This paper reviews recent development of ultrasonic nondestructive evaluation and related technology with emphasis on quantitative approaches in theory and experiment, including numerical simulation, of ultrasonic waves, inverse scattering analysis and ultrasonic measurement with an arrayed transducer.

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The effect of pre-stress on the scattering of plane SH-waves from a circular cylindrical cavity in a compressible isotropic elastic medium, is studied. The complex function method is employed to analyze the incremental boundary value problem. The spatial variables (x₁, x₂) are mapped onto two different complex planes so that the series solution of the incident waves and the scattered waves are expressed as functions of two different complex variables. The coefficient of each tam in the series solution can be computed numerically from a set of linear simultaneous equations, which are constructed by satisfying the incremental traction-free boundary condition along the surface of the cavity. Varga material is assumed in the numerical examples. Varying the principal stretches, the effect of pre-stress on the dynamic stress concentration factor and the scattered energy is investigated.

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A multiscale decomposition of a volume integral equation is presented for analyses of scattered waves. The integral equation is constituted by dynamic Green's functions for a homogeneous space or a layered half space. The method for the multiscale decomposition is carried out based on the usage of the Haar scaling functions and wavelets. Several numerical calculations were carried out to verify the possibility of the Haar scaling functions and wavelets for the present type of the integral equation and to investigate the scale effects of the wave field on the scattering waves.

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This paper deals with the characteristics of the parametric excitation, which is one of the dynamic instability phenomena, of Submerged Floating Tunnel. In this study, it is assumed that the structure is moored by some tension legs and located in the water between seabed and water surface. The parametric excitation is caused by the time tension force of tension legs. The time-varying tension force arises when some dynamic loads such as regular waves act on the floating body and the body moves in the water. The analytical studies are carried out to confirm the possibility of the occurrnce of unstable motions by introducing Mathieu-type equations in this study and effects of tension leg arrangements, viscous damping, quadratic damping and external forces on the parametric excitation characteristics are investigated in particular.

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In this study, the local deformation of plates is approximated by a linear spring-mass model, and then the equivalent spring parameter is determined by an approximate method. The spring parameter is the function of the stiffness constant determined by a static solution, the initial velocity, mass of the impactor and mass of the plate. The validity and effectiveness are illustrated by numerical examples. The comparison of impact forces using proposed method and Hertz's law shows that this method yields very good results.

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Since Reissner and Mindlin proposed their classical thick plate theories, many authors have presented refined theories including transverse shear deformation Most of those plate theories are derived through expanding displacements and stresses into power series along the thickness. In general, the higher the order of the theories is, the higher the accuracy of those is. However, the conciseness of the classical theories has been lost. On the other hand, the importance of transverse load effect is not noticed in those plate theories. In this paper, we pay attention to formations of the load of plates. The formations of load are represented by rate parameters, which indicate portions of a body force and surface tractions. When we introduce the rate parameter for loads and consider the transverse normal stress distribution, we can establish a quite simple plate theory including transverse shear deformation. In addition, the new theory presented here gives us excellent results of a deflection and bending moments.

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Extensive study was conducted to examine carefully the characteristic of the normalized plastic work under undrained condition. The effect of both the principal stress direction, α, and intermediate principal stress coefficient, b, were explored as well. The results clearly show that undrained normalized work of sand is almost independent of relative density, confining pressure, and the confining stress ratio, but it is not unique with respect to α and b. The slope of normalized work which is known as dilatancy parameter μ reaches minimum value when α is set to value between 60° to 75° and b is near to 0.75.

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Deformation of sand due to both single and adjacent surface foundations was observed by means of a newly developed method of image analysis to measure displacement field in model soil. Development of deformed area and propagation of slip lines were illustrated and effectiveness of two adjacent foundations were discussed. The results showed that an additive 50% of ultimate bearing capacity is available if spacing of two adjacent foundations equals the width of each foundation. Otherwise the effect begins to vanish when the spacing exceeds 2.5 times of the width of each foundation, and works as if two individual foundations when the spacing exceeds four times of the foundation width.

