Stochastic meshfree method for elastic buckling analysis of columns

- A meshfree based numerical tool is developed for stochastic eigenvalue analysis of columns.
- Statistics of critical buckling loads are calculated using perturbation method and compared with those obtained from Monte Carlo Simulation.
- The solution and the computational time are compared with that of stochastic FEM.
- Robustness of the proposed stochastic meshfree eigenvalue analysis is shown.

This paper proposes a probabilistic approach for the solution of elastic buckling of columns, involving uncertainties, using stochastic element free Galerkin method. In the present work, modulus of elasticity is modeled as a homogeneous random field. Karhunen-Loeve expansion and shape function method are used to represent random field and their effectiveness is compared in modeling the same in a computationally viable manner. Both Gaussian and non-Gaussian field are considered for the present study. The stochastic eigenvalue problem is solved for first and second moment characteristics of buckling load, using perturbation analysis. Numerical examples of columns with different boundary conditions are solved. Monte Carlo simulation is used as a validation tool. The obtained results are found in good agreement with those obtained by Monte Carlo simulation.