Stochastic Finite Element Method for Nonlinear Beam

摘要

Stochastic finite element method is applied on nonlinear beam bending analysis. The influence of the randomness on the beam response is explained through the concept of variability response function based on the weighted integral method. This concept is extended to the nonlinear beam element with random flexibility. The material and geometric characteristics of the beam, elastic modulus and moment of inertia, are used to express beam flexibility. The beam flexibility is considered to be one-dimensional, homogenous, stochastic field. The stiffness matrix is expressed as sum of elastic and geometric stifness matrix. The stochastic element stiffness matrix is represented as linear combination of deterministic element stiffness matrix and random variables (weighted integrals) with zero-mean property. The concept of the variability response function is used to compute upper bounds of the response variability. The expectation and the coefficient of variation (variance) of the stochastic beam flexibility are used as input quantities for description of the random variables. The response variability is calculated using the first-order Taylor expansion approximation of the variability response function. The randomness of the beam response (deflection) is expressed as the function of the randomness of the flexibility.