The MAL (Method of Arbitrary Lines) is a technique of reducing a partial differential equation to a system of ordinary differential equations. It is known that relevant use of this procedure yields high accuracy in some problems of two-dimensional elasticity and elastoplasticity. Since the basic concept of MAL is simple and based on generality, it is expected that many problems in other fields will be effectively solvable by this method. In this study, we consider the application of MAL to 3D (three-dimensional) elasticity analysis. We first give a MAL formulation of 3D elasticity problems, and demonstrate its effectiveness and accuracy for a typical problem. The reported numerical results are compared with the exact solution or that of the finite element method (FEM).
A new hybrid genetic algorithm (GA) and a parallel genetic algorithm are proposed in this paper in order to improve the convergence of structural optimization. The fully stressed design, FSD, method and a GA were incorporated into the hybrid GA. In the parallel GA, the “island model” was applied to reduce the computation time. Stress analyses were carried out with a commercial FEM code to obtain the optimum solution with high reliability even in a complex model. As a result of the axi-symmetric shell model, the optimum solution by using the proposed hybrid GA was 50% lighter than that by using simple GA. Furthermore, the computation time using the parallel GA with 10 processors was reduced by up to 1/7 of the time using one processor. These methods were then used to optimize the thickness of a three-dimensional shell model of a CRT. As a result of the application, the weight of the optimum model was 25% lighter than that of the reference model.
A high-performance domain decomposition method (MVDDM) is proposed for the parallel finite element analysis using meshless virtual nodes along the domain interface. The domains, which are analyzed independently in parallel by the finite element method, are connected by the virtual nodes based on the moving least squares method. The conjugate gradient method is applied to the virtual nodes to obtain the solution on the domain interface. To verify this method, various two-dimensional problems are solved. The accuracy of the solutions are good enough for practical use, and the convergence of the conjugate gradient method and the parallel performance are improved with fewer virtual nodes. This method can be applied to the problem with non-conforming interface among domains. This method can also accelerate the convergence of the CG method.
In the present work, the relationship between structural and hardness properties of Al thin film sputtered on Si substrate were investigated by a molecular dynamics (MD) method. Stress and packing ratio were investigated in the relation to porosity, both of which reflect sputtering conditions. Generally, higher compressive applied stress resulted in higher hardness. The influence of porosity on hardness was clarified using a model that had pores introduced randomly to the film. It was revealed that hardness of films increased with increasing packing ratio. Although stress in the film was affected by pore size, hardness was little influence by it. Simulated results well corresponded to the experimental observation that hardness increased with decreasing porosity. When a pore distribution existed in the thickness direction, it was suggested that pores decreased their influence on hardness with increasing distance from the surface.
Elevated temperature structural design codes pay attention to strain concentration at structural discontinuities due to creep and plasticity, since it causes an increase in creep-fatigue damage of materials. One of the difficulties in predicting strain concentration is its dependence on the magnitude of loading, the constitutive equations, and the duration of loading. In this study, the author investigated the fundamental mechanism of strain concentration and its main factors. The results revealed that strain concentration is caused by strain redistribution between elastic and inelastic regions, which can be quantified by the characteristics of structural compliance. The characteristics of structural compliance are controlled by elastic region in structures and are insensitive to constitutive equations. It means that inelastic analysis can be easily applied to obtain compliance characteristics. By utilizing this fact, a simplified inelastic analysis method was proposed based on the characteristics of compliance change for the prediction of strain concentration.
Functionally Graded Material (FGM) is a heterogeneous composite material that consists of a gradient compositional variation of the constituent materials from one surface of the material to the other. These continuous changes result in gradient material properties. Since ceramic has good heat resistance and metal has high strength, FGM made by ceramic and metal can work at super high temperatures or under a high-temperature-difference field. It is a primary to reduce thermal stress by selection of different effective material properties for the intermediate composition of the EGM and to prevent destruction by thermal stress. FGM is manufactured at a high temperature and then residual thermal stresses are produced during cooling to room temperature. In this paper, the elastic-plastic thermal stresses induced in a ceramic-metal FGM plate (FGP) taking the fabrication process into consideration are discussed. The region near the heat resistant surface is produced by metal particle reinforced ceramic while the region near the cooling surface is vice versa. As the metal and the ceramic near the middle region of the FGM are perfectly mixed, it is impossible to consider the particle-reinforced material. In this study, the FGP is divided into three regions. First, the region near the cooling surface is metal rich and then the metal is considered as a matrix while the ceramic is considered as particles. Second, the region near the heat resistant surface is ceramic rich so that the ceramic is considered as a matrix while the metal is considered as particles. Third, in the middle part between the previous two regions the metal and ceramic are perfectly mixed. In the third region macroscopic analysis is considered because the difference between the volume fractions of the ceramic and the metal is small and it is difficult to consider one of them as a matrix or particles. The effects of the distribution parameter of the composition and the fabrication temperature on the thermal stress variations are discussed.
If a beam is subjected to impact load or distributed load locally, the height of the cross section in the beam directly under the load is deformed. In order to estimate accurately the deformation of the cross section height and the transversely normal and shear stress components, a consistent higher order deformation theory of orthotropic beams is proposed. In order to verify the validity and effectiveness of the proposed theory, the analytical solution of a simple cantilevered beam problem is obtained and compared with the existed elastic solution. It is found that the displacement and stress components are identical to the corresponding solution of the Airy stress function in elasticity theory, and the deformation of the cross section height and the transversely normal stress are also estimated reasonably.
