Eddy currents in a conductor moving in a non-uniform magnetic field in a static coordinate system are expressed as the superposition of the term by the partial derivative of the magnetic vector potential with respect to time and by the gradient of scalar potential in a stationary-conductor coordinate system. In this study, we proposed the general equation of “gradient of scalar potential is zero” condition (GSPZ condition) throughout the conductor. Additionally, under satisfying the GSPZ condition, we propose the method of obtaining the magnetic damping force from both the magnetic flux densities and the eddy currents calculated using the Biot-Savart law and Fleming's left-hand rule for the parallel-motion-type eddy current damper (GSPZ-A method). The precision of the GSPZ-A method is similar to that of the three-dimensional finite element method (3D-FEM); however, the effect of the secondary magnetic field was not considered. In this study, the GSPZ condition for the parallel-motion-type eddy current damper of a rectangular magnet and conductor of arbitrary dimensions was established. Furthermore, the GSPZ condition was applied to two types of eddy current dampers—one composed of the single square magnet and the other of the combined square magnet with oppositely aligned magnetic poles. The magnetic damping forces calculated using the GSPZ-A method were compared with those obtained from the 3D-FEM and experiments. As a result, the errors from the GSPZ-A method to 3D-FEM for the single and combined magnets were 10 and 0.4 %, respectively.
Titanium and its alloys are widely used as orthopedic devices for fixation of bone fractures. A combination of low elastic modulus and suitable implant plate thickness, to adjust the stiffness of the implant plate, can improve the healing process. The present study investigates the effect of titanium plate stiffness on the bone formation during the early stage of healing in rabbit femurs. Materials with different elastic moduli, Ti-29Nb-13Ta-4.6Zr (TNTZ) and Ti-6Al-4V ELI (Ti-64), were used as implant plates, and the effect of plate thickness on the bone healing ability was explored. Two types of titanium implant plates of thickness 0.5 mm were used, and after three weeks, the femurs were harvested. Bone cross-sections of the femur were analyzed using scanning electron microscopy, hematoxylin & eosin staining, and Vickers hardness test. Fixations using both the implant plates showed almost similar bone structures but different average total callus areas. Fixation using the TNTZ implant plate resulted in a larger area of callus formation than that using the Ti-64 implant plate of same thickness, but the callus hardness was almost similar. Therefore, we conclude that an overly flexible fixation system results in an excessive callus formation and delayed union. Suitable implant characteristics can result in enhanced bone healing, superior bone properties, such as improved hardness.
In this paper, a domain integral method to evaluate the J-integral along with a singular patch method for three-dimensional linear elastic fracture mechanics analyses using Isogeometric analysis (IGA) are presented. The analyses are carried out using a singular patch method that can realize the square-root singularity in the stress distribution in the vicinity of the crack front. The sizes of IGA elements adjacent to the crack front are generally much larger than those of finite elements in the crack analysis. The proposed domain integral method enables a pointwise evaluation of the J-integral at a point on the crack front curve. To achieve it, integral domain with a very small thickness is set at the crack front. To examine the accuracy, the proposed methods are applied to the problems of semi-elliptical crack problems with high aspect ratios. Stress intensity factors are computed by the J-integral method. The proposed methods are found to evaluate the stress intensity factors accurately.
To solve the serious problem of residual swirl of flue gas and gas temperature deviation between two sides at furnace outlet in a 330MW tangentially fired boiler, a numerical simulation on combustion under multiple conditions was proposed. The effect of SOFA nozzle tilt angle on the residual swirl and gas temperature deviation of furnace exit was carefully studied. In addition, a monitoring system for cross-section temperature fields at furnace exit was designed. Four flame detectors were installed on a section of furnace exit. Through processing flame radiative image, the temperature fields of the section were detected. Combined with field experimental conditions, the SOFA nozzle vertical angle experiment was carried out with detection system. The results show that as SOFA nozzle swings downward, it is beneficial to weaken the residual swirl of flue gas and reduce the gas temperature deviation of boiler.
A class of optimization problems which are formulated using solutions to boundary value problems of partial differential equations (PDEs) as equality constraints is called PDE-constrained optimization problems. Specifically, when the variable in the optimization problem is given by a function defined in the PDE, the problems are classified as PDE-constrained non-parametric optimization problems. The topology and shape optimization problems of density and domain variation type, respectively, are included in this category. This paper is written to convey the idea of the author who worked on this topic for over 30 year, unlike the usual review papers. After showing real images of the problems, the author’s theoretical image is introduced. Based on the theoretical image, basic questions about the structure of the problems when viewed as a function optimization problem are proposed. The author’s answers to these basic questions are presented in the next section. Based on the understanding, some numerical results in which anxious phenomena are observed are presented and their causes are discussed. The expectation of applying the basic theory to real-world problems is presented using examples. Applying the theory of shape optimization problem of domain variation type, a problem finding the optimum shape of a sole in sports shoes that maximizes the stability under keeping the ideal cushioning is introduced. Applying the theory of topology optimization problem of density variation type, a problem identifying the muscle activity in a tongue during swallowing is explained. From these examples, it is concluded that PDE-constrained non-parametric optimization problems can be effectively applied to real-world.
In this study, we performed in vivo impact experiments emulating physical contact between humans and personal care robots and evaluated the conditions resulting in bruise injury due to subcutaneous hemorrhage and injury resistance. Anesthetized live pigs were used as alternate specimens, and the experiments were performed using a self-made free-fall impact tester. We investigated the existence of subcutaneous hemorrhage and performed its quantitative evaluation by hematoxylin and eosin (HE) staining of soft tissue samples at the site of the impact load. The results showed that bleeding, adopted as the indicator of bruise injury, occurred when the total energy transferred (an index of injury resistance) was 46.8 kJ/m2. Further, when the net energy transferred was used as the injury resistance evaluation index, the threshold value for bleeding was 30.3 kJ/m2. When the maximum stress was used as the injury resistance evaluation index, the threshold value for bleeding was 1.14 MPa. To investigate the possibility of adopting the injury resistance threshold of the alternate specimens obtained in this study as the injury resistance threshold of humans, we studied the capillary bleeding resistances of the test specimens experimentally. We compared these values with the capillary resistance of humans and examined the bleeding capillaries’ fragility.
A time-saving finite element method (FEM) based approach for structural topology optimization with exact boundary representation is proposed in this work. The optimization process consists of two loops. The first loop adopts a fixed and fairly coarse mesh. Afterwards, the second loop reconstructs the material domain and hence the boundary representation becomes exact. A novelty of this work is that our two-loop approach is realized with the domain reconstruction (not just remeshing). The convergence of the second loop is only made possible by imposing the volume constraint in an exact fashion. The proposed approach can save a substantial amount of computational time while allowing the exact representation of boundary (no grayscale throughout the second loop). For the two-loop approach, its computational time can be reduced to merely 13.6% of that for the single loop approach. The optimized structure is also found independent of mesh size. In addition, the two-loop approach resolves the issue of a deteriorated connectivity of the reconstructed domain Ω once the constrained volume is set extremely small.