Welding in the World

, Volume 62, Issue 5, pp 905–912 | Cite as

Application of the stochastic finite element method in welding simulation

  • Zheng LiEmail author
  • Benjamin Launert
  • Hartmut Pasternak
Research Paper


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.


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



Kronecker symbol


primitive randomness


i-th eigenvalue


Lagrange multiplier


mean value


i-th random variable

ρHH(X1, X2)

correlation function


standard deviation


i-th eigenfunction


j-th basic eigenfunction

(Ω, F, P)

probability space


K-L expansion matrices

CHH(X1, X2)

covariance function


statistics moments



H(X, θ)

random field


mapping coefficient matrix


correlation length


truncation order


position vector


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Copyright information

© International Institute of Welding 2018

Authors and Affiliations

  1. 1.Brandenburg University of TechnologyCottbusGermany

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