A brief historical review of two versions of Saint-Venant's principles for algebraic and exponential decay is presented. Using a model problem, transition from algebraic decay to exponential decay is demonstrated. Next, Saint-Venant's solutions and their characteristics are surveyed for members which may be anisotropic and inhomogeneous. A quantity of technical interest in Saint-Venant's problem is decay length which characterizes the attenuation rate of end effects. We collect decay length for typical bars. Finally, we review a semi-analytical finite element formulation suitable for treating Saint-Venant problem (Saint-Venant's solution and decay lengths) for anisotropic and in-homogeneous cross sections in which the properties do not vary along the axial coordinate.

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This paper describes a new method for determining appropriate parameters of inelastic constitutive equations using the hierarchical neural network. The present method consists of three subprocesses. First, various behaviors of material under cyclic loading or creep conditions are obtained through numerical integration of constitutive equations for many combinations of their constant parameters. Each relationship between the material behaviors and the parameters is here called "learning data". Next, the hierarchical neural network is trained using the learning data. Finally, the trained network is utilized to determine appropriate parameters corresponding to actual material behaviors measured in laboratory tests. To demonstrate its performance, the present method was applied to the parameter determination of Chaboche's viscoplastic model under uniaxial loading and stationary temperature conditions. The experimental data referred to are cyclic hysteresis curves of about 60 cycles and a stress relaxation curve. The results clearly show that the present method is a powerful tool for determining appropriate parameters of inelastic constitutive equations, referring to various material behaviors simultaneously.

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This paper describes the application of a hierarchical neural network to the identification of a crack hidden in a solid with the electric potential method. The present method of crack identification consists of three subprocesses. First, sample data of identification parameters vs electric potential values are calculated by the finite element method. Second, the error-back-propagation neural network is trained using the sample data. Finally, the trained network is utilized for crack identification. The present method is applied to the identification of a two-dimensional crack in a plate, and then applied to the identification of a semi-elliptical surface crack in a plate with electric potential values measured on the back surface. The accuracy and efficiency of the method are discussed in detail.

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A measuring system of strain distribution has been developed to analyze the mechanical behavior of polymer film. The system is composed of the material testing section and the image processing section. A lattice pattern is printed on the specimen surface. During material testing, the deformation of the pattern is recorded by a VCR camera. After the test, some parts of the recorded image data are digitized. Each datum is treated as follows : (I) smoothing to remove naise, (II) selection of the areas including a crosspoint using the image recognition technique based on the neural network, (III) determination of the coordinate of the crosspoint using the minimum square method, (IV) formation of the triangular mesh model, (V) determining the strain distributions of the specimen computed by applying a similer method used in the finite element method. To demonstrate the applicability of the present method, the strain distributions of a dumbbell-type specimen of polyethylene film under tensile testing are determined using this system.

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Moire interferometry can measure two-dimensional in -plane displacement distributions from x- and y- directional fringe patterns obtained by two sets of two beams. If the four beams are incident simultaneously, not only are the two-directional fringe patterns recorded on one image, but also other fringes are recorded simultaneously. In this paper, a method using Fourier transform is proposed in order to extract the necessary fringe pattern. An image of two-directional fringe pattinge with carriers obtained simultaneously by the four beams is recorded, and each directional first harmonic of the Fourier spectrum of the image is filtered for the purpose of selection. The phase distribution of the inverse Fourier transform of each directional first hamonic provides each directional displacement distribution.

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Moire interferometry is a method of measuring submicron displacement distribution using two or four collimated beams incident to the specimen diffraction grating. In this paper, in order to form these two or four beams, a transparent diffraction grating is used. Two types of transparent-type diffraction moire interferometry are developed. One uses oblique incident beams for measuring one-dimensional displacement. The other uses normal incident beams for measuring one-or two-dimensional displacement components. In the latter, the 0th-order diffraction beam is noise. This noise is removed using a light control plate which was developed recently. By using this diffraction moire interferometry, a compact system for microdeformation measurement is developed.

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Mode I interlaminar fracture was studied using double cantilever beam (DCB) specimens of unidirectional carbon fiber/epoxy composites. Moire interferometry was employed to measure crack opening displacement (COD) in the vicinity of a crack tip. Measured values of COD were compared with those theoretically obtained. It was found that the slope at the beam root of the specimens plays an important role in increasing the values of COD. Fracture toughness G_I was evaluated by two kinds of methods, and the results were compared with those of the COD measurement.