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The authors have been investigating an inverse problem of determining the position and the shape of unknown cracks in a material using velocity waveform data of the ultrasound measured with a laser interferometer. In our previous works, however, only the vertical velocities have been utilized in the crack determination, despite the fact that the horizontal and vertical velocities on the surface of the material are calculated numerically using time domain elastodynamic BIEM in 3D. We measure the particle velocities from the directions tilted from the normal direction to obtain both the horizontal and vertical velocities using the vector decomposition rules for these velocities. We can determine the unknown cracks more accurately using the horizontal and vertical velocity waveforms than using only the vertical velocity waveforms.

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For the maintenance of civil structures, it is important to characterize the flaw geometry. The linearized inverse scattering method is improved with the aim of applying it to the civil structures. The method utilizes the scattering amplitude in an elastic solid for reconstructing the shape of flaws, and the low frequency component of measured wave data plays a key role. The ultrasonic wave in low frequency range has potential to propagate deeply in the structural component and reflect back from flaws. In this study, data processing techniques to extract the scattering amplitude from the measured waves are discussed and a convenient method to obtain a reference waveform is proposed. And, concrete specimens that contain flaw models are prepared and experimental measurements are carried out to confirm the performance of the method.

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Defect shape reconstruction ability of Synthetic Aperture Focusing Technique (SAFT) is investigated by numerical simulations. The numerical model employed is an infinite plate with an embedded cavity. Two types of cavities are considered. One is a circular cylinder and the other is a rectangular slit, both having the dimensions comparable to the incident wave length. Array sources/receivers of anti-plane waves are placed on a plate surface, and time domain scattered waveforms are calculated for every transmitter-receiver combination to simulate data collection by an SH-wave array transducer. Sets of array data simulated thus are fed into SAFT, and the cavities of given shapes are reconstructed. Comparing the resulting SAFT images one another, the effect of transducer position, source width and multiple wave paths on the shape reconstruction ability of SAFT is investigated. It is shown that aperture angle defined in the present study is an important concept to understand the effect of transducer position and of the multiple wave paths. It is also shown that the larger source width degrades SAFT images, but the degradation mechanism considering directivity of the incident field are explained.

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In this paper, a newly derived algorithm to detect damage and predict its location in structures using changes in vibration measurements is presented. First, an existing algorithm of damage detection is reviewed and the new algorithm is formulated in order to detect damage and improve the accuracy of damage localization using low frequency range. Compared to the existing damage detection algorithm, the new algorithm showed the ability to detect and localize damage more accurately using very low frequency range without the need for measuring higher modes.

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This paper proposes a practical method for back-calculating Mohr-Coulomb strength parameters c and φ based on the shock loading test in which an weight falls to ground surface. The displacement of the weight which is obtained by the time integration of measured shock acceleration is shown to be reliable. Strength parameters c and φ are back-calculated so that those minimize the difference between measured and calculated displacements. It is possible to estimate correct c and φ by using a few numbers of c-φ relationships obtained from some tests with different falling height of weight.

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During the 1948 Fukui earthquake, most of the heavily damaged areas concentrated in the Fukui plain covered with thick Quaternary deposits. This suggests that the Quaternary deposits can be one of the most important factors to elucidate the damage distribution. In this study, the S-wave velocity structure of east-west cross section of the Fukui plain has been estimated based on microtremor array observation. Vertical microtremors were observed at 8 sites around Fukui plain. The Rayleigh wave phase velocities were estimated from a spatial autocorrelation analysis. The phase velocities at each site were inverted to a vertical S-wave profile using a genetic algorithm. For the inversion analysis, initial S-wave models were set by using the correlation between the phase velocities of the Rayleigh wave and the travel-time-weighted average S-wave velocities of the sites. It was confirmed that the estimated S-wave velocity structures are harmonized with existing boring profiles and elastic-wave reflection surveys.

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This paper describes the new algorithms for highly accurate displacement field measurement system to measure the infinitesimal deformation of solids. The proposed methods are based on digital image analysis. The first method, namely, “PIV with vernier” employs the pixelshifting method to increase the resolution of the image and thus, improve the accuracy of the measurement. The second method, namely, “relaxed spatio-temporal gradient method” can handle the field with displacement gradient. Combining these two methods, measurement can be performed with wide dynamic range and the deformation of the solids can be measured with the accuracy of 1/30 pixel.

