This paper presents a theory on the imperfect bifurcation behavior at the emergence of parallel shear bands on uniform materials, and that of the statistical variation of the strength of these materials which often is governed by this emergence. It is shown by means of the group-theoretic bifurcation theory that the emergence can be explained as a symmetry-breaking bifurcation if the underlying symmetry is exploited to model the local uniformity of materials. The mechanism of the stochastic variation of uniform materials can be modeled in the theory of bifurcation by ascribing such variation to the stochastic variation of initial imperfections among them, which turns into the variation of the strength through imperfect bifurcation. Further, with these imperfections modeled to be normally-distributed multi-variate random variables, the probability density functions of the critical load (strength) are derived.

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In this paper, we present the image analysis of the progress of deterioration of kaolin on the basisof the group-thoretic bifurcation theory. The digital images of such deterioration are obtained from the photos of kaolin under shear by an image scanner. These images, which are expanded in terms of the double Fourier series, are classified with reference to the rules of bifurcation. As a consequence of these, a realistic simulation of the progress of deterioration is realized on the basis of a firm theoretical basis.

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Young's modulus and Poisson's ratio of intact rock foundation can be obtained by a uniform load plate bearing test, if both vertical and horizontal displacements under the foundation are measured at a certain distance apart from the plate and by substituting these observed displacements to developed equations, which relate the vertical loads to the vertical and lateral displacements in the semi-infinite foundation.

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The driving force of fracture phenomena is the released energy by crack extension, which is expressed with J-integral in two-dimensional special case. In this paper, a generalization J_ω (u, X) of J-integral is proposed, which has two parameters ω and X, in 2-D and 3-D general cases. Here u stands for the displacement vector. The symbol X express the vector field derived from the crack extension, and ω the domain where we get the information. The generalized J-integral J_ω (u, X) is the sum of the integral P_ω (u, X) over the line/surface ∂ω and the integral R_ω (u, X) over the domain ω. The formula J_ω (u, X) is derived in 1981 from the mathematical research of 3-D quasi-static fracture problems by the author. The integral Rω (u, X) is well defined for the weak solution of the variational problems from elasticity, by which we can express the energy release rate and applicable for finite element method.

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In this paper, we analyze the path-independent E-integral for a frictional crack subjected to remote compressive loads using the finite element method. We find that the E-integral of the complementaryenergy type gives the energy release rate under the proportional compressive loads with a high accuracy. We then obtain the closed form solutions of the work change rate for a frictional crack under the several loading histories, and find that the E-integral also agree well with the obtained solutions for several loading histories.

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In this paper, we investigate crack extension behavior for a linear elastic body with a parallel interacting crack which interrupts the extension of a main crack. We discuss the crack extension behaviors based on maximum energy release rate criterion. We compute the energy release rate at the onset of crack kinking, of all the crack tips, using the E-integral which is path independent even for a path containing stationary crack tips. As a result, assuming the isotropy of fracture toughness of the body, we find the optimum position of interacting crack that interrupts the extension of a main crack, and find the energy release rate that tensile fracture strength of the body becomes the largest.

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In the post-buckling analysis of axially compressed thin-walled cylindrical shells, we can use two kinds of strain-displacement relation, i. e. Donnell type and Flügge type. Former is relatively simple, but is not so correct (due to shallow assumption) when a shell becomes long. In this study, the Flügge type is employed and more accurate euilibrium paths in the post-buckling region are traced numerically. In order to estimate the snapping or bifurcated paths, the energetic evaluation is also applied.

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This paper presents structural identification of shear frame models, which were tested on a shaking table.Random excitation test data were used to identify structural parameters in frequency domain Genetic algorithm coupled with a modified Marquardt method was employed for parameter identification. The identified stiffness showed an excellent agreement with that obtained from a static test. Effect of sensor arrangement on identified results was theoretically investigated and compared with the experimental results by changing the number of sensors and their locations. Good agreement between the theory and the experiment was observed. It was found that the 1st floor was the most important sensor location among all possible locations.