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In order to investigate inhomogeneity effects in elastic-plastic fracture, A533B steel and HT80 steel, which have considerably different yield stresses, were chosen. The moire interferometry was used for direct measurements of the crack-tip behavior in the homogeneous CT specimens of A533B and HT80, and in electron-beam-welded inhomogeneous CT specimens of these two materials. Two-dimensional moire gratings with relatively low frequency of 300 lines/mm were used to follow large plastic deformations. The near-tip deformations were compared with the corresponding HRR singular fields. Large inhomogeneity effects were observed in the moire fringe patterns as plastic deformations proceed.

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This paper proposes a novel technique for the characterization of strain gage dynamic response. The strain gage to be tested is glued on the side of a metal bar, which is called Davies' Bar. A projectile strikes one end of the bar and a pulse elastic wave is generated. The pulse passes through the gage and reflects at the other end of the bar. The reflection generates a very small transient displacement. The measurement of the displacement using a newly developed laser interferometer enables the derivation of the input transient strain to the strain gage using Skalak's analytical solution. Comparison between the input strain and the strain gage output gives the frequency characteristic of the strain gages. The experiment showed the phase lag and the insufficient sensitivity of gages in the transient response. Comparison with Oi's results gave a good agreement.

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This paper treats an inverse problem for estimating the magnitude and direction of an impact force acting on a body of arbitrary shape. It is shown that three directional components of the impact force vector can be estimated from responses measured at more than three points of the body by means of deconvolution. It is pointed out that the impact force cannot always be estimated satisfactorily since the inverse problem is ill-posed and/or ill-conditioned in some situations. For improving the estimation accuracy, the singular value decomposition technique is adopted. The validity of the present method is demonstrated through an experiment in which an impact force acting on a simply supported beam is estimated from strain responses measured by strain gages.

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Development of an expert system for ultrasonic testing can contribute to improvement and standardization of inspection level if the technique and experience of the UT engineer can be incorporated as the knowledge database. Then, it is considered that such an expert system will be a way to solve the shortage of UT engineers in the near future. The present system has been originally developed as a system having a knowledge base system and inference engine which are combined with a blackboard model and frame model. In the developed expert system, which is unified with a man-machine interface, it may be advantageous to use a production rule and a forward inference. The inference was performed in two steps. The candidates for weld flaw were firstly inferred from the welding condition, and then the final flaw was determined from the UT data. When the present expert system was applied to diagnosis of the weld flaw of the welding structure, the results obtained by the present system agreed with those obtained by the UT engineer up to about 90%. It can then be confirmed that the expert system is available as a method of inference for weld flaws, using ultrasonic testing data.

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The stress and strain in the viscoelastic body calculated numerically are not very reliable because it is difficult to optimize the modeling of the analytical object. The method of numerical and experimental hybrid stress analysis in the viscoelastic body is proposed in this paper. In this hybrid method the photoviscoelastic birefringence obtained from the stress and strain calculated numerically and the experimental one measured by the photoviscoelastic technique are compared in obtaining high reliability of the numerical results. As a concrete example, the thermal stress generated in the epoxy resin beam, when it is rapidly cooled from high temperature, is analyzed by this hybrid method.

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A simplified optical method based on photoviscoelasticity is proposed for measuring the transient stress and strain generated in a two-dimensional photoviscoelastic body. First, the fundamental equation for the simplified optical method is derived from the relation ships between the stress, strain and birefringence in the two-dimensional photoviscoelastic body based on the linear photoviscoelastic theory. As an example of the application, transient stress, strain and birefringence produced by nonproportional loading under a constant temperature are measured by using the simplified optical method. Next, these stresses and strains under the same conditions are theoretically calculated based on the linear viscoelasticity. The effectiveness of the simplified optical method is assessed by comparing the results.

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Optical birefringence is measured by a high-frequency modulation method using a photoelastic modulator and polarized laser. This measurement has the high sensitivity required to measure very small birefringence produced by stress. By this measuring method, the magnitude of the difference of principal stresses and those directions are obtained directly and quantitatively. The photoelastic properties of glass, polymethyl metacrylate (PMMA) and two kinds of epoxy resins are measured with the equipment. The distributions of optical birefringence corresponding to stress distributions are measured for bonded glass plate with epoxy resin. The residual stress caused by the bonding process is evaluated. This stress measuring method is applicable to detection of the small stress distribution of transparent solid materials.