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In this study consists of the following two topics, one is the interpolation of the tunnel mouth temperatures using Semi-Variogram which is a stochastic procedure, and the other is the identification of the tunnel inner temperatures using actual observation data. In the former study, temperatures of tunnel mouth can be defined by a simple formula, and it is interpolated by Semi-Variogram. In the latter one, tunnel inner temperatures are identified by the observation data from several tunnels. And estimated temperatures are compared with some actual observation data. Finally, numerical examples are worked out to demonstrate the usefulness of this estimation method for heat insulator design of planning tunnel

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The first author has proposed to use Akaike Bayesian Information criterion (ABIC) to adjust relative weight between objective and subjective information in inverse analysis in order to overcome the problem of ill-posedness. The method has been applied to various civil engineering problems in the past and found to be very effective. However, the reason for this effectiveness was not necessarily clearly explained. In this study, an attempt is made to explain the behavior of ABIC from the viewpoint of information entropy. It is found that ABIC chooses the estimates of parameters that maximize the reduction of information entropy from the entropy given at the beginning of the analysis. This fact actually extends the use of ABIC to wider selection of the prior information, i. e. not only choice of prior variance but also alternative prior means can be examined using ABIC as a criterion. The findings are not explained theoretically, but also illustrated using a simple numerical example.

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The structural damage identification analysis is performed for tower-type truss categorized as a cantilever-type structure in the frame work of inverse analysis. As the inverse analysis method three kinds of filtering algorithm based on Wiener filter, projection filter and parametric projection filter are effectively used under the consideration of stochastic properties based on observation data. In order to verify the characteristics of each filter, a practical sized tower-type truss modeled as planer truss is selected in performing numerical example. The notable characteristics of each filtering algorithm in applying inverse analysis are made clear through numerical simulations.

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The purpose of this research is to propose a numerical method for the problem of the identification of the elastic coefficients in linear elastic wave field: Determine unknown Young's modulus and Poisson's ratio from the knowledge of the plural sets of simultaneous displacement and traction on the surface of an isotropic, linearly elastic bounded body. The elastic body is supposed to be a state of the plane strain. We assume that the density is known in the elastic body. In this research, the Lamé coefficients are identified instead of determining unknown Young's modulus and Poisson's ratio. To determine the unknown Lamé coefficients numerically, we adopt the adjoint numerical method. The minimizing problem with some constrains is introduced by using variational method. To find the minimum, a technique based on the projected gradient method is proposed. By numerical experiment, we discuss about the efficacy of our algorithm.

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Knowledge of regional groundwater flow behavior is important in water management. However, modeling and estimation of aquifer parameters for very complex aquifer system, like the one considered here for Osaka area, by mathematical models is notoriously difficult. This paper concerns with such complex aquifer system by relatively simple model that is the tank model, so as to understand the major mechanism of such aquifer system. The major difficulty in developing such model is the trade-off between the fit of the observed data to the model response and reliability of the parameter estimation. Random start optimization procedure together with Akaike's Information Criterion, AIC, has been employed to overcome this problem. A stable model is established which is believed to be reliable to simulate the groundwater flow pattern of the Osaka plain aquifer. The results also suggest disconnection of some regional aquifers as well as inflow of seawater to the deeper layers in the studied period. A tank model associated with the optimization technique and statistical procedure proposed in the study offers a promising approach in reliably understanding the mechanism of a complex regional groundwater flow system such as studied in this paper, Osaka plain aquifer system.

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Estimation of uncertainties is one of the important issues in civil engineering problems recently. K-L (Karhunen-Loeve) expansion is known to represent stochastic field and used in Spectral Stochastic FEM. K-L expansion has a close relation to the theory of generalized inverse matrix. The new method with K-L expansion is proposed for inverse analysis of stochastic field. In the method, the generalized inverse matrix is applied to stochastic field and extended to the case with apriori information on another field which has a relation with the field of unknown parameter.