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A heat conduction problem of massive concrete structures is dealt with in this paper. The analysis for the problem requires boundary conditions such as the heat transfer and heat absorption due to solar radiation on the surface of concrete structures, both of which are difficult to estimate under frequently fluctuating weather conditions. It is shown in this paper that these boundary conditions can be recursively and simultaneously identified from observationusing the extended Kalman filtering technique incorporated with the finite element method. Also, solution accuracy and stability dependent upon prior information are studied.

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In impact analysis, system identification techniques have increasingly become an important research topic for safety evaluation of structures. In most system identification approaches, the information on input and output response must be known. However, it is difficult to accurately measure the input information. This paper is concerned with a method for estimating the impact load from deformation and strain responses on the beams. An estimation algorithm is based on the Kalman filter, which has been a powerful tool to solve the identification problems for non-stationary state parameters. Numerical examples of simulation with and without noise using two transfer matrices based on Markov process are considered. The comparison of the identified and the true time histories of impact force shows the usefulness of the proposed algorithm.

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This study deals with a numerical method for equivalent linear identification of nonlinear systems with the help of the extended Kalman filter, where a technique of local iterations of the filter by Hoshiya et al. is applied to attain efficient identification of nonlinear behavior of systems. A bilinear histeretic restoring system is numerically analyzed to demonstrate the accuracy of the method.

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A study of optimal sensor locations based on the credibility of a model estimated by back analysis is one of the recent topics. In such studies, it is significant to make clear the meaning of the credibility of a model estimated by the back analysis. When the credibility of the model is estimated, it is very importanto consider the compliment of the subspace forthe back analysis, otherwise we reach the wrong conclusion that the less unknown parameters model is the more reliable one. In this paper, we perform the numerical calculation which shows the relationship between the number of unknown parameters and the estimated credibility of the model. Then the methodology to divide the total unknown parameter space into the subspace for the back analysis and the complement is presented and demonstrated through numerical example.

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Seven sets of pile loading test data in Bangkok are introduced to estimate parameters used in the pile displacement analysis model based on the superposition of Mindlin's elastic solution of the first kind. Two models are developed: one considers the slippage between a pile and soil, and the other not considering it. The inverse analysis procedure applied is the extended Bayesian method (EBM) in which the observation data and the prior information are appropriately matched by ABIC. ABIC is also employed to identify the two different models. The results exhibited the capability of the EBMin overcoming the illposedness that are often encountered in this kind of geotechnical inverse analysis and in identifying the better model.

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Geostatistics is a popular method to infer heterogeneous distribution of hydraulic conductivity. However, there are many cases where enough data to create the detail distribution are not obatined. From the point of view of enviromental and mechanical coupling problems, the fine distribution is better than the coarse one such as zoning method. It is presented in this paper that the full heterogeneous distribution of the finite element model is inferred by Baysian back analysis method. The simulation resutls out of geostatistical approach are used as a prior infromation. Kriged distribution is applied as a average one. It is found that the equivalent heterogeneous model can be introduced by the proposed method and the detail distribution is difficult to reproduce although.

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Regression analysis is the most classical but still a very useful back analysis in social sciences. Multicollinearity is one of the most serious ill-posedness and many conventional regularization methods have been provided. The paper focuses on the multicollinearity problem and attempts to compare the theoretical and practical characteristics among regularization methods. The paper discuses principal component regression and ridge regression which are the most well-known ones among them. It is shown that they are compatible with the traditional regularization methods in inverse analysis. The two methods are applied to regression analysis of land price in order to demonstrate their practical characteristics.

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This paper shows some interpretations of spatial interaction models applied in socio-economic analysis including location analysis and transport analysis. Parameter estimation of the models, activity allocation problem with capacity constraints and derivations of variants of entropy model can be regarded as inverse problems. In perspective of development of socio-economic modeling, merits of inverse problem are described.

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A boundary element method is applied to reflection and scattering problems of a cylindrical wave by a defect near a free surface in a two dimensional half space. The source of the cylindrical wave is assumed to be located enough far from a defect. On this assumption, reflected waves at a free surface are easily calculated using a ray theory. With incident and reflected waves as known terms, scattered fields due to the interaction between a defect and a free surface are analyzed using a boundary element method. The proposed method shows much better accuracy than the boundary element method involving only the incident wave as a known term. Application of our method to a simulation of an ultrasonic testing for a thick plate is addressed.

