Nonlinear finite element analysis with applications to laser forming and welding

Laser forming is an emerging manufacturing technology which can be used to form parts to a complex shape efficiently and effectively. Researchers have been trying to develop a systematic methodology for determining the heating pattern to form a final desired shape by laser forming. However, due to the complexity of the characteristic behaviors of laser forming, no such methodology has been developed yet. Therefore, the application of laser forming to industry is very limited.; The systematic methodology of laser forming includes two tasks: (1) Develop an efficient model to accurately predict the final shape for the given forming parameters. For a multi-scan laser forming process, this task requires nonlinear large deformation analysis to consider the significant effect of change in geometry caused by each scan. (2) Develop an algorithm to optimize the heating pattern to form a shape close to the required sphere shape. Sensitivity analysis and numerical optimization can be applied to solve this problem.; Finite element modeling of laser forming plays a fundamental role in developing such the systematic methodology of laser forming. In this thesis, the following computational work has been completed. (1) Based on the investigation of the effectiveness and requirements of Lagrangian and Eulerian finite element models for laser forming process, an efficient 3D Lagrangian model for a single scan has been developed. The material nonlinearities such as the temperature or history dependent material properties are considered in the model to accurately simulate the weakly coupled thermo-elasto-plastic process. (2) Large deformation formulations for elastic process has been implemented to capture the geometrical nonlinearity due to the large displacements or strains of a part. In a multi-scan problem, each scan will cause a significant change in the geometry of the part (curvature effect). This curvature effect can not be neglected for the multi-scans problem. (3) The sensitivity formulations for large deformation analysis based on the Total Lagrangian method has been presented. The sensitivities of the shape with respect to the design parameters are calculated analytically, which can be used for optimization problem of laser forming. (4) A 3D to 3D decoupled applied plastic strain method has been developed and evaluated by analyzing the welding distortion of a large and complex multi-welded structure. The numerical results show that decoupled plastic strain method is only qualitatively accurate for modeling angular distortion in large welded structures. (5) An optimization algorithm based on decoupled strain analysis has been developed to determine suitable forming parameters for forming a desired shape.