A sensitivity analysis scheme of the boundary value problem of Poisson equation by using Trefftz method is described in this paper. An inhomogeneous term of Poisson equation is approximated with the polynomial to derive the particular solution related to Poisson equation. The solution of the problem is approximated with the superposition of the T-complete function of Laplace equation and the derived particular solutions with unknown parameters. The parameters are determined so that the approximated solution satisfies boundary conditions. Since the T-complete functions and the particular solutions are regular, direct differentiation of the expression leads to the sensitivities. The present scheme is applied to some numerical examples.

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A three-dimensional (3D) groundwater flow analysis system applying the element-free Galerkin method (EFGM) is presented. The EFGM have been applied to many problems, but a complete system that can handle 3D composite domains consisting of several materials of complex shapes, such as geological structures, has not yet been developed. Some of the challenges to be addressed are the geometry definition of analysis objects, the method of node collection for constructing shape functions, and reasonable design of the system as a whole. In our system, a unique mesh data called consistency-free mesh assembly (CMA) is introduced. A CMA is a simple assembly of meshes permitting incompatibility between adjacent meshes and overlap of meshes. The CMA is easy to generate and brings great advantages to EFGM. Some 3D numerical examples show integrating EFGM and CMA solves the problem of conventional 3D mesh generation.

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The present paper describes four kinds of methods to enforce essential boundary conditions in conjunction with the stress analysis method, which utilizes structured cells and boundary segments to discretize the weak-formed governing equations and the related boundary conditions. The proposed methods for enforcement of essential boundary conditions include the method using multipoint constraint, the Lagrange multiplier method, the penalty function method and the direct method discretizing the modified variational principle. The aspects of the implementation of these methods are outlined and the analyses of two-dimensional elastic problems having small deformation are performed. The calculated results are compared with the theoretical and conventional FEM results to illustrate the accuracy

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In this paper, the solid tetrahedron element with drilling degrees of freedom is presented. This element has only four nodes. Each node has three translational components and three drilling ones. By using this element, the high level of analytical accuracy can be obtained. On the other hand, the free mesh method creates tetrahedron elements locally around every nodal point. Consequently, the element with intermediate nodes is not available to the free mesh method. However, the proposed solid tetrahedron element with drilling degrees of freedom is especially effective to the free mesh method, because it has no intermediate nodes. In this paper, the feature of accuracy of this element is shown through several numerical examples, and the effectiveness of the free mesh method is also described.

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Recently, the necessity of large-scale finite element analyses is increasing due to the development of new technology in engineering area. In these analyses, the time and cost of mesh generation processes are becoming larger and larger. Meshless method is expected to solve this problem, and many meshless methods have been developed in these years. In this study Meshless Local Petrov-Galerkin (MLPG) method which is one of meshless techniques is used to analyze two dimensional elastic problems, and its usefulness is examined. Fracture mechanics problems are also analyzed, and then energy release rate and stress intensity factor are calculated using J integral calculation, and highly accurate results are obtained. Using these parameters, the crack growth problem under mixed mode. loading condition is solved. It is shown that the data generation for MLPG analyses is much easier than that of FEM. This is the advantage of MLPG method.

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The objective of this study is to apply the element-free Galerkin method (EFGM) to the dynamic crack problem for evaluating dynamic fracture mechanics parameters. The EFGM is first applied to a stationary crack problem under dynamic loading. Then we apply the EFGM to a generation phase problem of dynamic crack growth. Both results obtained from the EFGM analysis are compared with those of the FEM analysis using a very fine finite element mesh or the moving singular element technique. It is found that the EFGM analysis has enough accuracy both for a stationary crack problem under dynamic loading and for a dynamic crack problem, compared with the FEM analysis. Moreover, the EFGM has the advantage of selecting arbitrary integral paths or moving integral paths for the J-integral without restriction of elements in the EFGM.

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Conventional FEM requires that the boundary of the element just matches the crack line to perform stress analyses of structures containing cracks in the field of fracture mechanics. These modeling processes are rather complicated and cannot be performed easily even if the automatic mesh generation technique is utilized. Recently, Belytschko et al. proposed the extended finite element method (X-FEM) based on the concept of partition of unity, and applied this method to the evaluation of the stress intensity factors and perfoming the crack extension simulation. The X-FEM can be used to simplify the modeling of continua containing several cracks and hence perform effective stress analyses related to fracture mechanics. This paper describes the two-dimensional thermal stress analysis of structures containing cracks. Stress intensity factors having mixed modes coupled with mode-I and mode-II are evaluated by M₁-integral method in conjunction with X-FEM. This method is examined in numerical examples of elastic and thermo elastic analyses. The numerical results show that X-FEM is an effective method for performing thermal stress analyses and evaluating stress intensity factors.

