The cavitation erosion of the hard chromium plating on steel was studied by vibratory erosion tests. The mass loss vs. exposure time curves are divided into three stages. The first stage is the process of the erosion of hard chromium in itself. The base metal below the interface begins to be damaged in the second stage. The third stage appears when the plating layer has fallen off in massive particles. The mass loss rates in each stage are larger in 3% NaCl solution than those in ion exchanged water because intercrystalline fracture occurs. The effects of plating thickness on the damage in each stage were also discussed. The life of plating as an erosion resistant coating increases in propotion to the thickness in ion exchanged water. In 3% NaCl solution, however, it is smaller and increases no more than about 50 μm in thickness.

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The preceding paper has shown that the increase of polyalkylene glycol (PAG) polymer concentration results in a decrease of fin cracks and an increase of vertical cracks, because of the clouding point (81°C) of PAG sol.. This paper deals with the effects of the clouding points of quenchant on the quench cracking of a SUJ 2 bar. The clouding point is affected enormously over pH 13.0 of the PAG quenchant and goes down to 43°C at pH 13.5. The high cooling rate of the PAG quenchant is obtained by the low clouding point quenchant. Therefore, the behavior of quench cracking in the pH 13.5 PAG sol. is similar to that of water. When SUJ 2 was quenched from austenitizing temperature 800°C, a considerable tensile stress existed on the surface area of all specimens, regardless of their pH values. A gel permiation chromatogram shows that the thermostability of PAG quenchant is excellent under sever conditions.

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This paper is concerned with a theoretical aspect of proof testing of ceramics. In the case when slow crack growth occurs during the unloading process of proof testing of ceramics, the truncation strength S_{f min} (minimum Strength after proof testing) becomes lower than the proof stress σ_p. The equations for S_{f min} in such a case were derived by Evans and Ritter. However, existence of the three distinct regions I, II and III in da/dt-K diagram was not fully taken into account in their equations. Thus, in this paper, a detailed analysis was carried out taking account of the actual crack growth characteristics, and the equation for S_{f min} was derived. A convenient diagram for determining the proof testing condition was also proposed.

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Near-threshold fatigue crack properties were investigated for a low-alloy steel, Cr-Mo-V, and a stainless steel, SUS 403, at temperatures ranging from room temperature to 550°C. Fatigue tests were conducted at frequencies of 0.5, 5, 50 Hz under P_max-constant, ΔK decreasing conditions to prevent crack closure. The thickness and composition of oxide deposits were evaluated by Auger electron spectroscopy, scanning electron microscopy, and X-ray diffraction techniques. The conclusions can be summarized as in the following. (1) Effective values of the threshold stress intensity range increased with increasing temperature and decreasing frequency for Cr-Mo-V steel, while they were independent both of temperature and frequency for SUS 403 steel. (2) Fatigue crack growth rate was accelerated with increasing temperature and decreasing frequency for Cr-Mo-V steel. The rate is independent of frequency for SUS 403 steel, although acceleration occurred at elevated temperatures. (3) The fatigue threshold and growth properties at elevated temperatures are strongly related to the oxidation process of the bare surface at the crack tip.

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Creep-fatigue tests were conducted with 2 1/4 Cr-1 Mo steel at 550°C in air and a vacuum of 0.1 and 100 μPa for separating the environmental effect from the pure creep-fatigue behavior. In a vacuum where no environmental effect was detected, creep-fatigue life reduced when tension going time exceeded compression going time, or when a positive mean stress developed. A good correlation exists between a creep-fatigue life and a fracture mode. When the fracture mode was predominantly transgranular, no life reduction occurred. On the contrary, when it was predominantly intergranular, a significant life reduction was observed. Environmental effect was also examined qualititatively. The extent to which the environment affects depends strongly on the wave form. The above observations are compared to those obtained with 304 steel in the authors previous study.

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In modern design, it is an important task to estimate fatigue life. Although many fatigue data sheets have been published for various materials, they have large scatter, and it seems to be difficult to predict the precise fatigue lives from the raw data directly. In this paper, an effective and convenient method based on the small crack growth law and tensile strength is presented for predicting the fatigue life of plain members. The validity of this method is checked from its application to the data sheets by the National Research Institute for Metals and in other workers' experiments. The prediction is in good agreement with the experimental results over a wide range with the exception of stresses right near the fatigue limit.

