Welding in the World

, Volume 62, Issue 5, pp 905–912

# Application of the stochastic finite element method in welding simulation

Research Paper

## Abstract

Due to the uncertain microscopic structure of the material, the strength of the material exhibits strong randomness. This randomness results in uncertain response of the structure in the sequentially coupled thermal-mechanical analysis by welding simulation. Because of the limitations of deterministic welding simulation, the stochastic finite element method with random field will be introduced into the welding simulation, so that the welded structure can be more accurately calculated in the stability and reliability structural analysis. Particularly, it is necessary to propose reasonable distributions of residual stress from welding simulations based on statistical and reliability theories. This paper is intended to implement the stochastic finite element method in the welding simulation using a general-purpose simulation program and to demonstrate the potential of the proposed approach. Furthermore, the statistical distribution function of the welding simulation response is obtained by maximum entropy fitting method. Then, a numerical example is presented by the proposed method.

## Keywords

Stochastic finite element method Random field Maximum entropy fitting method Welding simulation Steel structures

## Nomenclature

δij

Kronecker symbol

θ

primitive randomness

λi

i-th eigenvalue

λn

Lagrange multiplier

μ(X)

mean value

ξi(θ)

i-th random variable

ρHH(X1, X2)

correlation function

σ2

standard deviation

φi(X)

i-th eigenfunction

ϕj(X)

j-th basic eigenfunction

(Ω, F, P)

probability space

Aij,Bij

K-L expansion matrices

CHH(X1, X2)

covariance function

E{ϕn(x)}

statistics moments

H

Entropy

H(X, θ)

random field

Je

mapping coefficient matrix

lD

correlation length

M

truncation order

X

position vector

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