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When performing computer-aided stress analysis using photoelastic image data, difficulty in accuate extraction of the boundary contour of the specimen and the image data near the boundary is often experienced since there exist many kinds of unavoidable noise due to the fluctuation of the source light intensity, the resolution of optical equipments and the characteristics of interference phenomena. It is, however, essential to determine the boundary contour of the specimen and the image data on and near the boundaries, because of the requirement for solving boundary value problems regarding the equilibrium equations of stresses. Accordingly, it is desirable to develop an efficient method for construction of approximate contour and boundary values preserving the feature of the specimen boundary. In thi paper, the authors discuss a new plane-spline function method for automatic construction of the specimen boundary, where an algebraic plane curve is fitted to each set of measured points which corresponds to respective ramification, after considering the boundary as a simple arc and dividing it into finite ramifications.

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This paper describes the strain gage method for determining the stress intensity factor of a edge crack in a strip subjected to transverse bending. The kinds of edge crack are single edge crack and double edge cracks. This paper proposes two methods of stress intensity factor analysis. One of them is the method using only one datum of the nearest gage at the crack tip ("1 point gage method"), and the other is the method using 5-gage data in the extrapolation ("5 point gage method") . The strain gages used in this paper are super-small-sized strain gages consisted of 5 grids, gage length 0.15 mm and pitch of gages 0.5 mm. The 4-point bending tests of a strip were carried out using the universal testing machine. For the single edge crack, the accuracy of the stress intensity factors determined by the experiments are within ±10 percent, except for the data of crack length a/W=0.1 by the 5 point gage method, compared to the analytical values. For the double edge cracks, the accuracy is within ±16 percent.

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Adhesion strength evaluation of molding compounds is a critical issue in structural design and material selection of IC plastic packages. However, since conventional adhesion tests can only give apparent adhesion strengths which include the effect of residual stress, their results cannot be used for design. This paper proposes a new method which can experimentally separate residual stress from adhesion strength. In this method, three-point bending tests of ENF specimens are performed in two opposing directions. Residual stress can be canceled simply by averaging the apparent strengths for these two directions. The method's validity was studied by experiments and stress analyses of specimens composed of an IC molding compound and Fe-42Ni lead frame material. Adhesion strength was expressed in terms of the stress intensity factor of the interface crack, K_i. It was confirmed that constant strengths can be obtained independently of specimen dimensions.

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Joining residual stresses at the ceramic near the interface were measured nondestructively by the X-ray method for the Si₃N₄-S45C joints. Four specimens of different sizes were used to clarify the influence of size on the distribution of the residual stresses and the change of the intensity of the stress singularity. Analytical studies on the joining residual stresses for the Si₃N₄-S45C joint specimen were performed using the finite-element method. The intensity of the residual stress singular field is proportional to the ratio between the interface length and the interlayer length. It is also proportional to the interface length raised to the λ power.

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In the present study, a series of dynamic and quasi-static lateral compression tests for three aluminium alloys, 2014-T1, 2017-T4 and 7001-T6, were carried out to examine the effects of loading rate and the wall thickness of tubes on the deformation of circular tubes and on the location of fracture. A finite-element analysis was also performed to find the relationship between magnitude of stress and occurrence of fracture during deformation. In this FEM analysis, a modified deformation model was introduced to continue the calculation after partial fracture occurred in tubes. The load-deflection curves of circular tubes obtained from the FEM analysis showed good agreement with those obtained from the experiments. The deflection at which fracture occurred could be predicted well by the FEM analysis. Absorved energy per unit volume of specimens tested at dynamic and static rates was increased with the increase of the wall thickness of tubes.

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This paper presents a method for automated measurement of Vickers hardness using image processing techniques. The study is focussed on the measurement of indentations by a Vickers hardness tester placed on an unclean surface which includes polishing flaws or stains. The boundary of the indentation is not clear and it is not easy to separate the indentation part from the material surface in the TV image from the microscope. The author developed new methods to detect straight lines from the digital image. These new methods were applied to detect edge lines of indentations. The value of Vickers hardness was calculated from the area within the detected lines. The result showed that these methods can estimate edge lines of indentations accurately. It was found that the accuracy of this method is good enough for practical use.

