Inverse problems have had a significant impact on various fields of science and engineering, and are attracting considerable attention of scientists and engineers. This paper presents an overview of the inverse problems arising in the fields of mechanics and fracture of solids and structures. A definition of inverse problems is given. As representative examples of inverse problems, outlines and inversion schemes are described for the electric-potential CT method for crack shape measurements, inverse scattering acoustic source characterization, estimation of stresses and strains, determination of forces, parameter identification of systems, and inverse design. Difficulties encountered in the inverse analyses are discussed and methods to solve the difficulties are described. Prospective developments in inverse problems are suggested.

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This paper is concerned with the mixed boundary-value problems of an infinite plate with an elliptic hole, into which a smooth rigid elliptic plug is simply inserted. Since the infinite plate is subjected to a uniaxial loading (tension or compression) at infinity, apertures are produced along the boundary between the inserted plug and the hole. The contact pressure between the inserted plug and the hole is expressed in a convergent series whose differntial form is also convergent, so that the stressd and displacement generated along the boundary can be numerically analyzed by the pointmatching method. Using the numerical results for various elliptic shapes, the influence of interferencs is shown with the stress around an elliptic hole.

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An expression of the distribution of load in the screw thread of a bolt-nut connection which is subjected not only to axial forces but also simultaneously to tangential forces and bending moments is obtained in the following process. First, let an expression of the distribution of load in a screw thread be a polynomial of turning angle (angle of rotation of point moving along the helix of the screw) as the variable with undetermined coefficients. Next, using the above expression, calculate the resultant axial force, resultant tangential force, bending moment at the bearing surface of the bolt head, deflection and deflection angle of the bolt as a distance from the bolt head. Then, decide the undermined coefficients in the postulated polynomial by means of the linear programming method, so that the results from the above calculation with this polynomial approach the experimental results as closely as possible.

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Analyzing the stress distribution of an elastic body on which a dynamic load is applied has become important in relation to the reliability of machine elements. However, stress distribution has seldom been analyzed because of the lack of knowledge of the stress function including the term of inertia. This report derives an easy method which uses the complex stress function ; using this method, the stress distribution of an elastic body such as threads is determined.

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An analytical method of contact status between magnetic heads and magnetic tapes as well as the results of such an analysis are explained. Tape deflection is obtained in the form of the influence coefficient "A_ij" created as a point "i" when a unit load is applied to a point "j". The contact status is clarified by adopting a theory of increments in which calculations are successively made while causing a head and tape to gradually make contact with each other. The contact length upon the head differs depending on the values of the head radius, tape tension, tape rigidity and degree of protrusion of the head. The actual measurements were achieved by utilizing the interference fringe pattern created between the head and the transparent tape. The experimental results are in close accord with the numerical results.

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The squeeze effect of lubricating oil filling in a surface crack was calculated by using the finite element method. An incremental procedure was presented to solve the two-dimensional Reynolds equation combined with the relation of the oil pressure to the crack opening displacement. As the crack is closing, the squeeze action increases the pressure of the lubricating oil, which tends to open the crack. For the constant crack depth, a=10 mm, the pressure produced by the squeeze action increases with a decrease in half-length of the the crack, c. The contour lines of the pressure are roughly parallel to the surface of the plate, and so this pressure distribution is similar to those of a through crack in a thick plate. The distribution of the stress intensity factor due to the squeeze pressure is not significantly affected by the half-length of the crack, c.

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A plane elasto-static problem is solved for two bonded elastic and isotropic strips with a T-shaped crack. The T-shaped crack consists of a crack perpendicular to the interface and an interface crack. By means of the Airy stress function and Fourier transforms the problem is formulated as a system of integral equations. A new numerical method using only the Gauss-Chebyshev integration formula is proposed to evaluate the integral equations, although the complicated Jacobi polynomial expansion and integration formula were used in the previous literature. Stress intensity factors are obtained numerically for various materials and geometrical parameters, where the interaction between the cracks perpendicular to and on the interface is clearly shown.