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Fatigue crack initiation and propagation processes were investigated on plain specimens of an annealed 0.42% C steel and an age-hardened Al-alloy under torsional loading in air and in oil. The fatigue strength of a carbon steel is higher and that of an age-hardened Al-alloy is lower in oil than in air. The main reason is the difference of the oil effects based on the difference of the crack propagation mode in the two materials. That is, fatigue crack growth rate in the former is suppressed by the oil wedging action because of the Mode I propagation process, and that in the latter is accelerated by the oil lubricating action because of the Mode II propagation process.

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In this study, an ultrasonic angle beam method was newly applied to measuring fatigue crack closure. The received echo from the crack face is regarded as the diffracted wave from the crack tip, and it gives information on the crack tip shape. The crack opening load can be determined as the load at the maximum echo point in the load-echo curve. ΔK constant and single peak overload fatigue crack growth tests were carried out, and the crack opening loads were measured by the ultrasonic angle beam method and other conventional methods. It was shown that the ultrasonic angle beam method is quantitatively superior to other methods. Its applicability and utility compared with other methods are discussed.

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Corrosion fatigue crack growth and near-threshold characteristics of high tensile strength steel HT 60 (σ_B = 669 MPa) were investigated. Compact specimens were exposed to synthetic sea water under ΔK-decreasing and ΔK-increasing conditions at two stress ratios (R = 0.1 and 0.7) and at a cyclic frequency of 5 Hz. The results obtained were compared with that of high strength steel AISI 4340 (σ_B = 1 209 and 1 695 MPa) and are summarized as follows : (1) A da/dN-ΔK_eff relation in air can give a conservative estimation of da/dN-ΔK relations in sea water. (2) In the case of high R, however, crack growth acceleration at high ΔK regions appears to be controlled by the stress-assisted dissolution. (3) The crack opening stress intensity factor K_op detected by the back-face-strain method is the result of crack surface contact with the corrosion products and gives an overestimation of K_op at the crack tip.

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Corrosion fatigue crack initiation behavior was investigated in high-tensile strength steels in synthetic sea water. The materials tested were 50 kgf/mm² high-tensile strength steels, HT50, HT50-TMCP, and HT 50 weldment, and a 80 kgf/mm² one, HT 80. The tests were performed under rotating bending and plane bending at a frequency of 0.17 Hz with a load ratio of -1. Corrosion fatigue strengths of these steels were monotonously decreased with increasing numbers of cycles. The strengths of the base metal and weldment of HT 50 were similar. Corrosion fatigue cracks were initiated when a pit depth exceeded a threshold value. By assuming the pits as sharp cracks, ΔK values at the deepest points were calculated, and the mechanical condition for crack initiation of these steels was determined from the mean value of ΔK, ΔK^*_<CF>.

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Part-through surface fatigue crack growth rates of high-tensile strength steels have been measured in ASTM synthetic sea water at free corrosion potential and under a cathodic potential. The aspect ratio in synthetic sea water at free corrosion potential was larger than that in air ; while under a cathodic potential it was almost fixed and the same as that in air. At free corrosion potential at R = 0.1, the crack growth rate to inside da/dN was firstly faster than the one along surface dc/dN because the inside is under a plane-strain condition, and the O₂ concentration is lower than that at the surface. Afterwards, the da/dN and dc/dN were entirely the same as that of a through-crack type specimen, both at free corrosion and under a cathodic potential. Under a cathodic potential, the threshold values were remarkably high because the Ca and Mg deposits-induced wedge effect was so conspicuous.

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The fretting fatigue strength of SUP 9 spring steel under random loading was examined by clamping the contact pads of the same material. Random loading reduced the fretting fatigue strengths by a factor of 1.5. The linear cumulative damage rule held good for fretting fatigue under random loading. The relationship between the coefficient of the friction and the slip amplitude using root-mean-square values under random loading agreed well with that under constant loading. Prediction of fatigue life was made on the basis of the fracture mechanics analysis proposed in the previous paper, where the frictional force between the fretting pad and the specimen was taken into consideration. The predicted lives were in good agreement with the experimental results.

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A low cycle fatigue test and a micro-crack propagation test were carried out under push-pull loading on low carbon steel and on pure iron, with special interest in the relation between the fracture ductility and the low cycle fatigue life. Results show that the low cycle fatigue life is not sensitive to the change in fracture ductility of the material for the ordinary low cycle regime in which the development of small surface cracks leads to the fracture of the specimen, and that this is closely related to the evidence showing that the rate of microcrack extension is not appreciably affected by the fracture ductility of the materials. Calculation of low cycle fatigue life on the basis of the law of small crack growth proposed in recent years revealed that only a small difference in fatigue life appears in the high and low ductility materials.

