This paper summarises the successive development of the knowledge regarding shell buckling mechanics. Partly due to the major discrepancies between observed buckling loads and the prediction from theory, the buckling of shells has excited extraordinary interest since the beginning of the last century. The author reviews the historical changes in the understanding of the buckling mechanism of shells. Physical experiments made by the author in the past are compared with nonlinear numerical experiments carried out recently using an advanced finite element technique. It is shown that since measured geometric initial imperfection distributions are carefully installed, good agreement between the numerical simulations and the experimental results are obtained not only for buckling loads but also for postbuckling large deflection behaviour.

View full abstract

Spatially localized patterns are ubiquitous such as chemical blobs, discharge patterns, morphological spot, and binary convection cells. When they are moving in space, it is unavoidable that they collide each other, interact strongly and emit various outputs depending on incident angle and parameters. Moving localized spots in dissipative systems have their own internal hidden dynamics. Here "hidden" means that various types of instabilities are not visible when they are isolated, but those ones come out from the hidden state when they collide with each other or encounter defects when the propagating media is heterogeneous. They display rich dynamics such as rebound, annihilation, coalescence, and splitting through the collision process. A new approach is presented to clarify an underlying structure behind those dynamics. A key ingredient lies in a network of unstable solutions, which plays a crucial role to understand the input-output relation for collisional process. A remarkable thing is that there appears a time-periodic rotational motion as an output for the case of oblique collision. This approach is also useful to understand the dynamics of traveling spots in heterogeneous media.

View full abstract

Even if one or a set of structural member in building structures disappears suddenly due to accidental loads, the building should stand against vertical gravity loads, dead or live, not resulting the whole collapse.
According to these facts, a close-up of new concepts, such as redundancy and a key element, has been taken from a viewpoint of assuring robustness of a structure even if it receives unexpected disturbance.
This study investigates the structural redundancy and the effects of catenary action based on another resistant mechanism after failure mechanism formation obtained from the plastic analysis. The systematic plastic calculation and the non-linear push-down analysis are conducted on the framed structures.

View full abstract

This paper aims, first, to introduce an outline of the modified MMX-model, a double yield surface type model, in which the compression component is modified in order to improve its compatibility of compression property for test data of consolidation. Next, accuracy of the model is verified using analyses of 1D one-element and 15-element models by vertical loading stress. It is confirmed that the developed compression component of the model performs accurately. Then, data from thirteen years settlement record of an embankment on soft clay layers measuring 57.1m in depth and of a structure located 50m from the center of the embankment are used as a comparison index of performance of the model.
It is concluded that the modified MMX model can be used as a pre-calculation method in practice, such as for a method based on "performance-guarantee concept" with sufficient accuracy.

View full abstract

For the qualification of an ion thruster system for spacecraft, a time-consuming endurance test of more than 10,000 hours is required. To drastically reduce the cost and the time required for an ion thruster life test, a numerical tool called JIEDI (JAXA’s Ion Engine Development Initiative) is under development. The JIEDI code numerically estimates ion bombardment to an ion thruster’s grid material to predict the erosion rate of the grid material. Preliminary erosion rate analysis by the JIEDI code showed good agreement of erosion rate with a life test; the calculated grid erosion rate agrees with that of a life test within an accuracy of 40%.

View full abstract

This study evaluates the reinforcement effect and the fatigue resistance of RC slabs reinforced with carbon fiber sheet (CFS) and grid-bonded carbon fiber strand sheet (CFSS) where the concrete has deterioration RC Slab that assumes compressive strength has been reduced by salt or frost damage and RC Slab by which concrete compressive strength fills specified concrete strength. The study verifies the influence of concrete compressive strength on the reinforcing effect of these methods. The results indicate that CFSS grid-bonding reinforced RC slabs have greater fatigue resistance than CFS reinforced RC slabs. Further, if deteriorated RC slabs, where the concrete compressive strength has been reduced by salt or frost damage, are reinforced with the CFS or CFSS grid-bonding methods, the required fatigue resistance cannot be achieved, although the reinforced slabs are somewhat more resistant than unreinforced RC slabs. Accordingly it is necessary to check the concrete compressive strength of the RC slab during the inspection of a road bridge before applying CFS or CFSS grid-bonding reinforcement.