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Edge delamination is one of the major factors that determines the fatigue strength of composite laminates ; it is attributed to the existence of highly intensified interlaminar stresses in the neighborhood of the free edge. In order to develop an efficient method to prevent edge delamination, the effects of the geometrical shape of the free edge on γ^δ stress singularity are discussed in this paper for cross-ply laminates. t is shown that the order of stress singularity can be controlled by varying the geometrical shape of the free edge and that the singularity disappears for some combinations of the angles formed by the edge surfaces of the two neighboring layers with respect to their interface. In the case of multilayer laminates, it is also possible to eliminate stress singularity completely or to reduce its order drastically at all interfaces by slanting the entire free edge at an appropriate angle.

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Nowadays, due to the development of the sandwich core series and the progression of the higher degree of accuracy required for each thickness of sandwich plate, optimum design of the structural sandwich plate has been needed. We have found several papers on the optimum design of laminated plates. They deal with optimum density or optimum fiber direction of each ply, and optimum orthotropic layers under uniaxial and biaxial compression. But we have not been able to find any paper on the optimum design of a sandwich plate with a hole or notch which produces sandwich plate with a hole or notch, which searches least weight or cost per bending strength.

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The effect of probabilistic fiber orientations on the response of carbon-fiber-reinforced plastic laminated plates due to thermal load is analyzed by the stochastic finite element method based on the first-order perturbation technique. The fiber orientations are taken as a two-dimensional spatial stochastic process, and the stochasticity is represented by a trigonometrical autocorrelation function. Numerical examples are carried out in regard to the rectangular CFRP laminated plates subjected to a uniform temperature rise or a constant temperature gradient through the thickness. The variance of the thermal deformation and stresses is discussed for the input statistical property of the orientations.

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In stain measurements of plastics using foil strain gages, the temperature rise caused by power dissipated in the gage produces serious errors. A simple model for estimating the temperature rise is proposed, that is, a single strip representing a grid is bounded onto a half space made of plastic, and generates constant heat flux. A formula and diagram, by which the maximum value of the temperature rise can be estimated, are presented in this paper. The estimated temperature rise, T_max, is about 2 times as large as the measured one for actual gages bounded onto acrylic plates. The difference between both values is due to the incompleteness of the gage model and errors in the temperature measurement using a thermocouple. In spite of this incompleteness, the value of T_max can still be used to estimate the temperature rise of the actual gages. This value is more useful than the power density which is often used as a parameter for estimating the temperature rise.

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Integrity Tests of the Fast Breeder Reactor components are often conducted at an elevated temperature, say 550°C. Since high-temperature strain measurement using special strain gauges is costly and unappropriate for large and repeated strains, the authors have developed an optical strain measurement method and system based on computer picture processing and the triangulation principle. The present method enables us to measure the strain in specimen with curved surfaces. Its operation is also easy, because of the automatic distinction of marks from noises. The verification tests with a plate specimen and a cylindrical one are performed under elevated temperatures. The results show that the present method is very suitable to the tests under elevated temperatures and that the measurement error or strain is within 0.2% (2000μ), which is reasonable considering the limitation of hardware.

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A constitutive equation in rate-independent cyclic plasticity was presented with a new plastic potential function dependent on the field of resisting force against the movement of dislocations. By extending the model proposed in the previous paper for a uniaxial case, it was assumed in this study that each process of the cyclic deformation under multiaxial loading should be attached to the processes of either to or formation, and a simple rule of conversion from one process to the other was postulated by considering the stress history. Moreover, an effect of anisotropy, produced by cyclic deformation, was reflected in the internal structure variable which was one of three internal state variables describing the force field. The propriety of this equation without any yield surface has been examined with some experiments obtained from the axial-and torsional-load cycling tests with tubular specimens of a carbon steel.