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The X-FEM proposed by Belytschko et al. uses interpolation functions based on the concept of partition of unity and considers discontinuity of displacement fields near a free surface and a crack independently of the finite element mesh. This paper describes the application of X-FEM to stress analyses of composite laminates. The interpolation functions of plate and solid finite elements used in three-dimensional analysis are extended to perform static and eigenvalue analyses for natural frequency and buckling load of composite laminates with an open hole and an interlaminar delamination. It was shown that the fairly good agreement between X-FEM and the conventional FEM were obtained. X-FEM can model the discontinuity at free surfaces much easier than conventional FEM. Using such advantages can help us to perform adequate considerations for damage evaluation of the composite materials.

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In this paper, the multi-level finite cover method is extended to adaptive analysis and applied to the fracture analysis. Finite cover method (FCM) employs the concept of mathematical cover from Manifold method, and applied to the voxel analysis. FCM-CLSA enables the multi-level distribution of voxel. For the indicator of sub-division of voxel, a-posteriori error estimation and accuracy of geometric representation is considered. For the representation of crack propagation the removal of te voxel at the area where fracture occurred is proposed and by this approach it was shown that the representation of crack propagation can be carried out much easier than the traditional approach in which geometrical reprenentation of crack is needed, while keeping the necessary accuracy by keeping the size of voxel small enough where fracture occurs. 2 dimensional example of avalanche is shown to demonstrate the capability of the approach.

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Nested-finite-element methodology (NFEM) is an improved finite-element method to evaluate local concentrations of stress with nested sub-elements. NFEM was applied only to elastic and explicit inelastic problems, because it is unable to calculate residual forces accurately from stresses at integral points. I thus developed an algorithm that would allow implicit analysis of the elastic-plastic problem on the basis of NFEM. The algorithm has the following steps : (1) Calculate the displacements of nodes with elastic NFEM. (2) Calculate stresses at each integral point. (3) Modify stresses at “yielded” integral points in main-elements and sub-elements. (4) Extrapolate stresses from integral points in sub-elements to integral points in main elements, and (5) Calculate residual forces at nodes from stresses. All steps are repeated until the residual forces converge to an allowable limit. The stress extrapolation scheme is the most important part of the method. I developed the extrapolation algorithm based on the shape functions of an iso-parametric element. To conclude, elastic-plastic NFEM can be used to implicitly analyze the stress of inelastic materials.

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An embedded discontinuous finite element based on the enhanced assumed strain method is used to model interfaces between granular and matrix phases. Each element is defined by a unit cube whose vertices are the eight nearest sampling points of 3-D digital image. Interfaces in an element can be easily reconstructed by the edge-based iso-surface contouring algorithm. The contouring algorithm reconstructs up to four interfaces per element, while only one interface per element is modeled in finite element formulation. Therefore, an image processing algorithm is proposed so that the contouring algorithm reconstructs at most one interface. Some numerical examples, which are computed by using the homogenization method and a simple damage model of interface, are shown to discuss the applicability of the present modeling to granular composites.

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Formation of isolated chips in high-speed machining is simulated by Eulerian solution. The machining includes large deformation, material failure, and contact of a tool with a workpiece; therefore, its simulation is a challenging problem. The Eulerian solution is attractive to overcome the above difficulties because the computational meshes are fixed in space and new free surfaces can be generated without a special algorithm. The present work focuses on the simulation of the isolated chips involving material failure due to shear bands. The shear-localized isolated chips in the high-speed machining, which correspond with an actual experiment, can be simulated by the Eulerian solution.

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Using a voxel finite element method that allows us to integrate modeling and analysis of a complicated three-dimensional structure, a new numerical method for shape optimization problem was proposed here based on the traction method. A minimization problem of stress nonuniformity in the domain was formulated for a three-dimensional linear elastic structure. In this method, a domain variation that was obtained as a velocity field from a shape gradient function was accomplished by removal and addition of the voxel elements on the domain surface. First, a case study for a plate with fillets under compression verified that the desired velocity field based on stress nonuniformity was successfully expressed by the discretized domain variation using voxel finite elements. Second, case studies for cantilevers subjected to a concentrated and uniformly distributed forces demonstrated that the minimization of the stress nonuniformity was achieved by changing the domain shape. In addition, a possibility of the topological change as well as shape change was suggested using the proposed method.