View full abstract

An analysis of dynamic behavior is carried out in the case when dynamic load with a central symmetry is applied on the inner face of the cavity with a central symmetry in a thick-walled elastic-plastic-viscoplastic sphere. First, formulas are derived of propagation speeds of elastic-plastic-viscoplastic spherical waves. Second, the theoretical formula is analytically proved to be strain rate and stress rate dependent. Third, ordinary differential equations among physical quantities are derived along characteristic curves. Fourth, the propagation theory of spherical wave based on the elastic-plastic-viscoplastic constitutive equation is shown to contain one based on the elastic-plastic constitutive equation. Fifth, calculated examples are shown on the basis of the elastic-plastic-viscoplastic theory. Last, a comparison is done of calculated results based on the elastic-plastic-viscoplastic theory with those based on the elastic-plastic theory.

View full abstract

For circular cylinders, the Timoshenko beam theory, which includes both shear deformation and rotary inertia effects, can be applied by introducing the constant 0.9 or 6(1+ν)/(7+6ν) for the shear coefficient κ, where ν is Poisson's ratio. In this paper, we show that for the simply supported circular cylinders, firstly, both the first spectrum and the second spectrum can be determined exactly by the phase velocities of the transverse elastic waves in the Pochhammer-Chree theory. Secondly, from the Timoshenko beam theory, it is shown that the same results can be obtained by the new shear coefficient, which is constructed both by the phase velocities of the transverse elastic waves in the Pochhammer-Chree theory and by the ratio of the radius of the circular section to the wavelength. The new shear coefficient is obtained by a fourth-order equation for the angular frequency.

View full abstract

We consider a discrete version of phase field model based on the spring-mass system, and show some relation to the DEM type crack propagation model. We also briefly introduce our phase field model with two or three dimensional linear elasticity that is based on the Francfort-Marigo type energy⁸⁾ with the Ambrosio-Tortorelli regularization¹⁾. We show how it works in the case that the fracture toughness is spatially variable in some numerical examples for mode III fracture.

View full abstract

Multi-period repetitive (MPR) controllers were proposed by Gotou et al., in order to improve the disturbance attenuation characteristic of modified repetitive control systems. Using MPR controllers, transfer functions from the periodic reference input to the output and from the disturbance to the output of the control system generally have infinite numbers of poles. To specify the input-output characteristic and the disturbance attenuation characteristic easily, Yamada et al. proposed MPR control systems, named simple MPR control systems, where these transfer functions have finite numbers of poles. However, the parameterization of all robust stabilizing simple MPR controllers for the plant with uncertainties has not been considered yet. In this paper, we propose the parameterization of all robust stabilizing simple MPR controllers.

View full abstract

In this paper, we examine a design method for modified Proportional-Integral-Derivative (PID) controllers for multiple-input/multiple-output time-delay plants. The PID controller structure is the most widely used one in industrial applications. However, there exist plants those cannot be stabilized using PID controllers. In order to overcome this problem, the modified PID controller, which can stabilize any plant, was proposed by Yamada et al. Yamada, Hagiwara and Shimizu expanded the result by Yamada et al. and proposed a design method for modified PID controllers for time-delay plants. However, no method that guarantees the stability of a PID control system for any multiple-input/multiple-output time-delay plant has been published. In this paper, we propose a design method for modified PID controllers such that the modified PID controller makes the feedback control system for any multiple-input/multiple-output time-delay plant stable, admissible sets of P-parameter, I-parameter and D-parameter are independent from each other and the transfer function from the reference input to the output has a finite number of poles in order to specify the input-output characteristic easily.

