Implementation of Stochastic Processing Parameters in a General Finite Element Analysis of a Laser Welding Process

Abstract

The deterministic nature of finite element method for computational analysis is limited in describing the behaviour of actual processes which normally have certain degrees of uncertainties and deviations. Nevertheless, uncertainty factors can be incorporated into an FEM analysis using statistical approach to closely simulate real-life operating conditions. However, integrating stochastic parameters into commercial finite element solvers can be problematic, requiring the need for suitable interfacing using customized subroutine codes and implementation strategies. In this paper, a Monte Carlo approach was proposed for the incorporation of stochastic input parameter in a finite element analysis simulation of a laser welding process. A linear congruential generator together with a Box-Muller algorithm were used to generate normally distributed random numbers. The algorithms, written in Fortran77, was verified to be able to generate a gaussian distribution for 100, 1000, and 10,000 random numbers. The algorithms were then integrated into a user subroutine in MSC MARC/Mentat for the generation of variable laser power input values. A butt-welding simulation was executed using stochastic laser power input of, P having a mean, µ = 300 W, and standard deviation, s = 10 W. A simulation with constant power input P= 300 W was also conducted for comparison. The results show that the stochastic input values resulted in a minor increase in the calculated surface temperature of the welded plates, which was probably due to the increased laser power at several time steps in the simulation. The findings and methods in this work can serve as a guideline for the incorporation of stochastic parameter inputs into finite element analysis simulation.