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Computer memory saving algorithm for inverse analysis of heterogeneous hydraulic property was developed. Inversion for heterogeneous model needs so many unknown parameters. To compute inversion and to identify the large number of unknowns, high-speed inversion code must be used. For groundwater inverse modeling, the combination of SSVM (Self Scaling Variable Metric method) and adjoint state method, one of the most efficient algorithms for a problem of many unknown parameters, is used. This paper shows memory saving algorithm for this with keeping calculation speed. The memory of developed algorithm is almost proportional to N_p, the number of unknowns, while that of usual algorithm is almost proportional to N_p². By the method, a problem of even more than 100, 000 unknown parameters is possible to calculate with usual pc, when the problem is well-posed. Numerical case studies show the code of the algorithm is efficient.

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This paper presents vibration analysis of thick plates on the basis of the Mindlin plate theory and the theory of elasticity by using the spline collocation least square method which is an alternative free mesh method. No numerical integration is required in the formulation and the resulting matrix has the advantage of always being symmetrical To demonstrate an accuracy and convergence of the present numerical method, some numerical examples are solved and the results are compared with those obtained by analytical method and other numerical methods. It is seen that good accuracy and stable convergence are obtained.

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This paper presents free vibration of orthotropic thick plates using the spline element method based on the Reddy's shear deformation theory. The orthotropic plates are made of Aragonite crystal and wood (sitka spruce). To demonstrate the convergence and accuracy of the present method, several examples are solved, and results are compared with those obtained by other numerical methods based on the theory of elasticity, high-order shear deformation plate theory and Mindlin plate theory. Good convergence and accuracy are obtained. The effects of thickness/width ratio, shear elastic modulus ratio and elastic modulus ratio on frequency parameters of orthotropic thick plates are investigated. Lastly, the applicable limitation of the Reddy's shear deformation theory for strong orthotropic plates is also shown.

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A discrete method is developed for analyzing the free vibration problem of square plates resting on non-homogeneous elastic foundations. The fundamental differential equations are established for the bending problem of the plate on elastic foundations. The Green function, which is obtained by transforming these differential equations into integral equations and using numerical integration, is used to get the characteristic equation of the free vibration. The effects of the modulus of the foundation and the stepped thickness on the frequency parameters are considered. By comparing the present numerical results with those previously published, the efficiency and accuracy of the present method are investigated.

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Lateral torsional buckling often governs design of I-beams. Although vertical web stiffeners are extensively used to provide internal stiffening, their effect on lateral torsional buckling behavior is totally ignored in the design codes. Here, effect of stiffeners on cantilever beams studied under static uniform moment, uniform load, and end concentrated load. Finite element buckling solver has been used and then linear regression analysis for output data of finite element was conducted to produce simplified equation for the critical moment including stiffeners effect. The results show that stiffeners cause significant magnification in the critical moment than the basic critical moment of the case of beam without stiffeners.

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This paper presents an iterative method using piecewise valued basic vectors for solving linear systems with a symmetric coefficient matrix. The solution of linear systems is easily obtained by the proposed iterative method which repeats the following four operation. 1) Make the some independent systems in which total number of freedoms is reduced by Galerkin's method using the piecewise valued basic vectors. 2) Compute the approximate solution of these systems by other iterative method. 3) Obtain the best approximate solution of original linear systems by linking each approximate solution. 4) Update the proposed basic vectors by using the best approximation. Validity and efficiency of the proposed iterative method are studied and shown in several numerical examples.

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It is essential to predict train-induced vibration level by a numerical analysis with development of railroad technology. A 3-D analysis is required to obtain environmental vibration properties around a barrier with finite length produced by a moving load. In practice, however, a 3-D analysis using the conventional boundary element method requires too much computational time and memory. Therefore, it is necessary to develop a more effective numerical method for a 3-D environmental vibration analysis. In this paper, we propose the coupling method of a 2.5-D boundary element method and a 3-D Fast Multipole Boundary Element Method (FMBEM) to improve the computational efficiency for the dynamic problem due to a moving load. Firstly, a 2.5-D analysis is used to obtain the solution of a wave field produced by a moving load on a half space. Secondly, an FMBEM analysis for the time harmonic scattering problem by a finite barrier is carried out using the 2.5-D solution as an incident wave field. Finally, the time variation of the wave field for a train load moving in a parallel direction to the barrier is calculated by using the Fourier transform as numerical examples.