View full abstract

In this study, stability derivatives of a small unmanned aerial vehicle (UAV), which is fixed-wing aircraft whose wingspan and weight are approximately 1 m and 1 kg, respectively, are estimated accurately by a novel system identification method called wavelet filtered regression (WFR). Conventional system identification techniques such as filter error methods (FEM) have been used to obtain the stability derivatives of general aircraft; however, they cannot estimate those of the small UAV accurately, because small UAV flight is easily disturbed by process noise represented by wind gust. WFR has robustness against such disturbance by using time-frequency information provided by multi resolution analysis (MRA) of wavelet transform. The comparisons of WFR and FEM estimation results clearly show the advantages of WFR. The resemblance between WFR and subspace identification methods is also described.

View full abstract

We consider the solution of the Duffing type equation ü + au + bu ⁿ = 0, where u = u (t) is a real valued function. We state that the solution, through the variable transform v = u ^ν,ν = ± 1,±2,…, can be presented using Jacobi elliptic functions only when n = -3,2,3,5. Also we present the solution of n = 5 and show a relation of Malmquist-Yosida theorem.

View full abstract

We numerically investigated the peristaltic motions of an earthworm-like robot model with and without setae. The model was constituted of a Mass-Spring-Damper (MSD) unit which has taken the unsteady effects of a fluid into account. Though the model could move even if it did not have setae, direction and speed of its movement depended on the initial motion of the vibration. The earthworm-like seta was found to contribute to the determination of not only direction of motion, but also speed of the model. We tested different contact angles of the seta, different values of friction between seta and wall, and effects of density and viscosity of fluid around the body. The body moved most quickly when the contact angle of seta was 45 degrees. The speed of the earthworm-like robot was found to depend on the density of fluid and the friction acting on the seta during peristaltic motion.

View full abstract

We consider an envelope function for the multi-dimensional wave u (x, t) defined by a Fourier transformation. In [3] and [4] we showed that it satisfies a kind of Schrödinger equation when the angular function ω(k) is a second-degree polynomial. The result is an extension of B.T. Nohara [7] which treated the one-dimensional case. In this paper we extend the above results to the case whenω(k) is a general function which is not necessarily a second-degree polynomial and estimate the difference between two cases. From the result we show that a nealy monochromatic wave with a general angular function is an approximated solution of the Schrödinger equation. Furthermore we also show that a nearly bichromatic wave satisfies a nonlinear equation.

View full abstract

In this paper, dynamics of chemotaxis system is studied. Applying the invariant manifold theory for parabolic equations, we will show that the hexagonal pattern in chemotaxis system is destabilized with pure imaginary eigenvalues by a suitable choice of parameters.

View full abstract

We study the free-surface dynamics of rotational flow by time series analysis. In a flow driven by a rotating disk in a cylinder, the free surface irregularly switches between an axisymmetric shape and a nonaxisymmetric shape. This surface switching occurs in combination with significant elevation and elongation of the central part whose height has a strong correlation with the turbulent intensity. Although the number of degrees of freedom for the entire system is considerably large, the surface-shape dynamics indicates that the dimension needed to describe the major motion is much smaller compared with the whole system and the remaining part constitutes noise added to the major part. We have evaluated this conjecture by applying a diagnostic method and have clarified that the time series of the surface height is different from the white noise and the surrogate data of the original time series, both of which have no determinism.

View full abstract

A hamiltonian (H) system with a gradient term is studied from the viewpoint of the temporal behavior of the conserved quantities. If we take a suitable potential G, the conserved quantities approach constants which are given as free parameters.This property holds even if there is another conserved quantity in addition to the hamiltonian.Two examples are given in order to demonstrate this hamiltonian-gradient (HG) system. One is a simple harmonic oscillation and the other is a system of many point vortices. The latter is a typical hamiltonian system with two conserved quantities. Analytical and numerical results of the H and HG system are given and compared to each other, by using various explicit finite difference schemes, including the Euler's, Heun's, and the fourth-order Runge-Kutta methods.