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This paper describes an analysis of the influence of the adherends of different thicknesses and dissimilar materials on the stress distributiton of single lap joints rigidly supported at the joint edges under tensile load. Stress distributions and effects of Young's moduli of adherends and adherends thicknesses were investigated analytically and experimentally. Maximum shear normal stresses occur at the edge where the adhesive joints the adherend of lower inplane stiffiness. Experiments concerning the strains of adherends were performed. The analytical results were consistent with the FEM results and experimental results.

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The scattered light method has not been utilized very often in practical cases because of the need tremendous elaboration for data analysis and experimental difficulties. To facilitate this method, a compact set of polarized light sources with a thin, parallel band was fabricated using a high-intensity algon laser beam and a few cylindrical lenses and analyzed the integrated fringe pattern as the digital image data was analyzed. In this paper, we developed a convenient algorithm for computer-aided stress analysis of the integrated fringe. The authors propose a convenient technique to analyze the variation of the stress intensity factor K₁ of the CT type specimen from plane strain to plane stress state over the thickness of the specimen, using the system with the improved devices of scattered light photoelasticity. Regarding to K_III, we were also successful in obtaining accurate measurement by the same manner.

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Reflected photoelasticity is applied to the problem of an annulus with an inclined crack subjected to internal pressure. The iso chromatic fringes, which are observed during experiments, are processed using an image data processing an alyzer. Thinning images are obtained for each results and the data for analysis are collected from the image. The mixed mode stress intensity factors are analyzed using sufficient data sets.

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In the present study, the shapes of dynamically propagating crack fronts in relatively thick DCB specimens of PMMA (polymethyl methacrylate) were taken using a high-speed camera. The nature of mirrorlike fracture surfaces in PMMA was utilized to visualize the instantaneous crack shapes in high-speed photographs. This feature was also used in the trigger system for the light source of the high-speed camera. Precise measurements of instantaneous crack fronts appearing in the high-speed photographs were made using an image processor. The crack-front angles to the free surfaces are investigated in connection with the singularity behavior at the corner points.

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The strain in the vicinity of a crack tip was examined under cyclic loading by means of the grid method, where special attention was given to the strain behavior during one load cycle. Both the longitudinal and shear strains, ε_y and γ_rθ, were intensely developed in the directions of θ≒±60°ahead of the crack tip, where θ is the angle inclined with respect to the general direction of crack extension. The variation in the two strains during half a cycle was also extremely great in these directions. Such a strain variation was quite small in a V-shaped region situated between the two directions of θ≒50°∼60°and θ≒-50°∼-60°. One of the cracks which branched into these two directions finally grew. Then an "ear" was left at the position where the tip of another crack was located. The crack extension process in the midthickness region of the specimen seems to be different from the one observed on the specimen surface. Some analogy, however, was realized between the midthickness and surface regions through the SEM observations ; a quite deep groove was left on the fracture surface among typical striations in the former, corresponding to an "ear" formed in the latter. Therefore, it was suggested that consideration of the crack extension process through surface observations might provide some useful general information on the fatigue crack growth process.

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The instrumented Charpy impact characteristics of polycarbonate are investigated in terms of the effects of impact velocity and temperature. The results obtained are as follows : (1) The inertia load appearing in the load wave initiated by striking the test specimen against the hammer of the impact tester is corrected by a mean square approximation method. The maximum load and the absorbed energy can be determined by this method. (2) The maximum load and the specific absorbed energy per real cross-sectional area decrease with increase in the impact velocity. There is constant temperature taking the lowest load in the relationship between the maximum load or the specific absorbed energy per real cross-sectional area and temperature. The lowest load or energy is shifted to the higher temperature by the higher impact velocity. (3) The relationship between the dynamic fracture toughness, K_Id and K_I, or between K_Id and temperature is similar to the relationship between the maximum load per real cross-sectional area and the impact velocity, or between the maximum load and the temperature, respectively. (4) The patterns of fractured surface correspond to the instrumented Charpy impact characteristics when the conditions of impact velocity and the temperature are changed.