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A Voxel grid method combined with cut cells has been developed for simulating two-dimensional unsteady, viscous, and incompressible flows with arbitrary boundaries. The volume of fluid (VOF) approach based on finite volume method (FVM) is employed to accurately discretize the governing equation in Voxel cells that are cut by irregular boundaries. The precision of solution in the cut cells is ensured by special discretizations near the embedded boundaries. The accuracy and robustness of the proposed method are validated by simulating viscous flow around a stationary cylinder. Moreover, in order to verify the ability of this method to simulate the flow fields with arbitrarily moving boundaries, the fluid-structure interaction of bluff body in forced oscillation and vortex-induced vibration are also investigated by employing Voxel method developed in this paper, Calculation results show that lock-in phenomenon in wind engineering, in which the vortex-shedding is synchronized with the vibration of cylinder, is consistent with experimental data, the cylinder resonance state caused by vortex-induced vibration is also in reasonable agreement with results calculated by Arbitrary Lagrangian Eulerian (ALE) finite element method (FEM)

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A formulation of the Element-Free Galerkin Method (EFGM) for saturated soil with pore water is presented under Cam-clay model to overcome the difficulties which appear in the FE analysis. A weak form of the set of equations for the equilibrium of total nominal stress rate and the continuity of pore water is derived and its discretization, based on the usual EFGM strategy, e.g., the moving least square method (MLSM), is fumished within the framework of finite strain. Numerical discretization of the weak form leads to an updated Lagrangean scheme. Such a numerical strategy, in which the nonlocal characteristics incorporated is into the discretized continuity equation, is expected to be advantageous in avoiding the dependency of mesh type and size on numerical solution of strain localization problem. The stiffness matrix is numerically evaluated by the fourth order of the Gauss integration, and boundary conditions are treated with the help of the penalty method. To trace the bifurcation phenomena in the relation of load and deflection, several patterns of initial imperfection are given along the surface of soil specimen. Shear banding within a soil specimen can be introduced while avoiding the numerical difficulties which depend on mesh size in the corresponding FE analyses.

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Quadtree mesh system is developed for simulating two-dimensional unsteady, viscous and incompressible flows with heat transfer. Mesh is refined according to object geometries and where the gradient of physical value is larger than the threshold value. Mesh is coarsened where the gradient of physical value is smaller than the threshold value. The fractional volume of fluid (VOF) approach based on the finite volume method (FVM) is employed to reconstruct object surfaces with accuracy. Calculation results of heat flow simulation around a cylinder is in good accordance with experimental results.

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The anisotropic interface morphologies during directional solidification of a binary alloy, of which the preferred crystal orientation is tilted from the temperature gradient direction, are examined by using two-dimensional phase-field simulations, in which the effective finite element analysis with regular elements is applied as a numerical method. The effects of the strength of interface anisotropy and the crystal orientation on the primary cellular spacing and the crystal growth direction are shown under the fixed temperature gradient, pulling velocity, and concentration.

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In this study, two analytical solutions are obtained for the stress profiles in the fibers neighboring to a broken fiber in unidirectional composites. To this end, a hexagonal fiber array model containing a broken fiber is considered to derive differential equations based on a shear lag concept, in which matrix plasticity is simply taken into account by means of plastic secant modulus. It is thus shown that all affecting material parameters are consolidated into a characteristic value if a bilinear stress profile prevails in the broken fiber due to significant interfacial sliding. The governing equations are then analytically solved by assuming negligible stress concentrations in the second and third nearest neighbor fibers, respectively. The resulting two analysical solutions are verified by solving more generally the governing equations using a finite difference method. The solutions are, moreover, compared with 3D finite element analysis published in recent literatures, leading to the soundness of the present solutions and the effectiveness of the characteristic value.

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An instrumentation system has been developed to determine the elastic moduli of engineering ceramics and their composites from the sound produced by the impact of a fallen ball upon a specimen. In the system, a small rectangular bar specimen is suspended by thin ceramic threads. Using a fast Fourier transform analyzer, the natural frequencies are analyzed from the impact sound for the flexural and torsional vibration modes of the specimen. In the measurement, such a case sometimes occurs that it is difficult to distinct the correspondence between frequencies and eigen modes. In this paper, three-points bending and torsional test devices which employ the specimen for impact sound test were designed. Using the devices, elastic moduli of various materials were measured applying deformation theory for bending and torsion. The elastic constants evaluated by the impact sound test agreed well with those measured by the bending and torsional tests. A reliable measurement system was developed for elastic constants of anisotropic materials.

