This paper discusses evaluation of influence of microscopic uncertainty on a homogenized macroscopic elastic property of an inhomogeneous material. In order to analyze the influence, the perturbation-based homogenization method is used. A higher order perturbation-based analysis method for investigating stochastic characteristics of a homogenized elastic tensor and an equivalent elastic property of a composite material is formulated.As a numerical example, macroscopic stochastic characteristics such as an expected value or variance, which is caused by microscopic uncertainty in material properties, of a homogenized elastic tensor and homogenized equivalent elastic property of unidirectional fiber reinforced plastic are investigated. The macroscopic stochastic variation caused by microscopic uncertainty in component materials such as Young's modulus or Poisson's ratio variation is evaluated using the perturbation-based homogenization method. The numerical results are compared with the results of the Monte-Carlo simulation, validity, effectiveness and a limitation of the perturbation-based homogenization method is investigated. With comparing the results using the first-order perturbation-based method, effectiveness of a higher order perturbation is also investigated.
Summary. Transient temperature, displacement, stress and electric field intensities in a finite circular piezothermoelastic disk undergoing axisymmetric surface beating are examined. Exact solutions to the equations of equilibrium and electrostatics are obtained using a potential function approach based upon two piezothermoelastic potential functions, three piezoelastic potential functions and a piezoelectric potential function. The disk under consideration is assumed to exhibit hexagonal material symmetry of class 6 mm. The initial temperature of the disk is zero; thereafter one face is subjected to linear heat transfer from an adjacent medium (Newton's law of cooling), while the temperature of the other face remains constant. Both faces are taken to be free of traction. The cylindrical boundary of the disk is thermally insulated, electrically charge-free, and constrained against radial deformation. Numerical results are obtained for the stress and the electric potential distributions in a cadmium selenide disk.
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