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This paper presents a dynamic system consisting of a float, fluid and a vessel for a tuned mass damper, TMD. The mechanism of the system is very simple because of that, the system fills the vessel with fluid, and only floats the float on the fluid. A theoretical formula for a natural period of the dynamic system is derived from Euler's equation of motion with perfect fluid and the float. The natural period of system is related to the fluid density and the cross section and the mass of float mainly, and is related to the cross section of vessel inconsiderably. Some experiments show that the proposed formula of natural period is accurate and useful, and show the damping characteristic of the system.

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This paper proposes an NDE ultrasonic measurement modeling based on the linear time-shift invariant system (LTI system). We here show the entire modeling of the immersion ultrasonic testing (UT), that is the ultrasonic wave generation from an immersion transducer, the flaw scattering in the solid object and the reception by the transducer. The Multi-Gaussian beam model is introduced to express the wave propagation in both transmission and reception paths, and the scattered wave from flaws is calculated by the boundary element method. The present work introduces an effective simulation of the immersion UT because each component of the LTI system is individually characterized. The performance of this modeling is shown by simulations of the scattered waveform from internal and surface-breaking cracks.

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Incomplete LU factorizations (ILU), combined with the generalized minimal residual method (GMRES), are often regarded as the best ‘general purpose’ iterative solvers. The dual threshold incomplete LU factorization (ILUT) is a well-known ILU preconditioner. It is effective for general sparse linear systems. However, for dense matrices, the cost for the construction of this preconditioner is high. We thus consider the Crout version of the ILU preconditioner (ILUC) in this study. It is known that ILUC can compute much faster than ILUT for sparse matrices. We apply the ILUC preconditioner for the analysis of the boundary value problem related to the diffraction wave field around a Very Large Floating Structure (VLFS) and show that this preconditioner is, in some cases, effective for dense linear systems.

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A parallel fast multipole accelerated boundary integral algorithm for solving boundary value problems is presented in this paper. This paper focuses on the downward pass, the upward pass and the preconditioning process, which are considered to be the expensive parts in the FMM (Fast Multipole Method) algorithm. All of them are parallelized with OpenMP. The performance of the parallel fast multipole method is tested with two numerical examples, namely the crack problem for Laplace's equation in 2-D and the elastostatic inclusion problem in 3-D. From those numerical examples, we can say that the speedup achieved with OpenMP is satisfactory in spite of the relatively small amount of eflbrts for programmers and small change in the program structure. Particularly remarkable is the fact that the effect of this parallelization in the fast multipole method is more pronounced in large scale problems or in 3-D problems.

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This paper discusses parallelisation strategies of a time domain fast boundary integral equation method for three dimensional elastodynamics for a large shared memory parallel computer. The performance of the OpenMP parallelised code is examined. Also in the case of MPI-OpenMP hybrid parallelisation, a numerical solution of the scattering probrem with more than one million DOFs is shown. It is concluded that the parallelisation with OpenMP is very effective, and that larger problem can be analysed with MPI-OpenMP hybrid parallelisation.

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The progress of computer and numerical technique in recent years allows people not only complex numerical simulation but also resolution of inverse problems. In the inverse analysis, it is important to pursue higher quality of gradient computation. It is called as the sensitivity analysis in general. This is the most bone-crushing thema in the analysis. In this study, the authors propose the automatic differentiation as a new approach applied to the optimal control problems. The optimal control and identification problems in incompressible viscous flows are performed in this research. The Navier-Stokes equations with incompressibility constraint is employed as state equation for the viscous flow. The forward mode automatic differentiation computes the partial derivatives according to the differentiation rule of a composite function whenever basic operation is performed. This method is efficiently implemented by operator over-loading technique, which is depending on object oriented programming languages such as C++.