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In designing machine parts or structures which should withstand an impact load, it is fundamentally important to know the dynamic deformation of the materials at its contact part and the impulsive force generated at that part. The deformed shape at the contact part and the generated impulsive force have been measured when a Soft Magnetic Iron bar collides axially, perpendicularly against a devised sensing plate. It was found that a new truncated cone was formed at the contact end and that the conical angle of the cone depended only on the conical angle of the former cone before the collision. It was also confirmed that the generated mean stress on the boundary plane between the deformed part and the undeformed part at the impact end was constant. By comparing experimental results with calculated results using the theoretical relation proposed in previous paper, the effectiveness of the theoretical relation for estimating the impulsive force for Soft Magnetic Iron Bars is confirmed.

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The validity of the caustic method on the fracture problems of partially stabilized zirconia at room and elevated temperatures up to 1200°C is confirmed, and we investigated the dynamic fracture behavior of this material from the pictures taken using the apparatus of caustics together with an ultrahigh-speed camera of Imacon 790. Consequently, it is pointed out that dynamic fracture toughness K_Id is abruptly decreased as the testing temperature increases over about 500°C and the ratio of K_Id and static fracture toughness is increased from 2.0 at room temperature to 5.0 at 800°C. Moreover, it is ascertained that the crack-propagation fracture toughness is increased with the crack velocity at any testing temperature up to 1200°C and this tendency is decreased with the rise of temperature. Finally, an example of the visualized acoustic emission wave is shown. It is revealed that the velocity of this AE-wave is slightly decreased as the temperature rises and it coincides with the Rayleigh wave speed of this material.

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In order to study the fatigue behavior of an age-hardened Al-alloy 6061-T6, rotating bending fatigue tests of plain specimens were carried out. The initiation and propagation behaviors of cracks were investigated by the successive observations of the surface. In the present material, many cracks longer than 1 mm at the later stages of cycling are initiated. The scatter characteristics of propagation behavior for these cracks are analyzed by assuming the Weibull distribution. Moreover, the length distribution of all the cracks longer than 0.01 mm and initiated within a specific region (area : 20mm²) are examined. The region was set on the replicas gathered from the midsurface of a specimen.

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Measurement of the strength for composite materials is very difficult because those failure processes imply various failure modes, which are, for example, an interlaminar delamination, a destruction of matrix and an interfacial fracture between a fiber and a matrix. However, that strength is the most important characteristic in structural design using composite materials. Hence we try a fractural progress analysis of composite materials using a quasi-3-dimensional analysis method under a tensile load. A quasi-3-dimensional model is constructed of shell elements and beam elements which represent fiber and matrix, respectively. The fractural progress analysis of the composite materials is carried out to evaluate this proposed model. The precision of the analysis is very good. Therefore we confirm that this proposed model can simulate a transverse crack an interlaminar fracture.

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The degradation of a plain woven carbon fiber/epoxy composite under tension-tension fatigue loading was studied in this paper. An almost flat S-N diagram was obtained for this composite. As high as 85% fatigue strength of the static strength at 10⁶ cycles was recorded. The residual strength after both static and cyclic loadings is higher than the static strength. A typical S-shape stiffness reduction against logarithmic cycle number is found for the high-cycle-fatigue specimens. However, sudden fatigue death of the specimens occurs with no indications in both S-S curves and AE events. Parameters of the parabolic function which fits the convex S-S curve represent the stiffness reduction better than the observed stiffness. Microscopic examination of the fracture surface was conducted. From those observations, a fatigue damage process mode is proposed.

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Residual strength tests were carried out on spheroidal graphite cast iron by means of a rotating bending fatigue test machine. In order to study the fatigue damage process, the scatter of the test data was estimated by means of Weibull distributions, and also, fatigue crack propagation behaviors and crack length distributions on the surfaces of the smooth specimens were investigated. For each testing of the two stress levels 294.3 MPa and 245.3 MPa, thirteen specimens were used in order to obtain the exact fatigue lives. The residual strength tests were conducted on the basis of these fatigue lives at the two stress levels. The dispersion of residual strength and residual strength degradation for the stress level 294.3 MPa occurred from the stage of cycle ratio 0.5. The cumulative probability of crack length distribution for each cycle ratio at the stress level 294.3 MPa showed that the distributions of longer crack length increase as cycle ratio increases. The greatest cause of the scattering of residual strength was considered to be the occurrence of various long cracks.

