The creation of the finite-element mesh is a very cumbersome process, especially for geometrically complex and large-scale models. On the other hand, the meshfree methods do not require such mesh data in an explicit fashion. Among the meshfree methods, the element-free Galerkin method (EFGM) has attracted interest since the computational implementation of the method is quite similar to that of the finite element procedures. Furthermore, EFG has been reported to be as competent as the finite elements in various types of problems. However, it has been indicated that when compared to FE analyses. EFG computations generally require more time due to the implementation of the moving least-squares approximation scheme. In this study, a hybrid modeling methodology implementing both the FE and EFG procedures for a given domain is reported. The penalty function method is implemented to approximately satisfy the continuity constraints for the displacements at FE-EFG interfaces. A data structure is also proposed for the parallel computation using this hybrid method. Linear equation solver module from GeoFEM software is adopted as the parallel middleware, allowing for efficient and effective parallelization. Effectiveness of the present scheme is shown through the two-dimensional elastostatic problems ranging up to I million DOFs, by comparing the CPU time and parallel efficiency among FE (GeoFEM), EFG and the hybrid methodologies.

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We propose a new algorithm to plot principal stress trajectories in plane systems. Much time and labor with experience are required in order to draw trajectories from the result of the photoelastic investigations. The possibility of branching or joining of trajectories cannot be disregarded, when the method of tracking principal stress direction from element to element is used. Our algorithm, on the contrary, plots the principal stress trajectories as the contours of the direction function which is evaluated from the result of FEM using the constant strain triangular elements. Direction function is a two dimensional scalar field whose value is constant along principal stress trajectories. Two function values for the first and the second principal stress of each node are computed by solving the simultaneous liner equations with rectangular sparse matrix. The unit direction vectors of principal stress given by FEM determine the matrix. When the scalar field forms a spiral surface, the unique value of the direction potential of each node is obtained by putting the discontinuity along a polygonal line in the finite element mesh. The line density of the trajectories with broken line pattern in the output figure is read as the magnitude of the principal stress declining toward the free boundary.

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Initial transient behavior of a tall-building-model due to a strong near-source earthquake has been studied based on the numerical simulation using the code MSC. Dytran. It was found that stresses occurred in the initial transient stage exceeded the yield stress of material in many columns, in the case of elastic-plastic building model, and that those exceeded the tensile strength of material in many columns, in the case of elastic building model. Through discussing on the dynamic properties of the structural material with the rate dependency of strain hardening rate of the material, the possibility to be occurred the brittle fracture of column even at strain rate in the range of 0.1∼1 s_-1 was pointed out. These results show very possibility that a high stress sufficient to lead the initiation of damage such as local fracture and crack can be reached in some parts of the tall-building-model due to a strong near-source earthquake.

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In the topology optimization analysis of continuum, the checkerboards, that is the fomation of regions of alternating solid and void elements ordered in a checkerboard-like fashion, often appear in the optimum solutions. In this paper, a nodeless hybrid element is proposed and this element is applied to the topology optimization analysis of continuum in order to solve the checkerboards problem. The proposed hybrid element is fomulated based on the idea of nodeless element proposed by Kawai et al. and the stress assumed element proposed by Sekiguchi and Kikuchi. The homogenization design method is used for the topology optimization analysis of continuum. Some examples of two-dimensional problems are shown to demonstrate the effectiveness of the proposed element in the topology optimization analysis of continuum.

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In this paper, a non-iterative, algebraic method for an inverse source problem of the three-dimensional Poisson equation is proposed. The method is based on the multipole expansion of potential by N point sources. We show an relation between the source strength, the source positions projected onto the complex plane and the expansion coefficients of the potential. This relation can be transformed into the algebraic equation of N-th degree for the projected positions of the N sources with the coefficients expressed by the expansion coefficients. Thus, by projecting the three-dimensional sources onto two orthogonal planes, the strength and the positions in the three-dimensional space can be estimated. The number of the sources is also obtained by the property of the minor determinants of the matrix composed of the expansion coefficients.