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This paper presents a new mesh re-generation technique for free surface flow analysis based on interface-tracking method. The incompressible Navier-Stokes equation based on arbitrary Lagrangian-Eulerian description is used as the governing equation. The SUPG/PSPG formulation is employed for the finite element discretization. The coupled non-linear finite element equation systems are linearlized by the Newton-Raphson iteration method. As numerical examples, the present method is applied to the sloshing problem and the broken-dam problem in rectangular tank. The efficiency of the present method is shown by numerical results.

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This paper presents a lattice Boltzmann method (LBM) for incompressible flow simulation applicable to complicated flow domain using unstructured triangular mesh. The LBM simulates microscopic collision and streaming of fluid particle and evaluated the macroscopic velocity and pressure from the computed particle distribution. For the computation of collision step, the 2-dimensional 9-speed lattice BGK model was employed as a collision operator. For the streaming step, the cubic interpolation scheme based on CIVA was employed to interpolate the particle distribution function. The present method was applied to the analysis of the square driven cavity flow and the flow past a circular cylinder.

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This paper presents a mesh generation technique based on the 3-D Delaunay triangulation and boundary surface recovery system. The Delaunay triangulation is usefully introduced as basic tool of automatic mesh generation. However, the Delaunay tetrahedrization still has problems. One of them is problem of recovery of boundary surface. In the Delaunay tetrahedrization, recovery of the boundary surface is complicated work. Using Both the Delaunay tetrahedrization and the advancing front method is make it possible to recover the surfaces. However the tetrahedra, which are generated by the advancing front method, do not satisfy the condition of Delaunay tetrahedra. It is necessary that the domain is filled with Delaunay tetrahedra, when the Delaunay tetrahedrization is carried out. As a new approach to the construction of boundary surfaces, Delaunay tetrahedrizetion itself is applied. Constrained Delaunay tetrahedrization is presented. This constrained Delaunay tetrahedrization provides simple and benefit system of surface recovery.

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A new finite element formulation with bubble functions for the incompressible Navier-Stokes equations are proposed in this paper. As the numerical approach, the spacial discretization is applied the mixed interpolations for velocity and pressure fields by the bubble element and linear element, respectively. Two-level three-level finite element approximation based on bubble functions is used for the discretization. To verify applicability of presented method, standing vortex problem and cavity flow are performed for the numerical examples.

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A computational method for 3D incompressible flows is developed on the unstructured collocated-grid system. In the prediction procedure of the MAC algorithm, the CBP (Cell-Boundary Pressure) scheme is utilized to obtain the estimated velocity components at cellcenter points. In order to preserve the fluid mass with sufficient accuracy, a C-HSMAC method, whose validity has been shown in the structured collocated grid system, is implemented in the present method. In addition, the proposed method is parallelized on the basis of a domain decomposition method by setting up the overlapping tetrahedron cells. The advantage of the C-HSMAC method and the availability of the parallel computation are investigated through the computation of a cavity flow. The applicability to 3D flows in a curved duct is also discussed.

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Taking advangage of a semi-analytical finite element, we apply it to the Stochastic FEM in order to show its applicability of sensitivity analyses of micro-structures of composites. As an example, a rock slope reinforced by rock bolts is modeled by a composite material, and interaction of resisting stresses and densities of rock bolts is examined by the present mothod. One kind of optimization based on the results is tried to determine a suitable densities of rock bolts. The similar optimization is demonstrated for a beam of fiber-reinforced concrete to show another possibility of the present method in designing structures of composite materials.

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We investigate the relation between the macroscopic behavior and the intergranular and intragranular effects by applying the multi-scale analysis method, which is based on the mathematical homogenization theory combined with the constitutive models in crystal plasticity. Here, the macro-scale material behavior of polycrystalline metals is characterized by evaluating the mechanical behavior in the micro-scale geometrical structure. The numerical simulations are carried out by means of some micro-scale structual models of a polycrystalline aggregate, each of which has a different grain shape from others. These results suggest that we should take intergranular deformation into consideration to evaluate the effect of micro structures and that the grain shape has almost no effect on the macroscopic material behavior of polycrystalline metals.