View full abstract

We studied the three-dimensional steady flows of an incompressible fluid in a square cavity of spanwise aspect ratio 6.55 with a sliding lid. Numerical simulations were carried out for the Reynolds numbers Re ranging from 100 to 400. A combined compact finite difference scheme with high accuracy and high resolution is adopted to calculate derivatives in the equations. Streamlines and the Poincaré sections are obtained from the velocity fields of the steady flows. There are localized streamlines for Re from 100 to 300 and globally moving streamlines which correspond to chaotic motion for all Reynolds number range. In the Poincaré sections, similar structures as those in a cubic cavity which result from the localized streamlines are found in the region near the end-wall.

View full abstract

We study the mathematical structure of localized convection cell solutions in a binary fluid mixture. These solutions are not observed in Rayleigh-Bénard convection in a pure fluid in which the concentration field is homogeneous. In particular, a solution representing time-periodic traveling localized convection cells (periodic traveling pulse, PTP) has not been obtained even numerically because this solution requires two unknown variables to be determined: group velocity and temporal period in the comoving frame with the group velocity. We have applied an integrated numerical method to obtain the PTP solution as well as the steady, periodic, and traveling solutions. Therefore, we can treat all classes of solvable solutions under the integrative framework. By using this method, a global bifurcation structure containing a variety of solutions including PTPs is obtained and the phase dependence of the collision of counter-propagating PTPs is investigated in detail.

View full abstract

We have developed a new lattice Boltzmann model which can simulate supersonic flows described by the compressible Euler and Navier-Stokes equations. The model is based on the free-molecular-type kinetic equation whose basic calculation system was devised by Sone in the year 2002. Our proposed scheme is superior to the existing lattice Boltzmann method (LBM) in the following two points: (I) supersonic flows can be simulated; (II) any transport coefficients can be chosen freely according to our convenience. Several numerical simulations are carried out to confirm the above merits of the scheme. Numerical results agree well with the corresponding solutions of the Euler and Navier-Stokes equations even for supersonic flows.

View full abstract

We study the Euler equation concerning compressible isentropic gas and examine total mass and total energy conservations in the whole space in multi-dimensional case.

View full abstract

The effects of transport properties (viscosity and thermal conductivity) and surface roughness were compared experimentally to investigate non-self-similar Mach reflection phenomena in weak shock waves. The effect of the transport properties was changed by varying the initial pressure ahead of the incident shock in experiments conducted at Karlsruhe (KIT) and Saitama (SIT). By introducing a non-dimensional distance based on physical properties behind the Mach stem, the difference between the results under various experimental conditions was diminished, and in some cases the results almost coincide with each other within the error in angle measurement. In order to investigate the effect of surface roughness, further experiments were conducted at SIT using models with rough surfaces. The results were compared with those for smooth surfaces. The effect of surface roughness turned out to be small compared with the viscosity effect, proving the effect of transport properties to be dominant. The fact that the discrepancies between the SIT and KIT experiments vanished after introducing the non-dimensional coordinate may possibly be ascribed to inaccuracy in angle measurement at KIT.

View full abstract

A particle-in-cell approach using a fixed mesh and a set of Lagrangian markers is developed to numerically solve fluid-structure interaction problems. On the basis of a basic equation set for systems involving incompressible Newtonian fluid and neo-Hookean material, which has been formulated in a full Eulerian framework (Sugiyama et al. (2010) Comput. Mech., 46, 147), the conservation equations are solved on the fixed mesh. A numerical evaluation of a hyperelastic stress is combined with the Lagrangian markers, on which a left Cauchy-Green deformation tensor is temporally updated to quantify the solid deformation level. The simulation method is verified and validated for axisymmetric flows inside a neo-Hookean tube subjected to a pressure gradient. Further, the method is applied to tube flows containing discoid biconcave particles.

