P. Michaleris

Design sensitivity analysis: Overview and review

Design sensitivity plays a critical role in inverse and identification studies, as well as numerical optimization, and reliability analysis. Herein, we review the state of design sensitivity analysis as it applies to linear elliptic systems. Both first- and second-order sensitivities are derived as well as first-order sensitivities for symmetric positive definite eigenvalue systems. Although these results are not new, some of the derivations offer a different perspective than those previously presented. This article is meant as a tutorial, and as such, a simple two-degree-of-freedom spring system is employed to exemplify the sensitivity analyses. However, the concepts presented in this trivial example may be readily extended to compute sensitivities for complex systems via numerical techniques such as the finite element, boundary element, and finite difference methods.

Residual stress and distortion modeling of electron beam direct manufacturing Ti-6Al-4V:

In this work, a finite element model is developed for predicting the thermo-mechanical response of Ti-6Al-4V during electron beam deposition. A three-dimensional thermo-elasto-plastic analysis is performed to model distortion and residual stress in the workpiece and experimental in situ temperature, and distortion measurements are performed during the deposition of a single-bead-wide, 16-layer-high wall built for model validation. Post-process blind hole–drilling residual stress measurements are also performed. Both the in situ distortion and post-process residual stress measurements suggest that stress relaxation occurs during the deposition of Ti-6Al-4V. A method of accounting for such stress relaxation in thermo-elasto-plastic simulations is proposed where both stress and plastic strain are reset to 0, when the temperature exceeds a prescribed stress relaxation temperature. Inverse simulation is used to determine the values of the absorption efficiency and the emissivity of electron beam–deposited, wire-fed Ti-6Al-4V, as well as the appropriate stress relaxation temperature.

Mitigation of welding induced buckling distortion using transient thermal tensioning

Abstract Welding induces residual stresses in structures and may cause buckling distortion if the stresses exceed the critical buckling stress of the structure. Reducing the welding heat input or increasing the structural stiffness reduces or eliminates buckling distortion. However, where, because of the design constraints, structure geometry and weld size are fixed, the transient thermal tensioning process is effective in reducing buckling distortion. An experimental verification and demonstration of transient thermal tensioning for minimising welding induced buckling distortion is presented. Conventional welding was carried out to demonstrate buckling distortion and establish a baseline case. Buckling distortion was eliminated using transient thermal tensioning during welding under the same welding conditions. After buckling distortion was eliminated, angular distortion became evident, which was eliminated using mechanical restraints alongside transient thermal tensioning. Residual stress measurements were obtained using the blind hole drilling method and a comparison of residual stresses for the baseline panel and for the panel with transient thermal tensioning is presented.

Investigation of Lagrangian and Eulerian finite element methods for modeling the laser forming process

Laser forming is an effective and efficient manufacturing technology. Both Eulerian and Lagrangian approaches can be applied on modeling the laser forming process. In this paper, 3D Eulerian and Lagrangian finite element models of various lengths are created for simulation. The results of Lagrangian approach are in good agreement with the experimental results reported by Kyrsanidy (J. Mater. Process. Technol. 87 (1999) 281.) Results of models with various lengths, indicate that the specimen length has significant effect on the angular deformation of the plate in the laser forming process. The Eulerian approach is nearly 2 orders of magnitude faster than the Lagrangian approach, especially for long parts, which are common in the real production. However, the angular deformation is over predicted using Eulerian approach and further development is needed.

Prediction of buckling distortion of welded structures

Abstract A predictive distortion analysis approach for welded structures is presented. Two-dimensional thermomechanical welding process simulations were performed to determine the residual stress. The critical buckling stress and the buckling mode are computed in a three-dimensional eigenvalue analysis. A technique employing decoupled two- and three-dimensional approaches is used to predict the occurrence of buckling distortion. Experimental validation of the prediction has been carried out in the laboratory. Welding experiments were carried out using welding conditions identical to those in the finite element model. The computational results are then verified by experimental observations.

Evaluation of 2D, 3D and applied plastic strain methods for predicting buckling welding distortion and residual stress

Abstract Welding induces residual stresses which in thin section structures may cause buckling distortion. The magnitude of longitudinal residual stress is critical in the prediction of buckling distortion, which affects numerous welding applications in the ship building, railroad and other industries. The objectives of this paper are to overview and evaluate modelling procedures for bucking distortion. Moving source two-dimensional (2D), three-dimensional (3D) small deformation, 3D large deformation, and 2D–3D applied plastic strain analyses are evaluated by comparing computed residual stress and distortion against experimental measurements. Guidelines for modelling welding distortion are developed along with an assessment of the efficiency and limitations of the various analysis methods.

