Structural reliability optimization using an efficient safety index calculation procedure

The objective of this paper is to conduct reliability-based structural optimization in a multidisciplinary environment. An efficient reliability analysis is developed by expanding the limit functions in terms of intermediate design variables. The design constraints are approximated using multivariate splines in searching for the optimum. The reduction in computational cost realized in safety index calculation and optimization are demonstrated through several structural problems. This paper presents safety index computation, analytical sensitivity analysis of reliability constraints and optimization using truss, frame and plate examples.     

Multidisciplinary optimization of gas-quenching process

Distortion as a result of the quenching process is predominantly due to the thermal gradient and phase transformations within the component. Compared with traditional liquid quenching, the thermal boundary conditions during gas quenching are relatively simple to control. By adjusting the gas-quenching furnace pressure, the flow speed, or the spray nozzle configuration, the heat-transfer coefficients can be designed in terms of both the component geometry and the quenching time. The purpose of this research is to apply the optimization methodology to design the gas-quenching process. The design objective is to minimize the distortion caused by quenching. Constraints on the average surface hardness, and its distribution and residual stress are imposed. The heat-transfer coefficients are used as design variables. DEFORM-HT is used to predict material response during quenching. The response surface method is used to obtain the analytical models of the objective function and constraints in terms of the design variables. Once the response surfaces of the objective and constraints are obtained, they are used to search for the optimum heat-transfer coefficients. This process is then used instead of the finite-element analysis. A one-gear blank case study is used to demonstrate the optimization scheme.     

Sensitivity analysis based preform die shape design using the finite element method

This paper uses a finite element-based sensitivity analysis method to design the preform die shape for metal forming processes. The sensitivity analysis was developed using the rigid visco-plastic finite element method. The preform die shapes are represented by cubic B-spline curves. The control points or coefficients of the B-spline are used as the design variables. The optimization problem is to minimize the difference between the realized and the desired final forging shapes. The sensitivity analysis includes the sensitivities of the objective function, nodal coordinates, and nodal velocities with respect to the design variables. The remeshing procedure and the interpolation/transfer of the history/dependent parameters are considered. An adjustment of the volume loss resulting from the finite element analysis is used to make the workpiece volume consistent in each optimization iteration and improve the optimization convergence. In addition, a technique for dealing with fold-over defects during the forming simulation is employed in order to continue the optimization procedures of the preform die shape design. The method developed in this paper is used to design the preform die shape for both plane strain and axisymmetric deformations with shaped cavities. The analysis shows that satisfactory final forging shapes are obtained using the optimized preform die shapes.     

Design of forging process variables under uncertainties

Forging is a complex nonlinear process that is vulnerable to various manufacturing anomalies, such as variations in billet geometry, billet/die temperatures, material properties, and workpiece and forging equipment positional errors. A combination of these uncertainties could induce heavy manufacturing losses through premature die failure, final part geometric distortion, and reduced productivity. Identifying, quantifying, and controlling the uncertainties will reduce variability risk in a manufacturing environment, which will minimize the overall production cost. In this article, various uncertainties that affect the forging process are identified, and their cumulative effect on the forging tool life is evaluated. Because the forging process simulation is time-consuming, a response surface model is used to reduce computation time by establishing a relationship between the process performance and the critical process variables. A robust design methodology is developed by incorporating reliability-based optimization techniques to obtain sound forging components. A case study of an automotive-component forging-process design is presented to demonstrate the applicability of the method.     

Sensitivity analysis based preform die shape design for net-shape forging

A sensitivity analysis method for preform die shape design in net-shape forging processes is developed in this paper using the rigid viscoplastic finite element method. The preform die shapes are represented by cubic B-spline curves. The control points or coefficients of B-spline are used as the design variables. The optimization problem is to minimize the zone where the realized and desired final forging shapes do not coincide. The sensitivities of the objective function, nodal coordinates and nodal velocities with respect to the design variables are developed in detail. A procedure for computing the sensitivities of history-dependent functions is presented. The remeshing procedure and the interpolation/transfer of the history-dependent parameters, such as effective strain, are stated. The procedures of sensitivity analysis based preform die design are also described. In addition, a method for the adjustment of the volume loss resulting from the finite element analysis is given in order to make the workpiece volume consistent in each optimization iteration. The method developed in this paper is used to design the preform die shape of H-shaped forging processes, including plane strain and axisymmetric deformations. The results show that a flashless forging with a complete die fill is realized using the optimized preform die shape.     