View full abstract

A coupling analysis of thermal convection problems is performed in this work. By approximating the material derivative along the trajectory of fluid particle, the characteristic curve (CC) method used in this research can be considered as an upwind method. The most attractive advantage of this method is the symmetry of the linear system, which enables some classic symmetric linear system iteration solvers, like the conjugate gradient (CG) method, to be used to solve the interface problem of the domain decomposition system.
In order to implement a coupling analysis of the Navier-Stokes problem and the convection-diffusion problem, the CC method is applied to both parts, and the results of searching for elements in each non-stationary loop are shared by both. The code has been developed under the hierarchical domain decomposition system, and comparisons between the solvers based on the CC method and product-type methods have also been done.

View full abstract

Dielectric barrier discharge plasma actuators (DBD-PA) have been investigated for active control of flow separation around a MEL001 laminar airfoil. Tangential wall-jets with various speeds were produced in the vicinity of the DBD-PA at 30% chord position downstream from the leading edge of the airfoil. The flow separation control ability was evaluated at low Reynolds number, Re = 1.0×10⁴, in an open-circuit blower type wind tunnel with 200mm×200mm×600mm test section. By analyzing instantaneous and time-averaged velocity distributions around the airfoil using a particle image velocimetry system, the flow conditions induced by the DBD-PA to suppress the flow separation and minimize the drag coefficient were found for angles of attack α = 4.2^ο, 8.4^ο, and 12.0^ο degrees. At these angles, the lift-to-drag ratio of MEL001 airfoil drops significantly in this low Reynolds number regime, and our results suggest that the DBD-PA produces a significant performance improvement.

View full abstract

Numerical simulations for Typhoon Ioke (2006) are carried out by using the WRF model and that with the revised formulation of exchange coefficients for momentum (C_d) and enthalpy (C_k), in order to examine the influences of surface exchange coefficients in strong winds upon the structure and intensity of tropical cyclones. The simulated results show that the reduced exchange coefficients in strong winds do not significantly affect the minimum surface pressure of the tropical cyclone while the maximum wind speed at the surface increases significantly. Furthermore, it is found that the convective intensity is significantly decreased in the reduced—C_d case specifically in the eyewall region. It is also shown that in spite of the reduced drag coefficient at high wind speed, the surface convergence does not change.

View full abstract

We numerically examine the role of filaments in the axisymmetrization of an isolated elliptic vortex with a non-uniform vorticity distribution for a two-dimensional incompressible barotropic fluid. To quantitatively examine the role of filaments in the axisymmetrization, we first divide the vorticity field into a core region and a surrounding region. The former corresponds to the core of the vortex, and the latter corresponds to the filaments and a weak vorticity region just outside the vortex core. Second, we analyze the radial displacement of the maximum and minimum curvature points on a vorticity contour in the core region advected by velocities induced by the vorticity of those regions. This investigation shows that the vorticity of the surrounding region largely contributes to the axisymmetrization at both points, especially when the filaments are forming. Thus, we conclude that the filaments play a significant role in the axisymmetrization of the isolated elliptic vortex.

View full abstract

A group of new methods is proposed for numerical simulation of acoustic problems. Symplectic methods are known to be effective for long time integration of particle motions. They are also applicable to the partial differential equations. For the wave-like equations, it has been noted that methods with smaller phase lag are preferable. On the other hand, trigonometric fitting (TF) methods have been proposed for the integration of harmonic oscillators and other oscillatory problems. TF methods are capable of integrating with practically no phase error. However, their application is limited to the cases where frequency of the system is known beforehand. In order to utilize the advantage of these methods, symplectic spectral TF method is proposed in the present study. By combining the advantage of small phase error and the spectral representation of the waves, the method is capable of integrating the wave equations with extremely high accuracy. Performance of the method is tested for benchmark problems.

View full abstract

We propose a new simple method of constructing bivariate copulas, which evolve according to the time variable. It is proved that for any copula there exists a time-parametrized family of copulas which realizes this copula as the time tends to the maturity. Applications are also discussed.

