It has been shown that the significance of the positivity conditions in the collocation methods (CM), and the violation of the positivity conditions can significantly result in a large error in the numerical solution. For boundary points, however, the positivity conditions cannot be satisfied, obviously. To overcome the demerit of the CM, the over-range collocation method (ORCM) has been proposed. In the ORCM, some over-range collocation points are introduced which are located at the outside of the domain of an analyzed body, and at the over-range collocation points no satisfaction of any governing partial differential equation or boundary condition is needed. In this paper, it is shown that the positivity conditions of boundary points in the ORCM are satisfied by calculated results on the positivity conditions, while the positivity conditions of boundary points in the CM are not satisfied. The boundary value problems on the 2-D and 3-D Poisson’s equations and the 3-D Helmholtz’s equation are analyzed by using the ORCM and the CM. The numerical solutions by using both the ORCM and the CM are compared with the exact solutions. The relative errors by using the ORCM are smaller than those by using the CM, for both the unknown variables and their derivatives of 2-D problems and for the unknown variables of 3-D problems, and the relative errors of the unknown's derivatives of 3-D problems by using the ORCM are about same as those by using the CM. Convergence studies in the numerical examples show that the ORCM possesses good convergence for both the unknown variables and their derivatives. Because the ORCM does not demand any specific type of partial differential equations, it is concluded that the ORCM promises the wide engineering applications.