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Alternating two-load level torsional fatigue tests were performed using 3.5 Ni-Cr-Mo-V steel to investigate the influence of overloads on the fatigue damage in the crack initiation and propagation stages. The base block consisted of strain cycling of Δγ_p = 2% as the overloads and constant stress cycling of τ_H = 260 MPa, higher than the fatigue limit, or τ_L = 220 MPa, lower than the fatigue limit, as the baseline loading. Constant stress and strain cycling were also performed. It was found that torsional fatigue cracks tended to branch off under constant stress cycling, but did not branch off under constant strain cycling. Overloads always reduced the crack initiation life and the fatigue life. In the torsional fatigue, small-size cracks were easily initiated, but they propagated slowly in comparison with push-pull fatigue.

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Cyclic elastic follow-up tests were carried out on 2.25 Cr-1 Mo steel at 600°C. The behavior of the relaxed stress and the elastic follow-up strain at the first elastic follow-up process were discussed with simplified inelastic analyses. When the Norton's creep law and a virtual triangle of elastic follow-up were used, it was found that the elastic-creep analytical method was a most useful technique to predict the elastic follow-up response on 2.25 Cr-1 Mo steel, as well as on SUS 304 steel. An inelastic strain range Δε_in produced in the cyclic elastic follow-up process was also examined and was compared with an analytical approximation. From analysis and experiments, it was verified that the shakedown condition of a structure can be achieved with simple limitations of an effective relaxed stress after a certain period and an effective yield stress of the material, as defined by the proposed model.

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The present paper seeks to solve the transient thermal stress in an infinite, isotropic solid containing an annular crack. It is assumed that the transient thermal stress is set up by the application of the heat exchange by convection on the crack surface. By use of the finite difference method for only the time variable the analytical solution for spatial variables can be obtained. The numerical results are shown for the temperature and stress intensity factor.

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In the present article, Part 1 in this series of papers, a new one-dimensional wave equation is proposed which is convenient, practically, for studying longitudinal waves in rods having some inhomogeneities in physical properties and/or in geometry. The equation proposed is constructed by taking account not only of the lateral motions due to the Poisson's effect, but also of the distribution of longitudinal displacements across a section of the rod, which are calculated by the axisymmetrical Pochhammer's equation. An appropriate averaging of these effects brings one parameter into the equation, by which the two-dimensional problem is reduced to the one-dimensional one. Even though the present equation is very simple, the dispersive nature is well described over a relatively wide range of ratios of the diameter of the rod to the wavelength.

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The present paper is concerned with the experiments on the scattering of longitudinal dispersive waves in cylindrical elastic rods, where the elastic constants such as Young's modulus and Poisson's ratio become inhomogeneous along their axes due to local heating. Two stainless steel rods which are different in diameter and in length are heated locally at their intermediate portions and are then subjected to external impulsive load by impinging cylindrical bullets at one end of each rod. Strain waves detected by the semi-conductor strain gauges manifest dispersive reflected and transmitted waves. The results are inspected by means of the wave equation and the procedures proposed in Part 1 in this series of papers.

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The dynamic behaviors of a finite length bar with a continuously variable cross section colliding with a rigid wall are studied theoretically and experimentally. The impact end stress and the propagation of elastic waves along the bar are predicted under the assumption that the bar is thin, has small changes of its cross section. The analytical solution is obtained by the application of the Laplace transform. Numerical calculations are carried out for the case of truncated cones. The time variation of stress at the impact end and elastic waves along the cones are presented and compared with the corresponding experiments. The experiments are performed for two different truncated cones by impacting them on a "rigid" wall, termed a sensing plate which enables us to measure the impulsive force produced by the collision. The theoretical predictions are found to be in good agreement with the experimental results.

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In the collision between the flat surface of solid and of a sphere, it can be considered that a high stress will be occur, since an impact load is applied in a small local contact area. If an impact stress exceeds the yield stress of a material, the local deformation of the contact surface converts from elastic to plastic flow. Therefore, the impact load may be moderated. It is important when formulating the impact load that the effect of the local plastic deformation of the contact surface on the time history of a load due to impact is investigated. On the other hand, it is revealed by Hertz's theory that the relationship between a force and the amount of approach of both solids during impact is nonlinear. If it is postulated as being linear, there is not little what be able to apply it to analyze the dynamic impact problem. In this paper, the effect of the local displacement behavior in the contact process on the impact load is shown by the experiment of a collision between a plate of mild steel and a high hardness steel ball. The impact load is evaluated by a piezo electric plastic transducer. The limitation which the modified approach of Hertz's theory is valid, are distinguished.

