材料特性のランダム性を考慮した二, 三の有限要素解析

抄録

This paper describes the application of the finite element analysis to some nonhomogeneous materials of simple structures with some distribution in elastic properties, such as Young's modulus, Poisson's ratio and principal directions of elasticity, by employing a stochastical simulation. It is well-known from the extensive laboratory tests that the properties of soil and rock show some kind of distributions. In this study, the variations of stress and deformation in the plate with a circular hole, the rectangular plate subjected to an uniaxial uniform load and the semi-infinite plate subjected to a concentrated load were analyzed on the assumption that the values of the above elastic constants varied randomly from one element to another according to the normal distribution function. The elastic constants for each element were generated by a random process using a probabilistic Monte-Carlo simulation.
It has been found that the finite element analysis based on the randomized material constants for each element gives the mean values of stress and displacement which are not significantly different from those based on the fixed elastic constants, and yields a better prediction of a real structure. Thus, the safety factor used in the design of a structure can be estimated more adequately by considering the variations of stresses and displacements obtained by this process.