Forging preform design with shape complexity control in simulating backward deformation

This paper presents a preform design method which employs an alternative boundary node release criterion in the finite element simulation of backward deformation of forging processes. The method makes use of the shape complexity factor which provides an effective measure of forging difficulty. The objective is to release die contacting nodes in a sequence which will minimize the geometric complexity throughout the backward deformation simulation. This is done by calculating the effect of releasing each of a select group of boundary element nodes at each finite element solution step. The particular detached node which results in the minimum shape complexity factor will be released for the current step. This process continues for each backward step until the last few nodes remain in contact. This design method is demonstrated through the simulated forging of an integrated blade and rotor turbine disk blank. A preform shape developed by this method is compared with an empirically designed preform. Performance parameters for comparison include die fill, flash volume, effective strain variance, frictional power and die load. Comparing the results of the forward simulations indicates improved performance of the preform design using FEM based backward deformation method over that of the empirical design.     

Modified particle swarm optimization for a multimodal mixed-variable laser peening process

Optimization problems that result in shock, impact, and explosion type disciplines typically have mixed design variables, multiple optimal solutions, and high computational cost of an analysis. In the optimization literature, many researchers have solved problems involving mixed variables or multiple optima, but it is difficult to find multiple optima of a mixed-variable and high computation cost problem using an particle swarm optimization (PSO). To solve such problems, a mixed-variable niching PSO (MNPSO) is developed. The four modifications introduced to the PSO are: Latin Hypercube sampling-based particle generation, a mixed-variable handling technique, a niching technique, and surrogate model-based design space localization. The proposed method is demonstrated on the laser peening (LP) problem. The LP process induces favorable residual stress on the peened surface to improve the fatigue and fretting properties of the material. In many applications of LP, geometric configurations and dimensional integrity requirements of the component can constrain implementation of an optimal solution. In such cases, it is necessary to provide multiple alternatives to the designer so that a suitable one can be selected according to the requirements. It takes 24–72 CPU hours to perform an LP finite element analysis.     

Optimal design of a three tape-spring hinge deployable space structure using an experimentally validated physics-based model

An optimal design approach is developed for a self-driven, self-locking tape-spring under a pure bending load in deployable space structures. A novel hinge with three tape springs is investigated and designed via an optimization process. Firstly, we investigate the steady-state moment and maximum stress of the hinge during deploying and folding processes using physics-based simulations. Experimental analyses are then conducted to verify the physics-based simulation results. Secondly, a parametric analysis is carried out to prove that both the tape spring thickness and subtended angle have significant effect on steady-state moment. A Response Surface Methodology (RSM) is employed to define an optimal surrogate model aimed at maximizing the steady-state moment, subjected to allowable stress. Finally, the Large Scale Generalized Reduced Gradient (LSGRG) optimization algorithm is used to solve the optimal design problem. Optimization results show that steady-state moment is increased by 19.5% while satisfying a maximum stress constraint. The proposed method is promising for designing novel deployable structures with high stability and reliability.     

A global structural optimization technique using an interval method

This paper deals with a global optimization scheme for structural systems that require finite element analysis to evaluate the constraints or the objective function. The paper proposes a strategy for finding the global optimum using an interval method in conjunction with a multipoint function approximation. The highly nonlinear and nonconvex objective and constraint functions are first represented in the design space using linear and adaptive local approximations and these approximations are blended globally with the use of proper weighting functions. The interval method is then employed to trace the global optimum in the approximated function space. The procedure is tested with several examples with known global solutions and it is successfully applied to optimize the fiber-orientation angles of laminated composite plates for minimum deflections. Received December 22, 2000