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By using impact echo testing method integrit diagnosis of RC column is dealt with in this paper. Numerical simulation of stress wave propagation is used to interpret wave scattering around crack in concrete. Good agreement on crack location between numerical and experimental results is obtained in wave form analysis.

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Linearized inverse scattering method based on Born and Kirchhoff approximations is an approach whereby shape and location of defects are obtained together from ultrasonic backscattering waveforms. Here, capability of the algorithm to estimate geometrical properties of unknown defects is tested by the use of synthetic data for both volumetric defects and cracks. Numerical examples show that the method has versatility to estimate exact location as well as shape of defects provided rough location of defects is known.

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The homogenization method is examined in conjunction with the method of representative volume elements (RVE). When the digital image-based modeling technique enables us to model the complex geometry of microstructures, the boundaries of unit cells fail to have the geometric periodicity Nonetheles, the effective moduli are reasonably estimated by the homogenition with periodic boundary conditions. This fact is justified theoretically and simulated along with the notion of homogenization convergence. In adition to the convegence of effective moduli with respect to the size of RVEs, the microscopic mechanical behaviors are examined in comparison with macroscopic ones. Thus, the multiscale nature of the analysis modeling by the asymptotic homogenization is characterized by carrying out a series of linear and nonliinear numerical analyses.

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A method to derive an equivalent beam model of a non-standard beam-like structure that possesses periodic microstructures is proposed based on the theory of homogenization. The fundamental equations of the Euler-Bernoulli beam is briefly reviewed, and a formal asymptotic expansion of the principle of virtual displacement is applied. The homogenized equation of a beam imbedding heterogeneity of structural constituent and the equation defining the characteristic deformation of the microstructure are derived. Then, the equivalent stiffness of the homogenized beam model is reasonably defined. A few examples of application of this proposed method are presented and the validity of this method is examined through an error estimation.

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The homogenization method is applied to characterize the quasi-static behaviors of asphalt concrete. The macroscopic material properties of asphalt concrete are obtained by assuming the visco-elastic response of its microstructure consisting of aggregates and asphalt. Based on the derived homogenization formula, the numerical analysis is presented to simulate the global-local mechanical behavior of this type of composites.

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In this paper the homogenization method, which gives homogenized elastic constants of a composite materical, is applied to the the existing beam theory cosidering the effects of bending, torsion, compression and tension. Through a numerical example effectiveness of the present algorithm is discusssed.

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The concept of “ cover” is employed from manifold method into voxel analysis and applied to 3D solid analysis. The regular square or cubic cover is used and appropriate weight functions, cover function is defined. Also proofs are given on the linear independency of the approximate functions. The accuracy control by changing the degree of polynomials in each cover is carried out.

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In the solid elements problem with symmetry, it is a numerical calculation with a large scale EM that assembles the stiffness matrix of the solid elements analysis. It is taken away this problem, as the method improved analysis efficiency, the block-diagonalization method (BDM) based on “ group theory” has come to be utilized to exploit structural analysis of the symmetric finite elements. In this paper, it is expressed the outline of the BDM by the group products of symmetry, applied to high-symmetry of the solid elements using with simple symmetries. By the application of the finite solid elements, this group product is considered very useful method.

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In this paper new hexahedral mesh generation methods are proposed for the finite element analysis of groundwater flow and transport through fractured rock matrix. Proposed methods are based on Delaunay triangulation to divide whole domain into tetrahedra, and successively tetrahedra are subdivided into hexahedra. Through numerical testing of the proposed mesh generation methods we examine their efficiency and also the numerical solutions.

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A computational method has been developed for interaction of a thin, flexible membrane and wind flow around it. Restricing the computational domain as the 2D vertical plane, the membrane is discretized by truss elements and a geometrically nonlinear dynamic analysis method is applied to its motion. The ALE finite element method is employed for the flow analysis. A simple staggered algorithm, to solve the membrane and the flow alternatively, was unstable unless the density of the membrane is sufficiently large. An improved algorithm, where the excessive acceleration of the membrane due to the excessive fluid force is reduced by introducing inner iterations during each time integration step, was found effective to simulate a wind-induced flutter of the membrane stably.