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The free vibrations of an infinitely long cylindrical shell under axisymmetrical hydrodynamic pressures due to external and internal fluids are studied theoretically. The basic equations of motion for axisymmetric vibrations of such a shell are given, based on the bending theory. These equations are solved analytically by means of Fourier cosine transformation, and the general frequency equation for the coupled system is obtained according to a consideration of the dynamic interaction between the shell surface and fluids. Furthermore, seven special cases are derived from the general coupled frequency equation. The general frequency equation is calculated for some kinds of mass density of the internal fluid. Hence, it is shown that the effect of motion of external and internal fluids on the free vibrations of shell is notable.

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A method of elastic-plastic stress analysis based on the combination (FEM+BFM) of finite element method (FEM) and body force method (BFM) is developed. FEM+BFM has the advantages of both method (FEM and BFM) and has many possible applications. The line elements of BFM are located along the interface between the outer elastic domain and the inner elastic-plastic domains which are composed with FEM elements. In the present study, the method is applied to solve the problems of an elliptical hole contained in an infinite plate under various combined remote stress (σ_x∞, σ_y∞, τ_xy∞). The stress and strain concentration, the extension of plastic zone and the applicability of Neuber's rule under various combined remote stress (σ_x∞, σ_y∞, τ_xy∞) are investigated in details.

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This paper deals with a two-dimensional stress analysis of butt adhesive joints with a circular hole in an adhesive subjected to an external tensile load in order to clarify the effects of a small hole on the stress distribution and the tensile strength of joints. The effects of the location and size of a hole on the stress distribution are shown by numerical computations. For verification, photoelastic experiments are performed. The analytical result is in a fairly good agreement with the experimental one. Moreover, it is shown by numerical computations that the principal stress around a hole is larger than that of the interface between the adherend and adhesive ; and the stress concentration becomes larger with a decrease of the size of a hole.

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Multiple artificial geothermal cracks in a hot dry rock are treated. During heat extraction, the surface of the geothermal cracks are cooled by circulating fluid and thermal contraction of the rock occurs. Then the geothermal cracks begin to extend. The analysis is made on the basis of the two-dimensional theory of quasi-static thermoelasticity by using a periodic array model of the unequal multiple geothermal cracks, and the bifurcation growth of the interacting geothermal cracks is discussed with respect to stress intensity factors at the crack tips. Numerical calculations are carried out to show a stable bifurcation equilibrium path of the growth of the interacting geothermal cracks during heat extraction.

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In the previous study, the elastic-plastic fracture toughness, J_IC, and the elastic-plastic fracture resistance curve (J-R curve) were evaluated by using compact specimens for a carbon steel, STS 42, used for piping in nuclear reactors. Based on those results, the applicability of the two-parameter approach to carbon steel piping was examined in this study. The construction of the failure assessment diagram (FAD) was also attempted. The results obtained are summarized as follows ; (1) In the application of the two-parameter approach, it is essential to adapt the J-integral as a fracture criterion accounting for the strain-hardening effect. (2) Based on the FAD constructed, it is shown that the whole fracture process, from the fracture initiation to the unstable fracture (or the plastic collapse) including the stable crack growth, is predicted precisely for various sizes of specimen. (3) The failure assessment curve (FAC) defined in CEGB Report, R/H/R 6-Rev. 3, option 1 does not give a conservative prediction, and neither does the FAC in appendix 8.

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The linking and cracking processes of two neighboring holes in a thin sheet metal were investigated in detail to get quantitative information about the deformation behavior of voids in a ductile fracture. The holes deform into elliptical holes and crack with come intruding and/or protruding under tension, depending on the experimental variables of the inter-hole distance ξ_o/2r_o (r_o: radius), the two-hole arrangement angle φ₀ and the plastic strain. The complicated shape of the deformed hole is qualitatively measured and analyzed. The deformation of two holes having various arrangements of ξ_o/2r_o and φ₀ has also been analyzed by an elastic-plastic FEM, and the results are in qualitative agreement with the experimental data. Fracture ductility for the linking or cracking of two holes is approximately expressed by applying McClintock's fracture model for each volume which contains a hole at its center. The values of linking strain ε_Z, cal. and fracture strain ε_f, cal. by the equations are consistent with the experimental linking strain ε_Z, exp. and cracking strain ε_C, exp. where cracking strain is, of course, a few percentages smaller than the fracture strain in a ductile fracture.

