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Fokker-Planck linearization for non-Gaussian stochastic elastoplastic finite elements

  • Author(s): Karapiperis, K
  • Sett, K
  • Levent Kavvas, M
  • Jeremić, B
  • et al.
Abstract

© 2016 Elsevier B.V. Presented here is a finite element framework for the solution of stochastic elastoplastic boundary value problems with non-Gaussian parametric uncertainty. The framework relies upon a stochastic Galerkin formulation, where the stiffness random field is decomposed using a multidimensional polynomial chaos expansion. At the constitutive level, a Fokker-Planck-Kolmogorov (FPK) plasticity framework is utilized, under the assumption of small strain kinematics. A linearization procedure is developed that serves to update the polynomial chaos coefficients of the expanded random stiffness in the elastoplastic regime, leading to a nonlinear least-squares optimization problem. The proposed framework is illustrated in a static shear beam example of elastic-perfectly plastic as well as isotropic hardening material.

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