View full abstract

We reinvestigate the error in the time reversibility for a self-gravitational system of Komatsu et al.¹⁾, who showed an increase of the error with decreasing stepsize for a standard Verlet integrator, to identify the reason for the irreversibility under the many possible causes. For (reversible) velocity Verlet and implicit Runge-Kutta type of integrators, the dependence on the stepsize vanishes, but there is a lower limit for the exponential time evolution of the error. The exponent of the error in the reversibility corresponds to the Lyapunov exponent, which means it can not be overcome with improved numerical methods. Because reversible integrators are very often tested with few particle systems, our finding is important as a caveat that for many-particle system, even with reversible integrators and all other numerical errors well controlled, the system trajectories become irreversible if the nonlinear character of the system is too pronounced.

View full abstract

Phenomena which concern granular particles and porous media such as landslides and ripples in the sand of windy deserts are strongly connected with the fluid around the granular particles. To analyze these phenomena, a simulation method is necessary which yields both macroscopic and mesoscopic physical quantities of the system. For the combination of the discrete element method for the particles with a finite element method for the fluid of our research group we developed an automatic mesh generator based on a constrained Delaunay triangulation. The meshes in the resulting unstructured grid are equilibrated towards equilateral triangles for improved accuracy. The relaxation is performed by an integrator of zeroth order.

View full abstract

The discrete element method allows the simulation of complex behavior of granular materials without constitutive laws. While in two dimensions shape-effects are well established, in three dimensions there is no universally applicable simulation algorithm for non-spherical particles. We will first present a force model for convex polyhedral particles, using the "overlap" of non-deformed polyhedra as a "measure" of the elastic force and explain the overlap computation algorithm. With this elastic force model, we then show that the continuum-mechanical sound velocity can be recovered for a space-filling packing of cubic blocks. Further, we show simulation results for heaps for which we obtain realistic high angles of repose, which corroborates the reliability of our simulation method and which further more shows that with our method, a larger phenomenology is accessible than with round particles.

View full abstract

To develop a quantitative earthquake forecasting model, we experimentally estimated frictional parameters at a model plate interface during an earthquake generation cycle using realistic synthetic observational data. We used a 2-D fault model based on a rate- and state-dependent friction law to generate displacement data at observation points located above the fault plane during the latter half of an interseismic period, when fault slip is stable and slip rate is nearly constant. We estimated the likelihood of friction law parameters using sequential importance sampling (a particle filter). We accurately determined A — B, which represents the rate dependence of steady-state frictional stress, for an aseismic slip area around a circular seismic slip area using typical noise levels and observation point spacings. However, the characteristic slip distance d_c we estimated for the aseismic slip area contained large estimation errors. We found that the likelihood distribution depended on the noise level of the data rather than on the interval between observation points. Moreover, we found two ranges of A — B, one with high likelihood and the other with low likelihood, even when the noise level was too high or the data period was too short for detailed estimation. The likelihood data provided little information for determination of d_c, indicating that aseismic sliding during the interseismic period is much more sensitive to A — B than to d_c. These results indicate that interseismic displacement data are useful for estimating friction parameters, especially A — B values.

View full abstract

The Tricomi equation is solved numerically. Boundary value problems (BVPs) and ill-posed Cauchy problems (CPs) are considered. Problems are discretized by using the finite difference method (FDM) or the spectral collocation method (SCM). The numerical computation is carried out in the multiple-precision arithmetic. For BVPs both FDM and SCM work well. When the exact solution is a part of a global and analytic function accuracy of numerical results are expectable. They show that the maximum principle does not hold here. Some other BVPs are solved and numerical results are satisfactory. For CPs SCM works well but FDM does not. When the exact solution is a part of a global and analytic function accuracy of numerical results by SCM is expectable. Some other CPs are solved by SCM. Numerical results suggest that there exist some delicate problems as nonexsistence of the solution. They also show the effectiveness of SCM with the multiple-precision arithmetic in the numerical simulation for delicate problems.

View full abstract