Stress intensity factors in cracked bodies have been calculated by various calculation methods. Especially, the typical conventional method ; i. e., stress extrapolation method or displacement extrapolation method has an important advantage, namely convenience. But the accuracy of stress intensity factor by the methods is not so high because of error due to high order terms. In this paper, errors of stress intensity factors by the stress extrapolation method and the displacement extrapolation were investigated on a mixture mode-type crack model in an infinite plate. Finally, an improved technique called V-line extrapolation method is proposed to decrease the curvature of calculated extrapolation data, therefore higher accuracy can be obtained.
Failure lives of notched components in multiaxial fatigue were statistically estimated by Monte Carlo simulations for materials with different microstructures using a proposed crack growth model. An analytical algorithm for crack growth in a microstructure, which was modeled as an aggregate of hexagons, was based on competition between two possible growth modes. In simulations, various microstructure configurations, which resulted in distinct failure lives, were randomly generated for a material under consideration. Ranges of simulated life almost coincided with experimental results observed in four kinds of materials. The coefficient of variation and the shape parameter in the fitted two-parameter Weibull distribution function for the simulated life distribution were investigated to clarify statistical properties of the failure life in multiaxial fatigue. The life dispersion was found to be larger under a loading mode with a higher proportion of shear stress component and/or in a material with coarser grains.
It has been accepted not only that effective proof testing of ceramic materials demands rapid loading and unloading to prevent strength degradation but also that especially rapid unloading results in a truncation strength of σp (the stress just before very rapid unloading). Such an accepted interpretation in proof testings as above has been rechecked from an analytical point of view. The analysis reveals that as the loading and unloading rates increase, weaker samples tend to survive more easily. As a consequence. the truncated strength is not characterized analytically, and the Weibull curve will not have asymptote. The present analytical results come to the conclusion that the established theory in proof testing can not be accepted from the physical point of view.
The "Statistical Design Support System" produces a new practical optimal design method. It can be used even on nonlinear behavior. The optimization can be done with this system using a small number of calculation results. Therefore, the effect is especially significant when applied to a problem that needs large-scale calculation. The authors applied it to the optimization of design parameters of the occupant restraint system, and have tried to reduce the injury criteria of occupants based on the crash simulation. According to the improvement of interest and technology on vehicle safety, many countries have declared new safety assessments that are more severe than used one. In order to meet them all, it will be needed to consider some different crash situations simultaneously when vehicle safety equipment is designed. The authors made optimal design with consideration of different conditions of collision. This paper draws attention to the effectivity analysis and optimization.
Genetic algorithm (GA) is one of the most useful methods to optimize topology of structures. The performance of GA, however, deeply depends upon a rule of coding from a structure to a string (a chromosome), which must be decided before the execution of GA. An improper coding can cause a lot of unanalyzable structures to be generated in the process of optimization, which are separated into several pieces with no supporting or loading points. In this paper, a method to give such unanalyzable structures a fitness value based upon their topology using homology theory is proposed to raise the probability of obtaining the optimum structures. As numerical examples, topology of two-dimensional frames and three-dimensional structures consisting of triangular elements supported on a rigid wall and loaded vertically on a point distant from the wall are optimized under a constraint of constant weight. As a result, it was found that the proposed method increased the average fitness value and the number of optimum structures obtained in 100 trials of GA in comparison with other methods that considered unanalyzable structures to be useless.
In the present study, each member of a framed structure is subdivided with two linear Timoshenko beam elements at both ends and a cubic beam element based on Bernoulli-Euler hypothesis at the center. The adaptively shifted integration (ASI) techinique is used only in the linear Timoshenko beam elements. The proposed model is applied to the explicit finite element analysis of the crashing behaviors of impulsively loaded framed structures considering the effect of large deformation by the updated Largrangian formulation. Several numerical studies have been carried out in order to show the validity of the proposed numerical technique.
In this work, a finite element sensitivity analysis method for thermal stress and creep problems is proposed. The method is characterized by the semi-analytical direct differentiation approach, i, e., the formulation is based on the direct differentiation but the variation of internal force due to the perturbation of design parameters is evaluated numerically. Since the corresponding subroutine of an existing finite element analysis code may be used, it is unnecessary to manipulate the adopted constitutive relation at the sensitivity analysis stage. Thus, the proposed method can be applied for various temperature-and time-dependent problems. The effectiveness of the method is examined through two numerical examples.
This study is concerned with a new adaptive boundary element method based on sample-point error analysis for thermoelasticity under steady-state heat conduction. Mathematical formulations of the adaptive boundary element method are presented in detail for two-dimensional thermoelasticity. This scheme of adaptive meshing makes use of only the residual between the interpolated and calculated solutions as an error indicator. Adaptive boundary element analysis can be performed by simultaneously checking the 'displacement error indicator' and the 'temperature error indicator'. The h-and p-version mesh refinements based on this scheme are applied to some typical examples, and the usefulness of the proposed adaptive BEM is demonstrated through discussion of the results obtained.
A new solution scheme to solve the bending problems of beams by the boundary element method has been developed. The main points of this study are : (1) to improve the composition of the simultaneous equations by introducing a new formulation process, (2) to establish an algorithm without any variable at intermediate points and (3) to establish a generalized solution scheme for an inhomogeneous beam. In this report we will describe (1) and (2). The matrix size as well as the computing time is greatly reduced owing to the new algorithms. therefore, high efficiency in repetitive calculations is obtained. Using the present solution scheme, a much more efficient system for optimal designs using such as the genetic algorithm will be realized to build.
In this study, an analytical method for deriving a system of equations for thermoelastic problems for a medium with nonhomogeneous material properties is developed. An analytical method of development for isothermal problems of such a nonhomogeneous body has already been given by Kassir under the assumption that the shear modulus of elasticity G changes with the variable z of the axial coordinate according to the relationship G(z)=G0zm. However, no analytical procedure has been established for the thermoelastic field up to data. In this study, an analytical method of developing the three-dimensional thermoelastic field is proposed by introducing the thermoelastic displacement potential function and two kinds of displacement functions. Assuming that the shear modulus of elasticity G, the thermal conductivity λ, and the coefficient of linear thermal expansion α vary with the variable ζ connected to the dimensionless axial coordinate according to the relationship G(ζ)=G0ζm, λ(ζ)=λ0ζι, α(ζ)=α0ζk, the three-dimensional temperature solution in the steady state for a thick plate is obtained and the associated thermal stress components are evaluated theoretically. Numerical calculations are carried out for several cases, taking into account the variation of nonhomogeneous material properties and the numerical results are graphically demonstrated.
The objective of this study is to achieve a detailed understanding of the macroscopic and microscopic elastoplastic deformation behavior of two-phase composites : W-Ni-Fe alloys. The constitutive relations of W-Ni-Fe alloy and its microconstituents were measured by the Hopkinson pressure bar testing and usual compression testing, and then the elastoplastic deformation behavior of W-Ni-Fe alloys in nuiaxialcompression was analyzed using the micromechanics-based analysis method. The main conclusions are summarized as follows ; (1) The work hardening tendency of W-Ni-Fe alloy is in keeping with that of pure tungsten particle phase that is B. C. C. metal. (2) Measured flow stresses of W-Ni-Fe alloy under high strain rate loading are smaller than analyzed ones, due to local failure in the matrix phase of W-Ni-Fe alloy. (3) The compressive residual stresses in the particle phase are produced at the cooling stage in sintering. (4) The micromechanics-based analysis method can precisely analyze the elastoplastic deformation behavior of two-phase composites untillarge deformation.