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Cold spin proof testing effects on the high the temperature rotating strength of Si₃N₄ disks with bore were investigated experimentally. By comparing strength distribution of the virgin and the proof tested disks, we revealed that the rotating strength of disks at high temperature was improved by cold spin proof testsing. It was also revealed that the established evaluation method for ceramic components was effective in the prediction of the strength distribution of the proof-tested disks.

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A strain-controlled low-cycle fatigue test was conducted in air, using the specimen of 0.37% carbon steel coated with TiN by the physical vapour deposition (PVD) method. From the experimental results, the increase in fatigue strength of the coated specimen was observed under the region of low total strain amplitude, as compared with that of an uncoated specimen, because crack initiation was delayed by the hard coating film on the specimen surface which acted as a barrier to the egress of dislocations. On the other hand, fatigue strength of the coated specimen decreased at the rigion of high strain amplitude. Many cracks were induced at the substrate by flaws in the coating film. Flaw in the coating film on the specimen occurred at the static tensile strain of 0.34∼0.40 % and density of flaw increased with tensile strain. The value of strain amplitude at the reversal of fatigue strength corresponds to the tensile strain at flaw initiation of the coating film.

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An interferometric strain/displacement gauge (ISDG) system with a laser diode was developed to dynamically measure the crack closure behavior of small surface cracks. The timing of the laser radiation was controlled by a computer and was synchronized with the fatigue load. Smooth low-carbon steel specimens were fatigued. The crack mouth opening displacement of small fatigue cracks was measured dynamically as well as statically with the ISDG system. The crack opening stress was determined using the unloading elastic compliance method. The crack opening stress obtained at dynamic loading was smaller than that obtained at stepwise loading. The relationship between the crack propagation rate and the effective stress intensity range obtained at dynamic loading agreed very well with that for long cracks.

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The pheonomenological equation of the dynamic fracture for the brittle materials was derived making use of the results of the lumped mass spring model of the crack. We have used this equation to qualitatively analyze the effect of crack acceleration on the K₁-a relation and the fractured surface roughness obtained by Takahashi and Arakawa [Exp. Mech., 27 (1987), 195], where the quantities K₁ and a are the dynamic stress intensity factor and the velocity of the crack, respectively. The implication of this phenomenological equation on the theory of the dynamic fracture is also discussed.

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Rotating bending fatigue tests of three kinds of dual-phase steel were carried out on specimens with a circumferential notch in order to investigate the influence of microstructure on the fatigue strength of notched bars. The results obtained were discussed based on linear notch mechanics. The morphology of the slip observed at the fatigue limit for crack initiation σ_w1 is of a planar-type, which is due to the cyclic softening behavior in all of the DP steel. On the other hand, the morphology of cracks observed at the fatigue limit for crack propagation σ_w2 is strongly influenced by microstructure, and the deflection of crack pass is larger in a coarse ferrite grain than in a fine one. The notch sensitivities in the DP steel are high for crack initiation and low for crack propagation.

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This paper is concerned with tensile impact response of an infinite body with one or two annular cracks. The method of analysis is the body force method extended to elastodynamic problems, which was developed previously by the author. In this method, the solutions are obtained by superposing the elastodynamic stress fields of point force to satisfy the given boundary conditions. The dynamic stress intensity factors are obtained numerically, and the effects of the interactions between two cracks on the dynamic stress intensity factor are shown graphically.

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The CFRP laminated plate [0₆/90₆] sym under impact was analyzed by means of an approximated three-dimensional theory similar to that shown for the isotropic laminated plate. The impact force history due to the elastic sphere is analyzed by means of the Hertzian contact theory. In the experiment, the plate was impacted by steel spheres of φ5 mm and φ10 mm with almost equal impact energy by use of an air gun. The delamination of each interfacial boundary was observed with an ultrasonic microscope. The total amount of damage was larger for a smaller inpactor under equal impact energy. To explain this experimental result theoretically, the out-of-plane stresses on the interfacial boundaries were calculated. Theoretical results show good agreement with the tendencies of experimental results.