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This paper presents a constitutive model of plasticity that describes the cyclic stress-strain responses at large strain. A new equation of backstress evolution is proposed for an accurate simulation of the transient Bauschinger effect. An original idea of a non-isotropic-hardening surface defined in the stress space is presented for the description of the workhardening stagnation appearing under reverse deformation, as well as the strain-range and mean-strain dependencies of cyclic hardening characteristics. The validity of this model is confirmed by comparing the cyclic stress-strain responses calculated by the model with the experimental observations on two types of steel sheets (an aluminum-killed steel and a dual-phase high strength steel of 590 MPa tensile strength).

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Study by Y. Hirose and Z. Lin et al. (1994) can be applied to discuss the average elastic-plastic behavior of the composite material subjected only to axial stress. This composite material is composed of matrix and spherical inhomogeneities of isotropic perfect ideal elastic plastic materials. The volume of any inhomogeneity is very smaller than that of matrix, and the inhomogeneities fit tightly against the matrix. The criteria when the inhomogeneity becomes plastic first was found. It is shown that the yield stress of composite material σ_so increases with the increment of the total volume fraction of the inhomogeneities ƒ when the shear elasticity of the inhomogeneities μ^* is bigger than that of matrix μ. The overall stress at the first yielding is obtained.

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In order to evaluate damage state of randomly perforated sheets under biaxial deformation, a new method using the equivalent net stress derived from the damage tensor, which is obtained by the tessellation and stereological method, is proposed in this paper. Stress concentration around holes in a perforated sheet was calculated by the FE analysis and the comparison is made between the equivalent net stress and the results of the FE analysis. Equibiaxial tensile tests of perforated aluminum sheet were also carried out using the bulge testing equipment and the localized deformation between some holes in the sheet were observed. Both calculated and experimental results show that the proposed method can properly evaluate the damaged state of perforated sheet under biaxial loading.

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In flip-chip packages, bending deformation of the chip and substrates causes normal stress in the solder joints. In this paper, we study the influence of such normal stress on the flip-chip joint strength. Static loading tests and cyclic bending tests were conducted on flip-chip packages. The static loading test showed that long term loading on the flip-chip joints causes debonding at the interface between the solder bumps and the metal pads on the LSI chips. The cyclic loading test showed that such debonding also occurs under cyclic loading, and that the strain causing such a failure mode is much less than that causing solder fatigue fracture. The relation between the number of cycles to the failure of the debonding at the interface and the static loading test data is investigated, taking stress relaxation caused by creep strain into consideration.

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In this paper, generalized stress intensity factors of a three-dimensional rectangular crack meeting at an interface is analyzed. The body force method is applied to formulate the problem as a hypersingular integral equation where unknown function is a crack opening displacement. According to the behavior of the crack opening displacement near the crack front, the numerical method of the hypersingular integral equation is proposed, where the displacement is approximated by the product of fundamental density functions and polynomials. The calculation shows that the present method gives highly satisfied boundary conditions and rapidly converging numerical results. Generalized stress intensity factors are given for various combinations of the crack shape and elastic ratios.

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Laser cleaving is expected to become a new method for cutting inorganic brittle materials such as ceramics and glasses without generating particles or microcracks. However, an initial crack caused by this method often occurs at a short distance from a cutting line. By using computer simulation, we investigated the dependence of crack-initiation behavior on cutting conditions such as beam radius, beam movement velocity, and beam-injection position. The simulation shows that we can reduce the distance between the cutting line and an initial crack by selecting appropriate cutting conditions. When the beam-injecting position is fixed, positioning the injection near the plate edge effectively reduces the distance between the cutting line and the initial crack, while beam radius does not significantly affect the distance. On the other hand, when the beam-injection position is moved during cutting, reducing beam radius and starting the injection at the plate edge or outside of the plate are effective in reducing the distance.