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This paper presents an adaptive finite element formulation based on equal-order-interpolation for steady and unsteady incompressible Navier-Stokes equations. For the error estimation, the Zienkiewicz-Zhu's method is used based on a posteriori error estimation. The mesh generation for adaptation is performed using the Delaunay triangulation with h-refinement procedure. For the posteriori error estimation of unsteady flow problem, a statistic value of the error norm is used. Present formulation has the advantage of computational efficiency for the unsteady flow problem, particularly. The analysis of a cavity flow and the flow around a rectangular cylinder (B/D=4.0) are performed for the numerical examples of the steady and unsteady incompressible Navier-Stokes equations respectively.

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This paper presents a computational simulation method for river sedimentation problem which is considered moving boundary flow. We propose implicit FEM using mixed interpolation functions by the third order bubble function and linear interpolation function for shallow water equations and equation of continuity for sand. To control numerical accuracy, CG and Improved-BTD scheme are used for implicit scheme. Moving boundary technique is combined in this method to treat wet and dry area.

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A simple and highly-accurate scheme for solving the advection-diffusion equation is proposed in this paper. The proposed scheme is named HORNET scheme. The several model computations are carried out to verify the high performance of the scheme. From the results, It is found that the present scheme has almost the same accuracy as the existing highly-accurate scheme and will be easily treated because of its compactness.

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A computational technique for improving the accuracy of both recognizing the free surface and satisfying mass-conservation in fluid problems s presented. The Volume of Fluid (VOF) method does not take into account the transportation of interface gradients. Furthermore, because the advective equation of density functions is used for tracking free surface advection, a computational scheme having less numerical diffusion must be considered. Investigations of numerical diffusion in conventional numerical schemes indicated that the Cubic Interpolated Pseudo-particle (CIP) method associated with the Digitizer method (tangential transformation of density functions) is a less diffusive scheme. As numerical examples, slashing motion in a rectangular tank and broken dam flow are analyzed using the above CIP method. The accuracy of both recognizing free surface and satisfyi g mass-conservation is verified trough comparison with experimental and analytical solutions.

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Hydraulic transients in the underground channel system such as underground flood ways and sewer networks are investigated experimentally and numerically. The typical features of unsteady flows induced by the inflow discharge into the underground channel are clarified by the fundamental hydraulic experiments. It is shown that the hydraulic transients with the propagation of an interface between open channel flows and pipe flows can be reproduced by using the numerical model. The fundamental numerical model is refined to predict the interaction between overland surface flows and underground channel flows, considering the discharge through manholes. The pressure change of air confined in the underground channel is also considered in the model to reproduce the spout of underground flows over the land surface through manholes.

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Three different mass matrix methods for determining natural frequencies of thin-walled continuous beams are presented. One method is the exact method based on a general solution of the differential equation of motion for torsional vibration, and it is called the continuous mass method. The other two matrix methods are the lumped and consistent mass methods based on the approximate finite element approach. The mathematical relationship between the exact and approximate methods is discussed. The numerical results computed by the lumped, consistent, and continuous mass methods are given in tabular form, and the accuracy of natural frequencies obtained by these mass matrix methods is investigated.

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A static analytical method for unstable cable structures has previously presented by the authors, combining two C20level control method with the load control method, that is, modified two level control method. For such moored floating body anchored by the cables with large deformation, this method can be extended to some large kinematic equation on the basis of the principle of D'Alembert. This paper shows that a dynamic solution of the unstable cable structures can be solved by taking the inertia force into consideration of the modified two level control method above and using the central time difference method. As a numerical example, 6-member cable structure, is analyzed the process of large deformation, giving the forced displacements on the top of the cable.

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In finite displacement problems for which to define potential functional is difficult, stiffness equation is generally derived from virtual work equation. In such case infinitesimal rotational angles about three axes of rectangular Cartesian coordinates can be used as degree of rotational freedom. The rotational angles are useful to analyze structures subjected to moments about three axes at one node but may make tangent stiffness matrix not symmetric. In this paper accuracy of the formulation is discussed.