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This paper presents the experimental data of both the yielding and the rupture on beams of the circular cross-section with a radial hole to research the strength of a beam under stress concentration. The materials used were a mild steel (S25C) in the case of the yielding and both a plaster and a graphite in the case of the rupture respectively. From the experimental data it was found that both the yield and the rupture stresses of the beams are influenced not only by the diameter ratio of the hole and the beam but also by the diameter of the beam itself, and that the strength of beams decreases with the increasing diameter of the beam for the same diameter ratio.

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Mode I interlaminar fracture toughness of CFRP is evaluated using DCB (Double Cantilever Beam) specimens. Unidirectionally reinforced carbon/nylon laminates were used for the test. The fracture toughness value, Gc, was obtained by the area method, compliance method and nonlinear analysis. The Gc of 2 mm-thick specimen is 10-12 times larger than that of an epoxy specimen. However, in case of an 8 mm-thick specimen, voids and fiber-bridging are observed, and the fracture mechanism is complicated. Acoustic emission (AE) was also measured during the compliance test. It is shown that the viscoelastic and plastic effects should be considered in studing the fracture mechanism.

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As high speed rotary machines have been constructed, it becomes necessary to know what the stress causes in the rotating components under actual rotating conditions. This report investigates the stress intensity factor of an actual dovetail region of a rotating blade, obtained with the aid of the stress-freezing method. Using a parameter of (N/t) √(γ_m), consisting of polar coordinates γ and θ measured from the crack tip, the stress intensity factors K_I and K_II are determined.

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The torsional shearing stress on the surface of an aerofoil section was studied. The analysis was carried out in the polar co-ordinate system. The back edge point of an aerofoil section was located on origin and the chord of the blade was located on the polar axis. The stress function was deduced by adapting conditions to satisfy the Poisson equation and the boundary of the section. By substituting the stress function into the fundamental formula, the torsional shearing stress at any point on the surface of the aerofoil section was found. Also the area and the polar moment of inertia of the aerofoil section were studied by the method of complex mapping function. Consequently, the torsional rigidity of the aerofoil section was deduced. As an example, the shearing stress distributions and the torsional rigidity of the Clark-Y series Propeller were calculated.

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According to the spherical shell model of the plastically deformed domain presented by Hill, four yield points on the (0001) net plane of CdS are estimated by using two micro-indenters and by revealing two types of etch figures. The hollow crystals on the sinter produced at the higher temperature region reveal the asteroid-pattern as an etch figure, and the other hollow crystals on the wall of the reaction tube produced at the lower temperature region reveal the rosette-pattern as the etch figure. The main results obtained are as follows : (1) Using the micro-Vickers-indenter or the Rockwell-superficial-indenter, the yield point of the asteroid-pattern is estimated as 342 [MPa] or 362 [MPa], respectively. (2) Similarly, the yield point of the rosette-pattern is estimated as 297 [MPa] or 307 [MPa], respectively.

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An acoustoelastic technique is useful for nondestructive measurements of residual weld stresses. It is difficult, however, to distinguish the influence of the residual stresses and of the material anisotropy on results. In this study, a new method to evaluate the material anisotropy is proposed. To confirm its applicability and utility, experiments were performed using butt weld joints of a carbon steel. The results obtained are follows; (1) In the weld metal, a discontinuous point is found in addition to a minimum point on the oscilloscope traces of received echos as the ultrasonic transducer is rotated. (2) Based on the above result, a new method to separate the influence of the material anisotropy from that of the residual stress is proposed. Its applicability and utility are confirmed experimentally. (3) The material anisotropy of the weld metal is much stronger than that of the base metal.

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The stress analysis and stress relaxation in mitred bend subjected to internal pressure have been studied by means of the photoelastic stress freezing method. The experimental results show that stress concentration occurs in the wedge tip of the intersectional plane and it is considerably influenced by the bent angle. Then, the stress relaxation was obtained by planing the wedge tip.

