In this paper, the stress intensity factor K for the crack front line α − ε (1 + cosmθ ) , which is slightly perturbed from a complete circular line with a radius of α, is solved. The mathematical procedure chosen in this study is based upon the perturbation technique developed by Rice for solving the elastic problem of a crack whose front slightly deviates from some reference geometry. It is shown that the solution obtained for the stress intensity factor matches the results of a three-dimensional finite element analysis.
Recently, the indentation test has drawn attention as a new method for evaluating the interfacial fracture toughness, since its application enables the in-situ measurement using a Vickers hardness tester. An empirical formula for the stress intensity factor or J integral has been utilized to evaluate the interfacial fracture toughness from the indentation test. However, the method's applicability was restricted to a certain range of material combinations, which motivated this study. The object of this study is to find a general form of the interfacial J integral that can be applied to a wide range of material combinations. To accomplish this, the J integral was formulated by solving the interfacial fracture problem of the dissimilar material plate-shaped model with semi-elliptical crack located at the interface that is subjected to an indentation load modeled by point loads. Arbitrary material combinations and crack geometries were considered here. The validity of the J integral introduced here was confirmed by comparing to the numerical J integral evaluated by three-dimensional finite element analysis.
This paper presents theoretical solutions for cases of a two-dimensional isotropic elastic matrix containing two elliptical voids or rigid inclusions under anti-plane loading. These two ellipses have different long-axial radii, short-axial radii, inclining angles, and central points. Their geometries are arbitrary. The matrix is assumed to be subjected to arbitrary loading by, for example, uniform shear stresses, as well as to a concentrated force and screw dislocation at an arbitrary point. The solutions are obtained through iterations of the Möbius transformation as a series with an explicit general term involving the complex potential functions of the corresponding homogeneous problem. This procedure is referred to as heterogenization. Using these solutions, several numerical examples are presented graphically.
To fabricate a semiactive type of damper that is comparatively compact and has low mechanical loss, the author developed an electromagnetic damper using a brushless direct drive DC motor. The damper comprises a ball screw mechanism and a brushless direct drive DC motor that acts as a generator. The motor consists of a rotor and a three-phase stator, and it is installed at the tip of the screw shaft. The lack of contact between the rotor and stator is an advantage. When a linear motion is converted into a rotational motion by the ball screw mechanism, the rotor is rotated, and electrical driving power is generated by electromagnetic induction. The damping effect of each phase is caused by kinetic energy dissipation by the electrical resistances connected to each terminal of coils. In this study, a test damper is fabricated, and theories of resisting force and rise time are introduced. Performance tests are carried out to confirm the theories and the dynamic properties of the damper for two winding configurations, and the experimental results are compared with the theoretical results. The damping effect is greatly generated and smoothly, but saturated in high frequency range, and switched quickly by SSR. It is possible to make the damper more efficient, compact, and sensitive. Finally, theories and the dynamic properties of the damper are confirmed.
This paper proposes a nonlinear adaptive control method integrated with finite element approximation to obtain the model of the magnetic levitation system of 6 degrees of freedom. Since a magnetically levitated stage is free from friction, it is useful not only to position precisely, but also to measure small force applying to the stage. However, inherent nonlinear characteristics of electromagnetic force make it difficult to measure force correctly. Therefore in this study, with the aim to overcome this difficulty, a control method is proposed to obtain the model of the magnetic levitation system by adopting the manner of model reference adaptive control integrated with finite element approximation for the nonlinear characteristics of electromagnetic force. The controller can compensate the nonlinear characteristics by adjusting PD feedback gains using the obtained model. The parameters of inertia and the center of gravity are also identified to be reflected on a linear reference model. By compensating the nonlinear characteristics of electromagnetic force, the magnetic levitation system behaves as a linear system, which facilitates the position control and the force measurement. The efficiency of this method is shown in an experiment of improving the tracking trajectory control performance.