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The forming limit diagrams of proportionally prestrained brass sheets are experimentally determined for a combination of uniaxial and equi-biaxial tensions. From these FLDs and the theoretical ones predicted using a new plastic constitutive equation previously proposed by one of the authors (Gotoh) and a local necking condition, the n-th power hardening, Voce and modified Voce hardening laws are compared to determine the most suitable one for the brass sheet. Furthermore, the dependence of the FLDs on sheet thickness of the brass sheet is discussed.

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In the field of bar rolling, very little theoretical researches has been performed, because the flow of the material in bar rolling is complicated. Recently, we proposed a new energy method using finite element division ; this method was applied to the analysis of the flow of the material for two types of bar rolling : equare-diamond pass and round-oval pass. However another important type of bar rolling exists : square-oval pass. In this type, the side regions of the material are reduced earlier than the central region, whereas the central region of the material is reduced earlier in the former two types. Thus, the flow of the material of this type differs greatly from that of the former types. In square-oval pass, the material is deformed inhomogeneously, and the degree of freedom of the velocity fields must be increased for precise simulation of the flow of the material. In this paper, we have improved the method to lessen computation time and memory requirements. This method is then applied to the analysis of the flow of the material in square-oval pass and reasonable results are obtained for rolling properties such as width spread, strain rate distribution, folding of stress-free side surface, and others.

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It is well-known that the fatigue of metallic materials occurs due to the initiation of cracks and their subsequent growth. However, the number of crack nuclei is not provided deterministically. In engineering applications, this number is randomly variable and often significant, and should be taken into account in the evaluation of crack coalescence. In the present study, based on the numbers of initiated cracks, a statistical evaluation was made of the coalescence of cracks as a function of the number of stress cycles, and the fatigue life distribution was probabilistically derived from the above evaluation assuming that the failure occurs immediately after the coalescence of cracks. The analytical results obtained are in good agreement with experimental results of the fatigue life distribution.

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Most structures have a region where stresses concentrate, and the probability of fatigue crack initiation may be higher than in other parts. Therefore, to improve the reliability of an LBB (Leak Before Break) design, it is necessary to evaluate the growth and through thickness behavior of fatigue cracks in the stress concentration region. In this paper, fatigue crack growth behavior in a stress concentration region has been studied on 3%NiCrMo and HT80 steels. Stress concentration was caused by a fillet on the plate. The main results obtained are as follows. (1) Before cracking through the plate thickness, stress concentration has a remarkable effect on the fatigue crack growth behavior and it flattens the shape of surface crack. The crack growth behavior can be explained quantitatively by using the Newman-Raju formula and the stress resolving method proposed by ASME B&P Code Sec.XI. (2) The da/dN-ΔK relation obtained in a stress concentration specimen shows good agreement with that obtained in a surface-cracked smooth specimen. (3) The stress concentration caused by a fillet has little effect on the crack growth rate after cracking through the plate thickness. (4) By using the K value based on Eqs. (1) and (2), particular crack growth behavior and the change in crack shape after cracking through thickness can be explained quantitatively.

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JIS SNCM 439, S 35 C and SUS 304 steels were low-cycle fatigued with mean stress and strain under load-and displacement-controlled conditions. The cyclic J integral range, ΔJ, was not effective for the evaluation of the crack growth rate under test conditions accompanied by ratchet deformation. Therefore, the parameter of ΔJ/{1-(Φ_c^min/Φ_c^max)}⁰.2, which controlled the acceleration of the crack growth rate due to ratchet deformation as well as the crack growth rate under a fully reversed cyclic strain, was usefully proposed here, where Φ_c^min and Φ_c^max were the minimum and maximum crack-center opening displacements. The crack tip opening displacement range ΔΦ_t(200)=A(ΔJ)^q. In general, the power exponents, q, were smaller than the values of 1/(n'+1) or 1/(n+1) estimated by assuming the HRR singular field around the fatigue crack tip, where n' and n were the cyclic and monotonic strain hardening exponents of materials

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