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Moire interferometry is a useful method for measuring small displacement and strain distributions in the whole field of a specimen. However, it is difficult to make diffraction gratings and to measure small strain less than 10^-3. In order to use the moire intrferometry easily, we try to mass-produce sheets of diffraction grating by hot-press printing. By transferring the grating of the sheet, we can easily make a diffraction grating on a specimen. For improving the sensitivity of moire interferometry, we apply a multiplication method to the moire intrferometry. As a result, we can measure strain of the order of 10^-4.

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An analytical evaluation method of a singular domain integral in BEM inelastic analysis is described in this paper. A high order singular domain integral term originated from an inelastic strain rate is present in the internal stress rate formulation and, therefore, it is very difficult to calculate its principal value by numerical integration. However, an accurate evaluation of the internal stress rate is important to obtain a correct inelastic strain field at each load increment stage of nonlinear material BEM analysis. In the present paper, we derived a fully analytical form of the singular integral term for a plane problem by applying a triangular polar coordinate transformation which can reduce the order of singularity by one degree. Internal stresses for thermal strain problems and a plastic strain problem are calculated by this method. The accuracy and effectiveness of this method is discussed, compared with the conventional numerical integral method.

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An elastic-plastic finite element formulation on the basis of the shell theory is given for the analysis of axisymmetric sheet forming such as hydraulic bulging, stretching with a rigid punch and so forth. Gotoh's plastic constitutive equation with an approximation and his fourth-order yield function are used, as well as the conventional J₂-flow theory. Several numerical examples are made with the aid of a newly developed computer program in which isoparametric finite elements are used in order to conserve the continuity of the displacement and the slope across the element boundaries.

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In this paper, a set of inelastic constitutive equations of poly-crystalline metals is derived by combining finite deformation kinematics of a single crystal component and the shear stress-shear strain relation of a slip system based on a thermo-activated motions of dislocations. The interactions among grains are incorporated by "deformation gradient constant assumption". The equations are rather simple internal variable theory type. By using these equations, some fundamental effects of grain rotations on the inelastic behaviors of polycrystalline metals in a finite deformation range are clarified under complex loading and elevated temperature conditions. Some comments are made on the problem of plastic spin tensor.

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The practical possibility of twin-roll-type continuous casting for the manufacturing of metal sheet was examined experimentally with model metals of Sn-15% Pb, Sn-37% Pb and U-ALLOY. The temperatures in the molten metal and solidified shell were measured with an original measuring tool which used 40 thermocouples. Six representative types of casting and strips were observed in which good surface strips and breakouts were included. It was shown, in conclusion, that good strips could be formed by twin-roll continuous casting.

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A numerical algorithm for the two-dimensional solidification problem in the twin-roll-type continuous casting system was presented in this paper. Attention was focused on the elucidation of heat transfer and flow characteristics in both the liquid and solid phases. The bounday fixing method (BFM) was adopted to handle the moving boundary and the resultant transformed governing equations for the solid and liquid regions were solved separately by using the usual explicit-type finite difference scheme. The mathematical model presented covers a wide range of casting parameters since the two-dimensional transport in both phases was taken into account. Another objective was to provide design parameters for maintaining a continuous casting process, such as the roll speed, the roll spacing, the initial temperature of molten material, and the solidification profile with special attention given to the end point of solidification.

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In this study, a collision-induced vibration machine is produced by way of trial, and its performance is examined by the experiment. The experiment is carried out to investigate the response of a cantilever beam attached to a concentrated mass, which is built into the table of the collision-induced vibration machine and in which strain gauges are cemented. Simultaneously, a theoretical analysis is performed on the basis of the beam equation and a similar law for cantilever-beam models, which are made from different material and have different sizes, subjected to translational excitation at the base is theoretically induced. The validity of the similar law is experimentally confirmed as a result of the measurement of strain in the several cantilever-beam models mounted on the collision-induced vibration machine.

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The sensitivity function characteristics used in optimal design by successive approximation are presented to obtain the minimal weight shape of a two dimensional structure with the constraint of elemental maximum equivalent stress. The sensitivity based on the summation of strain energy in the structure is presented to minimize the maximum equivalent stress or the weight of the structure. The values of the components of the sensitivity for the strain energy are easily obtained using the method to precalculate the surface displacements. The values of the components of the energy coincided well with those of the equivalent stresses in the examples of the initial shape and the shape in the midst of the optimization. The optimal shapes of two dimensional structures are acquired using the sensitivities, which can be developed to plate beam and truss structures.

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