Optimization of thermal processes using an Eulerian formulation and application in laser surface hardening

A systematic design approach has been developed for thermal processes combining the nite element method, design sensitivity analysis and optimization. Conductive heat transfer is solved in an Eulerian formulation, where the heat ux is xed in space and the material ows through a control volume. For constant velocity and heat ux distribution, the Eulerian formulation reduces to a steady-state problem, whereas the Lagrangian formulation remains transient. The reduction to a steady-state problem drastically improves the computational e ciency. Streamline Upwinding Petrov–Galerkin stabilization is employed to suppress the spurious oscillations. Design sensitivities of the temperature eld are computed using both the direct di erentiation and the adjoint methods. The systematic approach is applied in optimizing the laser surfacing process, where a moving laser beam heats the surface of a plate, and hardening is achieved by rapid cooling due to the heat transfer below the surface. The optimization objective is to maximize the rate of surface hardening. Constraints are introduced on the computed temperature and temperature rate elds to ensure that phase transformations are activated and that melting does not occur. Copyright ? 2000 John Wiley & Sons, Ltd.

Sensitivity analysis of the thermomechanical response of welded joints

A computational procedure is presented for evaluating the sensitivity coefficients of the thermomechanical response of welded structures. Uncoupled thermomechanical analysis, with transient thermal analysis and quasi-static mechanical analysis, is performed. A rate independent, small deformation thermo-elasto-plastic material model with temperature-dependent material properties is adopted in the study. The temperature field is assumed to be independent of the stresses and strains. The heat transfer equations emanating from a finite element semi-discretization are integrated using an implicit backward difference scheme to generate the time history of the temperatures. The mechanical response during welding is then calculated by solving a generalized plane strain problem. First- and second-order sensitivity coefficients of the thermal and mechanical response quantities (derivatives with respect to various thermomechanical parameters) are evaluated using a direct differentiation approach in conjunction with an automatic differentiation software facility. Numerical results are presented for a double fillet conventional welding of a stiffener and a base plate made of stainless steel AL-6XN material. Time histories of the response and sensitivity coefficients, and their spatial distributions at selected times are presented.

Modelling welding residual stress and distortion: current and future research trends

Abstract Modelling of welding distortion and residual stress has been an active research area since the late 1970s. Significant progress has been achieved since, especially in the areas of material modelling and investigation of three-dimensional geometries. This paper discusses some of the more recent developments in modelling residual stress and distortion and suggests issues for further research. The topics include, consideration of thermal transport in residual stress and distortion modelling, the development of applied strain methods for very large and complex structures, modelling of friction stir welding, sensitivity analysis and adaptive meshing.

Evaluation of Applied Plastic Strain Methods for Welding Distortion Prediction

Large and complex structures such as ship panels generally have various types of welding-induced distortions including angular deformation, longitudinal bending, and buckling. Developing efficient methodologies for modeling welding distortions and residual stresses of large structures plays a critical role in industrial applications. Conventional transient moving source analyses on three-dimensional (3D) finite element models, where millions of degrees of freedom and thousands of time increments are involved, demonstrate the capability to capture all types of welding distortions, but proved to be computational costly. The 2D to 3D applied plastic strain method, where only longitudinal plastic strain resulting from 2D models is mapped to a 3D structural model, successfully predicts buckling and bowing distortions. However, it cannot calculate angular distortion accurately. In this paper, a 3D applied plastic strain method has been developed to predict the welding distortions for structures. In the applied strain method, six components of the plastic strain of each weld are calculated by performing a 3D moving source analysis on a small 3D model with a shorter length, then the plastic strain components of the small models are mapped and superposed to a large 3D structural model to obtain the final distortion results. An interpolation algorithm is developed for mapping between meshes with different densities. The effectiveness of the 3D applied plastic strain method is evaluated by comparing to the distortion results from 3D moving source simulations. The mapping algorithm is verified and the effects of the model size on the distortion results are investigated. The numerical results show that the applied plastic strain method accounts all distortion modes, but is only qualitatively accurate for the prediction of angular distortion.