Stochastic small perturbation based simulation technique for solving isotropic elastostatics equations. (English) Zbl 1326.74131
Summary: The paper deals with a stochastic analysis of random displacements governed by isotropic elasticity equations. The elasticity constants are assumed to be random fields with Gaussian distribution. Under the assumption of small fluctuations of elasticity constants but not ignoring their distribution and correlation structure, we derive the spectral tensor of the random displacement field. A randomized spectral representation is then used to simulate this random field numerically. The same approach was applied to the case of random loading. In this case, the intensity of fluctuations may be arbitrarily large. A series of test calculations confirm the high accuracy and computational efficiency of the method.
MSC:
74S60 | Stochastic and other probabilistic methods applied to problems in solid mechanics |
65C05 | Monte Carlo methods |
65N75 | Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs |
81U40 | Inverse scattering problems in quantum theory |
35J57 | Boundary value problems for second-order elliptic systems |
35Q74 | PDEs in connection with mechanics of deformable solids |