A simple and efficient stochastic meshfree method for linear eigenvalue problems in structural mechanics. (April 2022) - M., Aswathy; C.O., Arun
Abstract: A novel and simple stochastic meshfree method is proposed in the present study for the stochastic eigenvalue analysis of problems in structural mechanics. Young's modulus is modelled as homogeneous random field. Both truncated normal and lognormal distribution characteristics are used. The current work proposes to use Monte Carlo simulation (MCS) on a modified system of equations. Here, the stochastic stiffness matrix is approximated using Taylor series expansion as in perturbation methods. However, the method does not make any approximations for eigensolutions, which are also unknown functions of random variables. This enables the numerical integration of stiffness matrix and its derivatives outside the simulation loop. Unlike the direct MCS on system of equations, this simple but previously unexplored modification proposed, can result in accurate and more efficient evaluation of stochastic eigensolutions. A few numerical examples are solved using the proposed method; buckling of columns, buckling of thin plates and free vibration of beams. The probabilistic characteristics evaluated using the proposed method are found to be matching well with those obtained from direct MCS. Highlights: A simple and efficient stochastic meshfree method is proposed for linear eigenvalue problems in structural mechanics. The proposed method uses Monte Carlo simulation on a modified system of equations. An approximation using Taylor series expansion is used only for stiffness matrix. The full probabilistic characteristics of solutions of eigenvalue problem are captured. The simple modification reduces the computational time by around 50% compared to direct Monte Carlo simulation of system of equations, without loss of accuracy.