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A finite element formulation for the large displacement analysis of thin-walled beams is presented. The degeneration approach is taken in this formulation, so that the nodal degrees-offreedom in the beam element thus developed are all vector quantities. It is also noteworthy that the concept of bimoment which is significant in the classical theory of thin-walled beams needs not be referred to. The present formulation is therefore simple and straightforward. Numerical examples are solved and excellent agreement with analytical solutions is obtained, confirming the validity of the present formulation.

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A numerical analysis has been conducted to simulate and evaluate the strengthening effects of concrete beams with externally bonded fiber-reinforced plastics (FRP) sheets. Mixed finite elements are used to model the displacement discontinuities both in plain concrete body and along FRP-concrete interface where debonding caused by shear stress usually takes place_ From experimental results, several failure phenomena, including concrete shear failure, debonding along the FRP-concrete interface and FRP rupture, were observed. Through a parametric analysis on concrete tensile strength, bond strength of interfacial layer and thickness of FRP sheet, the numerical simulation has been conducted and the analysis results are compared with the experimental ones. Thus, the mixed finite element formulation is proved to be efficient in analysis of debonding propagation problems in FRP-reinforced concrete structures.

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When the composite member of I-section steel member and rigid urethane vibrates, the independent modes of the rigid urethane are generated at high-frequency region and the such modes are supposed to give the vibration reduction effect. In this paper, natural vibration analyses on local vibration of the composite members are carried out and the characteristics of the independent modes of rigid urethane are clarified. The discrete model which is the combination of finite strip method and finite prism method is applied and the parametric analyses of dimensions and material values of the rigid urethane are carried out. Based on these results, the boundary frequencies which generate the independent modes of the rigid urethane are obtained.

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The boundary-type integral formulations of domain variables were presented explicitly for three-dimensional initial strain problems using boundary element method. The domain variables were first represented by complete series of polynomial expansions, then the related domain integrals were transformed into the boundary ones with the aid of the intrinsic correlation among the integral kernels as well as the high ordered fundamental solutions. The applicability of the formulation was discussed briefly.

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FMM (Fast Mutlipole Method) has been developed as a technique to reduce the computational time and memory requirements in solving big sized multibody problems. This paper applies FMM to elastostatic crack problems in 3D, discretizing BIE (boundary integral equation) with piecewise constant shape functions. The resulting algebraic equation is solved with GMRES (generalized minimun residual method). It is shown that FMM is more efficient than the conventional method.

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This paper is concerned with the fast multipole boundary element method (FMBEM) in two dimensional frequency domain elastodynamics. The fast multipole method (FMM) is derived by the Galerkin vector in the elastodynamic field. The elastodynamic field is expressed as the sum of the longitudinal and transverse wave fields, and the Galerkin vector FMM is simply derived from the scalar wave FMM. Multipole expansions of the influence functions are derived to apply the FMM to the boundary element method. A numerical experiment showed that the complexity and the required memory are of O (N). As the example the multiple-hole elastic scattering problemwas solved using the FMBEM, and the results show the applicability of the method.

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The choice of proper time step is very important in solving nonlinear structural dynamic problems with proper integration precision and reasonable computational efficiency. In thispaper, a program is developed, with MATLAB, adopting an adaptive time integration strategy to analyze the dynamic responses of bridge piers. The time step in each time instant can be adjusted automatically according to the modal components of dynamic behavior of the system. The influences of some important controlling parameters on the computation accuracy are studied. It can not only assure the accuracy and keep valuable information but also improve the computational efficiency considerably.