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In the field of the fractography, fractal has been applied to investigate fracture mechanism. In this study, a new method detecting the transition point of fracture surface by calculating the local fractal dimension using Wavelet transformation is proposed. The high accurate evaluation is realized by using not the conventional self-similar fractal but anisotropic self-affine fractal "Hurst exponent" that is more suitable for fracture surface as an evaluation parameter. First, validity of our proposed method was verified by using the synthesized profile. Next, by applying our method to the brittle-ductile transition region of Charpy test specimen, the transition point was shown quantitatively. The homogeneity of fracture surface was checked in the case of TiAl creep and creep fatigue test specimen. Moreover, as compared with the conventional Box-Counting method for the self-similar fractal, it was found that our method with using self-affine fractal gave more exact Hurst exponent, and was suitable also for detection of the variation in local fractal dimension.

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The failure behavior around a crack tip in an adhesive joint is important in relation to the integrity of adhesive structures. The bond thickness is one of the important design parameters in adhesive structures. It has been reported that the fracture toughness of a crack in an adhesive joint depends on the bond thickness. However, the mechanism of the dependence has not yet been elucidated. In this study, we investigate the bond thickness effect on the fracture toughness of adhesive joints using a microscope. The damage zones around crack tips in adhesive layers with several bond thickness are observed. The distributions of damage zones and the shapes of rubber particles in adhesive layers are observed by an optical microscope. Additional damage zones are observed along the interfaces-between an adhesive layer and two adherends. As the result, the combination of the damage zone around a crack tip and the additional damage zones is related to the variation of the fracture toughness of an adhesive joint with bond thickness.

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The scarf joint of dissimilar-metal is useful to increase the bonded area. However, the optimization of scarf angle is required for maintaining the joint strength, because brittle intermetallic compounds are necessarily formed at the interface of dissimilar-metal. The design techniques on joint strength characteristics have not fully been clarified. In this study, stress singularities at the intersection of free surfaces and the interface of various dissimilar-metal were investigated using singular analysis. As a result, it was made clear that the no free-edge stress singularities existed in the range of scarf angles, that were determined by the combination of dissimilar-metal. Especially, it was informed that the no free-edge stress singularities existed at the scarf angle of 57° and 123°singularities in case of the copper and aluminum scarf joint. It was also confirmed using finite element analysis that the reduction of stress concentration could be observed by paying attention to the condition of no free-edge stress.

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Fatigue tests were carried out at frequencies of 20 kHz, 600 Hz and 100 Hz for low-temperature-tempered SNCM439 steel. Ultrasonic, high-speed servohydraulic and electromagnetic fatigue test machines were used for 20 kHz, 600 kHz and 100 Hz tests, respectively. The fatigue tests showed that fatigue properties were independent of the frequencies, while fatigue lives were distributed in wide range on the S-N diagram. Almost all specimens were broken from internal Al₂O₃ inclusions of various sizes between 9 and 82 μm. Fatigue lives were found to depend on the inclusion sizes. ODA, i.e. optically dark area, was observed in all specimens broken over 10⁷ cycles. ODA sizes were also independent of the frequencies. The scattered S-N diagram was found to be expressed by an unique curve by normalizing stress amplitudes σ_a with fatigue limits σ'_w estimated by Murakamis equation. The modified S-N diagram showed a clear fatigue limit between 10⁹ and 10¹0 cycles.

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Cantilever-type rotary bending fatigue tests were conducted on high carbon chromium steel in laboratory air at room temperature. Three kinds of specimens were prepared, i. e. fine particle bombarded (FPB), shot peened (SP) and untreated. Each specimen showed a step-wise S-N curve, but the transition stress below which subsurface crack initiation took place became higher in the surface-treated specimens than in the untreated specimen. The effect of the surface treatment appeared at stress levels above the transition stress of the untreated specimen, while it disappeared at stress levels below that stress. Subsurface crack initiation seemed to occur at the location where the superposition stress that was the sum of the applied tensile stress and the residual stress was the maximum. A fish-eye was always observed with an inclusion from which a crack initiated. Although the features of fish-eyes were somewhat different in three kinds of specimens, the fatigue lives were almost the same, indicating that the fatigue strength was not influenced by the surface treatment when subsurface crack initiation occurred. Regardless of surface treatment, fatigue life tended to increase with decreasing the stress intensity factor obtained by assuming an inclusion as a crack.