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In shape optimization, an optimal shape is generated by moving some nodes of an initial mesh. But there are many cases that meshes can not follow the movement of nodes. In this paper, the shape optimization technique using mesh superposition method is proposed. In the present technique, the shape of design domain is represented by local mesh to allow flexible shape control. The shape of the local mesh is controlled by basis vector method. Several examples which can not optimize in the conventional optimization technique are shown to demonstrate the effectivity of the present method.

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In the mesh superposition method, there was limitation that local mesh area must stay within global area. In this paper, for further flexibility of the modeling the method is extended to the case where local area exceeds the global area. Two techniques that allow exceeding local area are proposed. First technique is to make some part of the boundary of global and local areas agree each other, and 2nd technique is to employ connecting model that connect between global and local models. Several examples are shown to demonstrate the flexibility of the method.

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Log-normal distribution is widely used to approximate probability density distributions of uncertain parameters in stochastic problems. This paper presents an analytical expression of the expectation of the product of log-normal stochastic variable and polynomial chaos and it enables efficient computation of spectral stochastic finite element method in the context of log-normal uncertainties. Accuracy of the presented method is validated through numerical simulations and comparison with Monte Carlo Simulation.

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Welded joint is one of the most fundamental parts of steel structures. Residual deformation and stress have an influence on fatigue and ultimate strengths of the structure. A program code of the finite element method which deals with welding process was developed. In addition to the constitutive law which can consider viscoplastic behavior such as liquid-solid transformation, martensite transformation and large deformation could be taken into account. This paper describes the constitutive law and the verification test of the program code was carried out. The result of pad welding of a disk showed relatively good agreement with the previous studies and experiments.

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For cellular solids, exploiting its geometrical characteristics, authors have developed macroscopic continuum-microscopic frame multi-scale analysis. The planar cellular solids is subjected to out-of-plane bending as well as membrane loading when they are employed as box gabion or geogrid. In order to take the out-of-plane bending into account, we here develop a multi-scale, i. e. macroscopic thin plate-microscopic frame, method for planar cellular solids. For future extension to a class of nonlinear multi-scale analysis, we here propose a formulation based on the generalized convergence theory. To utilize the convergence theory for fourth order differential equation that is the governing equation of beam and plate, a functional which has deflection and rotation as its independent variable is defined.

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This paper presents the development of numerical method for unsteady seepage flow problems with phreatic surface. This method is new discrete procedure that applied the concept of hybrid model. Also, present method introduced the general weighting residual procedure with the subsidiary conditions. Compatibility of the potential on the intersection boundary is approximately introduced using penalty function instead of the Lagrange multiplier. In each element, we assume linear potential field with the head and the hydraulic gradient. The element node does not need to have the degree of freedom and is used only for recognition of the domain shape. In this study, we tried to analysis the unsteady seepage flow problems with phreatic surface to compare the experiment.

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Drainage improvement projects in agricultural fields such as improvement of drainage channel and pump station have been carried out to prevent the influence of inundation for yield amount. In this research, finite element model in consideration of drainage channel and road was constructed, and the movement of the farmland drainage was analyzed. In this model, farmland which is delimited by drainage channel and road was assumed as a block. Then, flow in drainage channel and each block was modeled by one-dimensional unsteady flow model and two-dimensional shallow flow model, respectively. The introduction of present model makes it possible to forecast the inundation of the agricultural fields without dividing into small finite elements for the reproduction of drainage channel and road.

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In two-dimensional problems, the utility of the membrance element with vertex rotations has been discussed and proved by a lot of researchers. Sekiguchi, Kikuchi and Cook developed the element with vertex rotations by different approaches. However, in this paper, the displacement field of those two elements is proven to be the same as mathematical meaning. Moreover, this proof is confirmed by the numerical examples. The problem of Cook's element which required long time to construction of element stiffness matrix is solved by this interesting fact.

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We propose a three-dimensional analysis method for evaluating elastic-plastic behavior of heterogeneous media by finite cover method (FCM) with interface elements. The installation of interface elements is to enhance the approximation in external displacement boundaries or material interfaces. Then, the performance of interface elements is examined for the degrees of weight function and the approximation at external boundaries and material interfaces. Finally, we realize the capabilities of the FCM with interface elements to characterize the elastic-plastic mechanical behavior of three-dimensional meso-structures of materials.

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