A laser speckle biaxial strain gauge was developed to measure local strains, εy, εz, at notch roots. Measurements were made on single edge-notched type 304 stainless specimens under fully reversed cyclic loading at both 673 K and room temperature. The strain ranges, Δεy, Δεz, and a ratio of those, φ=Δεz/Δεy, were discussed in terms of a proposed notch root deformation constraint parameter which consisted of a notch root radius, a thickness of the plate and a nominal stress level. It was found that the biaxial strain ratio, φ, was uniquely correlated with the proposed parameter for all the tested notches. It was also found that no change in the notch root strain range during the whole fatigue life was observed for the limited condition in which the constraint parameter took a sufficiently large value. Furthermore, the verification of Neuber’s rule in terms of the measured strain was discussed.
The speed of sound in conventional linear elasticity is determined only by the elastic modulus and the density of the medium. In actuality, however, the speed of sound depends on the stress and this dependency becomes nonlinear as the stress increases. This paper explains such phenomena by introducing the nonlinear elastic modulus. Additionally, the relationship between nonlinear elastic modulus up to the fourth-order and the internal stress is discussed through computer simulations and experiments for an aluminum specimen. In the simulation, it is shown that the third-order elastic constant contributes to the slope of the sound speed vs stress curve and the fourth-order one determines the curvature. Experimental results shows good agreement with the expected result and the ratio of third- and fourth-order elastic constants present significant changes in magnitude and with sign inversion after the internal stress, becomes larger than the yielding stress. These results show that the measurement of nonlinear elastic constants may enable internal stress evaluation.
In recent years, the fact that the nonlinear acoustic effect has a strong correlation to the microdeformation of materials has been considered to be useful for non-destructive evaluation (NDE) of material degradation. However, in the past, most research considered only the case in which the material degradation was distributed evenly along the path of the probing wave. In contrast, in this study, the nonlinear behavior of ultrasonic waves in a partially degraded material is considered. For this purpose, the finite difference method (FDM) model for the nonlinear wave equation is developed considering only 1-D longitudinal wave motion and the contribution of the partial degradation in the material to the measurable nonlinear parameter is analyzed quantitatively. In the simulation, three types of distribution of degradation are considered; single point, discrete distribution and continuous distribution. Simulation results reveal that the degradation level and the range of degradation have a strong correlation with the nonlinear parameter β which is estimated by measuring the harmonic generation. In order to verify the validity of this numerical analysis method, the simulation results in the case of continuous distribution of degradation are compared with the previous experimental results, and they are found to show a similar tendency.
The resonance frequency of a micro-cantilever employed in atomic force microscopy (AFM) is expected to be a measure of tip-sample contact stiffness representing the elastic properties of a sample. Quantitative evaluation of the elastic properties from measurements of resonance frequency is difficult, however, because contact stiffness is influenced by adhesion energy as well as elastic properties. In this study, we propose a new method of evaluating these properties quantitatively from the nonlinear response of AFM cantilever vibrations. The nonlinear vibrations are easily excited due to the non-linearity in the tip-sample interaction. To simplify the formulas derived for evaluation of contact stiffness and adhesion, we focus on the case of perfect contact, where the tip is always in contact with the sample surface. The elastic properties and the adhesion energy are separated by finding the optimal set of values which minimizes the difference between the theoretical and empirical relationship of resonance frequency versus amplitude.
In order to characterize the “Repeating-division type” and the “Island-delamination type” cracking patterns which are often observed in a brittle coating on a ductile substrate undr increasing biaxial tensile stress, computer simulations of the cracking processes were performed for the cermet or the ceramic coating which was thermally sprayed on the substrate of a low carbon steel. The simulation was carried out using the Monte Carlo method and the analytical equations which express the relationships among crack size, tensile stress, strain, thickness and material constants of the coating and substrate. In the simulation, many cracks which have been nucleated randomly on the coating grow to either of the above cracking patterns depending on the relative strength of the coating and interface. The simulated cracking patterns agree well with those observed in bulge experiments.
This paper deals with the influence of debonding damage between particles and matrix on a crack-tip field in a glass-particle-reinforced nylon 66 composite. In order to explain the influence of debonding damage on the fracture toughness, numerical analysis of a crack-tip field was carried out on the interface-treated and untreated composites by using a finite element method developed on the basis of an incremental damage theory of particle-reinforced composites. At the crack-tip region, the damage zone due to the particle-matrix interfacial debonding develops in addition to the plastic zone due to matrix plasticity. The damage development around a crack-tip depends on the interfacial strength between particle and matrix and the particle volume fraction. It is found that the debonding damage reduces the stress level around a crack-tip and acts as the toughening mechanism. The mechanical performance of particle-reinforced composites is obtained as a result of the competitive effects of the intact hard particles and the debonding damage.
A pair of integral equations are derived for a non-uniformly pressurized vertical planar crack of arbitrary shape in a fluid-saturated, poroelastic, infinite space of transversely isotropic permeability with its anisotropy axis perpendicular to the crack surface, by using the fundamental solutions obtained in a previous paper and the concept of a dislocation segment. This anisotropy assumption is more realistic for many oil reservoirs. The equations obtained relate normal tractions and fluid pressure on the crack faces to crack opening gradients and fluid injection rate per unit fracture area nad include the known integral equations for an isotropic permeability as a limiting case. These integral equations are intended to be implanted in a 3D hydraulic fracturing simulator.
Dynamic crack propagation and unloading behaviors of epoxy and PMMA were studied using the method of caustics. Single-edge-cracked tensile specimens were pin-loaded so that cracks could undergo both the acceleration and the deceleration process in one fracture event. The effect of loading position H1 was examined by measuring the stress intensity factor KID, crack velocity a and load P as a function of time t. Unloading rate P, time derivative of P, was also evaluated to examine correlation with the time variations of KID and a. The results showed that H1 was an important factor in the change of behaviors of KID, a, P and P.