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High frequency noise sometimes triggers computational instability in the dynamic response analysis of a high-degree-of-freedom nonlinear system, such as a dynamic nonlinear FEM analysis. This paper proposes a new time integration scheme that eliminates high frequency noise by a digital filter. In this scheme, digital filtering is performed as a part of the time integration process. This paper describes a theory and a computational process of the scheme, as well as required conditions. There is little condition for the frequency characteristics of a filter and in this paper two recursive filters are introduced. The applicability of the scheme is also discussed and it is shown that this scheme is applicable to a linear acceleration method but that further study is required for its application to a central difference method. Effectiveness of the scheme is shown through the comparison of dynamic response analyses of a simple nonlinear system with/without proposed scheme

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In this paper, a newly developed method on random response analysis of the non-linear, but non-hysteretic systems subjected to nonstationary exitation is proposed. At first, Fokker-Planck equation for single-degree-of-freedom systems is derived, then local uniform grid refinement (LUGR) method is applied to solve numerically the Fokker-Planck equation. In order to examine the simulation capabilities of this method, numerical solutions of simple linear systems are compared with those obtained by the theory. Finally, several solutions for the earthquake response of non-linear systems are given, and the validity of the newly proposed method are verified

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The fundamental mechanics of the assembly of rigid particles is clarified. In particular, the relationship between the upper bound theorem and the equilibrium conditions is mentioned in detail since the upper bound theorem is directly applied to solve the problem by using the linear programming method. Some numerical results are compared with those of a simple experiment by using Japanese coins.

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The necessary condition for multiple deformation rate was given by Hill. The condition is ΔsijΔvji=O, where Sij denotes the nominal stress rate, and Δ shows the difference between any two multiple solutions. We discovered that the necessary condition makes the difference ΔΛ of proportional coefficient in the constitutive equations under the associated flow theory indefinite at the critical state. The sufficient condition for the multiplicity is deduced from the requirement which makes the coefficient Λ indefinite. That is.sijεij=O, which requires that the hardening modulus h vanishes, and gives the relationship which influences upon the gradient CL of the critical curve. Since the relationship involves the third invariant J3 of deviatoric stress, the critical state cannot be uniquely determined by the pressure p and equivalent stress q alone. In the plane strain compression, the mode of shear plane can be predicted similar to the one observed in such experiments, based on the gradient CL of the critical state curve.

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Manifold Method (MM) is a newly developed numerical tool in analyzing both continuous and discontinuous problems. By employing the concept of cover and two sets of meshes, MM can simulate the small and large-scale deformation of materialsas well as the failure and movement of block system. In the present paper the original MM is extended by adding the consideration of crack propagation in failure process into the numerical procedure. The extended version of MM is then applied to simulate the initiation and propagation of cracks in dam foundation with weak zone such as faults and joints. The failure process and corresponding bearing capacity are predicted, and the computed results are compared with those of the experiment. It is convinced that the extended version of MM can reproduce the initiation of cracks and the failure process reasonably well.

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In this paper, impact resistance of RC columns due to lateral impact loads is discussed based on experimental results. In this study, shear-span length and rebar ratios in the longitudinal and lateral directions were taken as variables. Furthermore, the influence of the combination of axial static and lateral impact loads applied to column models on impact resistance is also discussed. Anchoring RC column model to a side wall, lateral impact loads were applied on the edge of the model by freely falling of a 200 kg steel weight with built-in load cell. The results obtained from these experiments are: 1) the impulse generated by impact load is almost equal to the input momentum of the steel weight, 2) the duration of impact load is in proportion to the shear-span length and 3) the impact resistance of RC column model may be estimated. with some safety margin by using the ultimate static capacity.

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Delayed failure of lightly/heavily overconsolidated soil due to swelling has been investigated through the soilwater coupled finite deformation computation. Here, the failure after excavation in an overconsolidated clayey ground and the seepage failure of laboratory model ground on dense sand are simulated under plane strain conditions.
In both examples, the ground exhibited progressive failure with fluctuating deformation rates under constant loading. This progression of failure is attributed to softening due to swelling of the soil itselfin the localized area and pore water inflow at varying rates to the soil elements in the zone.

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Nonlinear bending oscillation of RC column with softening of M-φ curve is dealt with in this paper. Simplified one mass system of column with weakly nonlinear M-φ relationship is modeled by Duffing equationand some typical behaviors of Duffing equation are shown in numerical results. And comparison of phase plane of horizontal displacement between actual results ofdynamic response of RC column and the results of Duffing equation has a good coincidence in the case of weakly nonlinear region of M-φ curve.

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