Estimation of residuals for the homogenized solution: The case of the beam with random Young's modulus

In this paper the estimation of residuals for the homogenized solution in elastic problem is taken into account. The case of the beam with Young's modulus randomly varying along the axis is considered. The analysis is performed by means of numerical simulation which is validated by comparison with particular solutions reported in the literature. The convergence to the homogenized solution and the behavior of the residuals are studied in terms of the parameter ɛ, which represents the ratio between the microscopic and the macroscopic scale. After validation with the literature results, the procedure is used to analyze the influence on the convergence of the correlation law of Young's modulus with log-normal distribution. Moreover the particular case of the two-phase beam is considered. The effect of different boundary conditions is also investigated.