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In this paper, a numerical computation of consistent tangent moduli using complex-step derivative approximation (CSDA) is presented, and its applications to finite deformation problems are demonstrated. The consistent tangent stiffness is needed to achieve quadratic convergence in integration for boundary value problems. However, some material models lead to complex formulations of the consistent tangent stiffness that can be difficult to implement. This study shows a simple, robust and efficient numerical approximation of the tangent moduli that can be easily implemented within commercial FE software. Especially, the CSDA is focused on for numerical derivatives. The CSDA is proved to be of second order for suitably small perturbation and does not suffer from inherent subtractive cancellations that limits the accuracy of finite difference approximations, such as the forward Euler method and the central difference method, in floating point arithmetic. The implementation and the accuracy of this approach is illustrated through several numerical examples.

This paper studies the static and dynamic characteristics of tilting-pad journal bearings (TPJBs) with the load directions different from either of the two typical load directions of LOP (Load On Pad) and LBP (Load Between Pads). Theoretical results show that the effects of the load direction on the static and dynamic characteristics are found in the range of low Sommerfeld number S and increase with the decrease of S. The cross-coupling terms of spring and damping coefficients are no longer zero if the load direction is different from LOP and LBP, but the cross-coupling spring coefficients are equal, which indicates that the non-zero cross-coupling terms of the spring coefficients do not cause the self-excited vibration.

With smooth objective functions and constraint conditions, gradient-based methods can be used to solve multi-objective optimization problems efficiently. However, when applied to structural sizing optimization problems, using the Finite Element Method (FEM) and a finite difference scheme to calculate sensitivities can be computationally expensive. The adjoint variable method can be used to reduce computational cost. In order to solve multi-objective structural sizing and shape optimization problems efficiently, this paper proposes using the adjoint variable method. The adjoint variable method efficiently calculates multiple sensitivities for objectives that involve structural responses and cuts down computational cost by reducing the number of sensitivity calculations required per design variable.

Oil film seals of large diameter sometimes show long-period cyclic deformation of the floating seal ring whose rotation is constrained by a stopper pin. Cyclic change of deformation and oil film temperature may cause fatigue damage of the seal ring after long-term operation. We present a theory for the mechanisms of thermal deformation and its periodic transformation, the results of which agree well with those of measurements, and which provides a practical design criterion to prevent this phenomenon.

This paper describes two kinds of velocity-command-type trajectory control systems of a two-link flexible arm and experimental results using joint actuators and an active mass damper. One servo system has been developed which consists of a trajectory controller based on model-following servo control for the imaginary rigid body coordinate and an elastic deformation controller on LQI control. This system was shown to be effective from the experimental results and has the merit that controller gains can be easily calculated as constant values in spite of the flexible arm nonlinearity. Another servo system consists of a trajectory controller for the elastic deformation caused by gravitational force and a vibration controller using an active mass damper, which was also found to be effective.

In this paper, we investigate the system dynamics of a one-link flexible arm affected by reduction gear friction. The natural frequency of the flexible arm lessens when the friction is larger and approaches that of a cantilever beam. The system damping changes with its natural frequency. Experiments were done in cases of both small and large frictions. The friction torque was nonlinear with viscous and Coulomb damping. Nonlinear and linearized calculations were shown to be in good agreement with experimental results.