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In order to study the fatigue damage of a Ni-base superalloy Inconel 718 at an elevated temperature, the plain specimens were fatigued at room temperature and 500°C. The crack initiation and crack growth behavior was monitored by the plastic replication method. Experimental results showed that the resistance for slip and crack initiation decreases due to the softening of matrix at elevated temperature. With regard to the crack growth at 500°C, the growth rate of large crack was accelerated, however the growth of microcracks less than 50 μm was suppressed. In addition to the fatigue tests under constant stress amplitudes, the fatigue tests under the two step loading was also performed to clarify the effect of change in stress amplitude on the fatigue damage. There was no effect of the change in stress amplitude on the crack growth behavior at room temperature. For low-to-high block loading at 500°C, the crack growth behavior was hardly affected by the change in stress amplitude. For high-to-low block loading at 500°C, however, the growth behavior of microcracks under a low stress amplitude was influenced by the high stress repetitions. The cumulative cycle ratio Σ(N/N_f) was calculated. The values of Σ(N/N_f) exhibit the distinct tendency determined by the load pattern and temperature. Above results were discussed from the viewpoints of the matrix softening and the oxide films formed at the elevated temperature.

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Computer simulations have been conducted to investigate the cluster formation process. Clusters can be expressed with some indices, including new ones. Growth of diffusion-limited aggregation (DLA) and ballistic aggregation (BA) are characterized by their indices, for example, cluster diameter, fractal dimension (D), density distribution along radius and so on. As the consequences of comparison between the both types of clusters, BA seems to be more harmful than DLA. Particle jump length (L) affects the cluster formation. When L is situated middle between DLA and BA, values of D, cluster diameter and cluster shape are also intermediate. From the fact that these new indices have great influence on structure formation, we can get possibility to identify the process which the clusters are generated in.

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Rotational bending fatigue tests were carried out on SCM 420 H steel modified by a combination of Wide Peening Cleaning (WPC) and carburizing, with special attention focused on the effect of surface residual stress on fatigue properties. By combining the carburizing and the WPC process, it is possible to generate a high compressive residual stress near the surface, while keeping a deep layer of compressive residual stress associated with the carburizing. The notched specimens modified by the combined process show significantly higher fatigue strength compared to those modified by single process of carburizing. This is because the extremely high compressive residual stress remained after stress cycling at the surface of the specimens modified by the combined process.

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To investigate the influence of casting defect on the fatigue strength of aluminum die casting materials, fatigue tests were conducted on four type of aluminum die casting materials. The fatigue strengths were evaluated by using the stair case method for small sample size (JSME Standard S02-1981 14 S-N testing method) and √area parameter model using the statistics of extreme values of casting defect. The main results obtained are as follows: (1) The origin of fatigue crack is casting defect caused by various die casting method except ADC24Z. (2) The square root of casting defect area (√area) follow the statistics of extreme values. (3) The fatigue limits predicted by the √area parameter model are in good agreement with the fatigue limits by the 14 S-N testing method.

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Nowadays, several optimal parameter design tools have been developed for the nonlinear structures. These traditional approaches manage only the expectation values of the design variables, the loading conditions, and the assembly processes, although it is sure that there is variation due to the manufacturing or the assembling errors. The neglect sometimes causes the failure of the structures. There is no doubt that it is a better way to carry out optimal design of structure with consideration of the variation of design parameters and assembly processes. In this study, a technique of reliability design with considering the variation of the design variables was introduced into the optimization method of the SDSS (Statistical Design Support System) to achieve the robust and optimal parameter design for the nonlinear structures, where the second moment method was applied to evaluate the structure reliability. The SDSS was proposed by Yokohama National University, and it is an integrated design system based upon the response surface methodology and the design of experiments. The parameter optimization can be carried out with this system basing upon a small number of case studies. As an application of the proposed approach, the design optimization of a hydraulic servo valve was carried out, and the variation of assembly factors was considered.

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