Prediction of residual stresses in multi-pass welded joint using Idealized Explicit FEM accelerated by a GPU

doi:10.1016/j.commatsci.2014.06.024

Computational Materials Science

Volume 93, October 2014, Pages 62-67

https://doi.org/10.1016/j.commatsci.2014.06.024 Get rights and content

Highlights

•
We developed a new analysis method named Idealized Explicit FEM (IEFEM).
•
GPU parallelization was introduced to IEFEM to attain further efficient computation.
•
The analysis accuracy of IEFEM was almost the same as the existing method.
•
IEFEM can dramatically reduce computing time and memory compared to existing method.
•
3-D multi-pass welding problem was solved by IEFEM in practical computing time.

Abstract

In the simulation of welding problems, the simulation scale is usually limited to the welding joint level. To achieve a larger scale, the authors propose the Idealized Explicit Finite Element Method (IEFEM) for shorter computing time and lower memory consumption. In addition, the proposed IEFEM is parallelized by using a Graphics Processing Unit (GPU).

The usefulness and validity of the developed method are investigated by analyzing a simple T-joint welding problem. A three-dimensional multi-pass moving heat source problem, which is very difficult to analyze with commercial FEM software because of its analytical scale, is analyzed to show the applicability of IEFEM to the large-scale welding problem. As a result, it is found that the parallelized IEFEM accelerated by a GPU on a single PC can analyze a large-scale problem having over 1,000,000 DOFs.

Graphical abstract

Introduction

In recent years, due to the development of computer hardware and simulation software, numerical simulations have been widely utilized for the mechanical analysis of actual structures. In particular, the Finite Element Method (FEM) has been widely used in design and production. Many studies have simulated the mechanical phenomena of welding by thermal elastic plastic FE analyses [1], [2], [3], [4], [5]. However, the simulation scale of these welding analyses is still limited to simple weld joints. This is because welding is a strongly nonlinear and transient phenomenon accompanied by plastic deformation and melting of materials. To achieve accurate simulation of three-dimensional stress and deformation, it is necessary to use a Static Implicit FEM, which may consume enormous computing time and memories in analyzing large-scale problems. To achieve shorter computing time and less memory consumption, various methods have been proposed [6], [7], [8], [9]. However, they are based on Static Implicit FEM and remain difficult for analyzing large-scale problems dealing with actual structures due to the increased memory consumption needed to construct the global stiffness equation.

In contrast, a Dynamic Explicit FEM [10] is utilized to analyze short-term and dynamic problems dealing with such impact phenomena. In the Dynamic Explicit FEM, the analysis progresses by solving equations discretized for each degree of freedom (DOF). It is not necessary to solve the global stiffness equation constructed and solved in the Static Implicit FEM. Therefore, the Dynamic Explicit FEM makes it possible for calculation to run fast with low consumption of memories. In addition, in the Dynamic Explicit FEM, it is possible to progress the analysis by performing calculations for each DOF and each element independently. This characteristic is very suitable for parallelization. However, in Dynamic Explicit FEM, the time increment is limited to a very small value due to the Courant condition. So, it is difficult to directly apply the Dynamic Explicit FEM to welding problems.

Regarding parallelization, the Graphics Processing Unit (GPU) developed to synthesize real-time computer graphics can rapidly process a large number of simple calculations, such as coordinate transformation. Therefore, the GPU is now gaining keen interest as a fast and parallel processor capable of processing certain complex procedures. In addition, the GPU is mass produced as a generic and inexpensive computer component. A computing system using the GPU enables very fast calculation in much lower cost than those of supercomputer systems and PC clusters. Consequently, General Purpose GPU (GPGPU) technology, in which the computing capability of the GPU is utilized for scientific computations other than computer graphics, is currently developing [11], [12], [13].

In this paper, a new numerical method named Idealized Explicit FEM (IEFEM) is developed to analyze welding problems based on the Dynamic Explicit FEM. GPU parallelization is introduced to IEFEM to achieve faster computations. IEFEM is applied to a simple T-joint welding problem to investigate the validity and usefulness of IEFEM. Further, IEFEM is applied to a 3D multi-pass welding problem with a moving heat source to demonstrate the applicability of IEFEM to a large-scale problem having more than a million DOFs.

Section snippets

Development of IEFEM

In the Dynamic Explicit FEM, the time increment is limited to a very small value due to the Courant condition. Therefore, the number of time steps becomes enormous in the analysis of welding, which has very long duration from the beginning of heating to the completion of cooling and is very difficult to analyze in realistic computing time. The Static Implicit FEM, which is generally utilized in welding mechanical analyses, must solve the global stiffness equation, which is composed of large

Parallelization of IEFEM using a GPU

In this section, parallelization using a GPU is introduced to IEFEM. A GPU has hundreds or thousands of computing units inside and very high capability for numerical operations, in comparison with an ordinal Central Processing Unit (CPU). Now, the GPU is attracting attention as a numerical processor for scientific use, because it is possible to inexpensively construct a high performance computing environment compared to that by servers or workstations. Especially, graphics processing, the main

Evaluation of performance of IEFEM by applying it to T-joint welding problem

To investigate the analysis accuracy and other characteristics, IEFEM is applied to a T-joint welding problem.

Application of IEFEM to multi-pass welding problem

In the previous section, the accuracy and efficiency of the parallelized FEM are verified. In this section, the parallelized IEFEM is applied to a large-scale moving heat source problem with 1.3 million DOFs, 430,000 nodes and 33 welding passes. This problem is extremely difficult to analyze by commercial FEM code because of its computational scale.

Conclusions

In this study, an Idealized Explicit FEM (IEFEM) was developed to decrease the computing time and memory consumption of large-scale analyses, such as welding mechanics problems. Parallelization using GPU is introduced to IEFEM to achieve faster computation. IEFEM was first applied to a T-joint welding problem to verify its validity and effectiveness. IEFEM was then applied to a multi-pass welding problem to show its applicability to large-scale problems. The following results were obtained.

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Prediction of residual stresses in multi-pass welded joint using Idealized Explicit FEM accelerated by a GPU

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Development of IEFEM

Parallelization of IEFEM using a GPU

Evaluation of performance of IEFEM by applying it to T-joint welding problem

Application of IEFEM to multi-pass welding problem

Conclusions

Sci. Technol. Weld. Joining

Sci. Technol. Weld. Joining

Sci. Technol. Weld. Joining

Trans. Jpn. Weld. Soc.

J. Soc. Nav. Archit. Jpn.

J. Shanghai Jiaotong Univ. (Sci.)

ASME J. Eng. Ind.