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The present paper treats an optimum design of CFRP stiffened panels under compressive and shear loads. Buckling analysis of stiffened panels is performed by approximate buckling formula on global and local buckling, which is based on the classical lamination theory. First in the present paper, the validity of approximate buckling formula is studied by comparing with the finite element analysis based on the Mindlin plate theory. Next, this approximate analysis technique is applied to a minimum weight design of wing box structures considering stiffened panel buckling. The optimum dimensions of stiffeners and laminate configurations are obtained by using nonlinear optimization technique. The validity of the present optimization approach is examined through the numerical results.

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The merits of the tube hydroforming (or THF) are the weight reduction and the high rigidity due to the closed-section structure of tube hydroformed automotive parts. The mother tube is bent and/or pressed in the preforming process of the THF process, in order to make the complex shape of preform before bulge forming process. The free bulging deformation, which appears in the initial and the middle of the buliging deformation in tube hydroforming process, is thought to be important in applying the mother tube to the THF precess. And the boundary condition of the tube end in THF process is thought to be the condition of open-end tubes, but many experiments in former studies are executed under the condition of closed-end tubes. This report shows the experimental results of the deformation behavior of free bulging of Electric Resistence Welded Tubes with open ends and also shows the analytical results of the influence of stress ratio at the center of free bulging shape from the viewpoint of THF.

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In order to study the subsurface crack initiation and propagation mechanism of high strength steel in very high cycle fatigue regime, computational simulation with fracture surface topographic analysis (FRASTA) was carried out for subsurface fatigue crack initiated specimens of high speed tool steel, JIS SKH 51, obtained from the rotating bending fatigue test in air. A remarkable area formed around the nonmetallic inclusion inside the fish-eye region on the fracture surface, which is a feature on the fracture surface in super long fatigue and named as GBF (granular-bright-facet), was observed in detail by a scanning probe microscope and a three-dimensional SEM. The GBF area, in which a rich carbide distribution was detected by EPMA, revealed a very rough and granular morphology in comparison with the area inside the fish-eye. It was clearly simulated by FRASTA method that multiple microcracks initiated depressively by the decohesion of spherical carbide from the matrix around a nonmetallic inclusion and coalesce each other into the GBF area during fatigue process. After the formation of GBF area, interior crack grew radially and the fish-eye pattern formed on the fracture surface.

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Surface crack growth behavior from pre-indentations of HIP-Si₃N₄ was observed under Rolling contact fatigue (RCF), and also under cyclic shear load. Near surface contact stress distributions were calculated by Hanson's analytical method, and the crack growth behavior was discussed in terms of stress intensity factors under rolling contact fatigue. It was found that the cracks grew in Mode II by shear stress (ΔK_II=3.0MPa·m^1/2, K_IImax= 1.5MPa·m^1/2 stress ratio R=-1). In order to confirm the effects of shear stress on surface crack growth, crack propagation tests under cyclic shear stress were carried out when the ΔK_II=2.4MPa·m^1/2 was lower than that of RCF. We found the following three features concerning Mode II crack growth. (1) The cracks grew by cyclic shear stress in Mode II (ΔK_II=2.4MPa·m^1/2). (2) Under the same ΔK_II=2.4MPa·m^1/2, the cracks grow more when K_{II max}=2.4 MPa·m^1/2 (R=0) than when K_IImax=1.2 (R=-1), (3) The cracks tend to stop growing when ΔK_II is lower than 1.2 MPa·m^1/2 (R=0). Comparing the features of Mode II crack growth obtained from the torsion fatigue tests and the RCF cracks, we conclude that the surface cracks are propagated in mode II (ΔK_II=3.0 MPa·m^1/2) under rolling contact fatigue.

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Cavitation erosion tests were carried out using vibratory apparatus to obtain the volume loss curve and the volume loss rate curve for aluminum oxide and pure copper. When the aluminum oxide was exposed to cavitation, the erosion originated at defects such as pores and holes. Particles were removed granule by granule, and the erosion pits spread throughout the speciment surface. The number of erosion pits increased exponentially. By the analyses of multiplication and annihilation process of the erosion pits, the model of the volume loss curve was established. The volume loss rate curve u and the volume loss curve V with exposure time were expressed by three parameters α, β and c in the following equation.
u=α/β1/1+e-^at, v=α/βt-ln (1+c/1+ce-^at)
Especially, the parameter c relates to a reciprocal of the initial volume loss rate, and was estimated to be low for the material with high initial defect density. As was expected, the value of c is lower for aluminum oxide than that for pure copper, and the value is lower for a roughened specimen of copper than that for a smooth specimen. It was concluded that the calculation based on this model corresponds well with volume loss curve and volume loss rate curve due to cavitation.

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