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Cold upsetting of a circular cylinder is often used to evaluate the cold forgeability of forming materials. The index of the forgeability is the critical strain at which a crack occurs on the expanding free surface of the upsetting cylinder. The forming limit due to cracking is investigated with the analytical method based on the modified criterion for the collapse of the unique solution, and the modes of cracking are determined by comparing stabilities from the forming limit to the two modes able to permit strain rate discontinuity on the plane of localized necking. Various experiments show the linear relationship with the slope of -0.5 in circumferential strain versus axial strain at the forming limit. The forming limit and the mode predicted are in very good agreement with the experimental results.

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The rotation of the grain in polycrystalline metal is caused by crystal slips in each grain. In order to clarify the rotation of a grain surrounded by neighbouring grains, a plane model is introduced in which an anisotropic elliptic inclusion is embedded in an isotropic matrix. Hill's quadratic yield function allowing for orthotropic anisotropy is adopted to express the slip in the inclusion. The deformation and the rotation of the inclusion are analyzed with the rigid-plastic finite element method and discussed based on the calculated results. The inclusion deformed by slip rotates so that the slip direction coincides with the tensile direction. The rotation of the grain is restricted when the shape of grain deviates from the circular shape.

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This paper deals with numerical solutions of singular integral equations of the body force method in interaction problems of notches and holes under general loading conditions. The problems are formulated as a system of singular integral equations with Cauchy-type singularities, where the densities of body forces distributed in the x-and y-directions are to be unknown functions. In order to satisfy the boundary conditions along the notches, several types of fundamental density functions are proposed ; then, the body force densities are approximated by a linear combination of the fundamental density functions and polynomials. The accuracy of the present analysis is verified by comparing with the results obtained by the previous method. The present method is found to give rapidly converging numerical results for stress distribution along the notch boundaries.

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This paper presents an analysis of bending problems for an anisotropic semi-infinite plate due to single moment, single-point discrepancy of slope deflection, dipole-moment, dipole-point discrepancy of slope deflection, and so forth, with various supported edge conditions such as fixed, free, simply and sliding supported edges. Distributions of bending moment and slope deflection under applied single moment for the above four supported edges are illustrated by some graphical representations as numerical examples.

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This paper presents an analysis of anisotropic semi-infinite body due to single force, single dislocation, dipole force and so on, with various surface boundaries such as free, fixed and two sliding conditions. The principal axes of elastic moduli of the anisotropic body under consideration may have arbitrary directions such as out-of-plane directions. Some typical examples are illustrated by graphical representations.

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By using the theoretical results for closed-form analytical solutions of in-plane problems containing elliptic cavity or elliptic rigid inclusion in an anisotropic two-dimensional elastic medium under point forces, dislocations and so on, several numerical examples are shown by many graphical representations. The previous results published by several authors for isotropic and anisotropic cases can be included as particular cases of our solutions.

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The present paper proposes an improved orthotropic elastic plate theory considering shear deformation and axial rotation in which the normal stress resultants are assumed to act on the cross section of the element. Comparisons with Reissner's, Ambartsumyan's, and Bert & Chang's theories are given by numerical examples for the case of buckling analysis of several orthotropic rectangular plates with all edges simply supported.

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A design method was proposed for the steel liner-anchor system on an interior wall of a prestressed concrete vessel of a LNG above-ground tank. The stress analyses were performed on the liner-anchor system to determine the forces on the liner and displacements of the anchor under concrete imposed strain. The model for the analysis consists of a series of springs that represents ideal flat liners, bent plates and anchors. An allowable value was given for the anchor displacement and the required diameter of the stud was derived to prevent fracture of the stud anchor. Elastoplastic analyses were performed on the liner plates under prescribed displacement to calculate the surface strain of the liner plates. The allowable value was determined for the liner surface strain and the lower limit value of the anchor spacing was determined to avoid rupture of the liner.

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This paper presents a new integrated FEM formulation for geometrically nonlinear analyses. There have been two methods to solve the so-called large displacement problem, i.e., the total-Lagrangian method and the updated-Lagrangian method, and two types of FEM programming have been conventionally written. It is shown in the peresent paper that these two types of programming can be combined by the use of the covariant components of the incremental Green-Lagrange strain tensor and the contravariant components of the second Piola-Kirchhoff stress tensor in the convected coordinate system. The difference is only seen in the transformation of the constitutive tensor components. The stiffness matrices for the solid and shell elements by this formulation are illustrated in detail, and advantages and disadvantages of the proposed method are also discussed.

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