Design Sensitivity Method Research Articles

Conservative reliability-based design optimization method with insufficient input data

Reliability analysis and reliability-based design optimization (RBDO) require an exact input probabilistic model to obtain accurate probability of failure (PoF) and RBDO optimum design. However, often only limited input data is available to generate the input probabilistic model in practical engineering problems. The insufficient input data induces uncertainty in the input probabilistic model, and this uncertainty forces the PoF to be uncertain. Therefore, it is necessary to consider the PoF to follow a probability distribution. In this paper, the probability of the PoF is obtained with consecutive conditional probabilities of input distribution types and parameters using the Bayesian approach. The approximate conditional probabilities are obtained under reasonable assumptions, and Monte Carlo simulation is applied to calculate the probability of the PoF. The probability of the PoF at a user-specified target PoF is defined as the conservativeness level of the PoF. The conservativeness level, in addition to the target PoF, will be used as a probabilistic constraint in an RBDO process to obtain a conservative optimum design, for limited input data. Thus, the design sensitivity of the conservativeness level is derived to support an efficient optimization process. Using numerical examples, it is demonstrated that the conservativeness level should be involved in RBDO when input data is limited. The accuracy and efficiency of the proposed design sensitivity method is verified. Finally, conservative RBDO optimum designs are obtained using the developed methods for limited input data problems.

Design Sensitivity Method for Sampling-Based RBDO With Varying Standard Deviation

Conventional reliability-based design optimization (RBDO) uses the mean of input random variable as its design variable; and the standard deviation (STD) of the random variable is a fixed constant. However, the constant STD may not correctly represent certain RBDO problems well, especially when a specified tolerance of the input random variable is present as a percentage of the mean value. For this kind of design problem, the STD of the input random variable should vary as the corresponding design variable changes. In this paper, a method to calculate the design sensitivity of the probability of failure for RBDO with varying STD is developed. For sampling-based RBDO, which uses Monte Carlo simulation (MCS) for reliability analysis, the design sensitivity of the probability of failure is derived using a first-order score function. The score function contains the effect of the change in the STD in addition to the change in the mean. As copulas are used for the design sensitivity, correlated input random variables also can be used for RBDO with varying STD. Moreover, the design sensitivity can be calculated efficiently during the evaluation of the probability of failure. Using a mathematical example, the accuracy and efficiency of the developed design sensitivity method are verified. The RBDO result for mathematical and physical problems indicates that the developed method provides accurate design sensitivity in the optimization process.

최적화 기법을 이용한 한국형 소형전술차량의 경량설계

One of various main jobs in the design of a new tactical vehicle is to develop the lightest chassis parts satisfying the required durability target. In this study, the analytic methods to reduce the size and weight of a lower control arm and chassis frame of a Korean light tactical vehicle are presented. Topology optimization by ATOM (Abaqus Topology Optimization Module) is applied to find the optimal design of the suspension arm with volume and displacement constraints satisfied. In case of chassis frame, the light-weight optimization process associated with design sensitivity method is developed using Isight and ABAQUS. By these analytic methods we can provide design engineers with guides to where and how much the design changes should be made.

Improved semi-analytic sensitivity analysis combined with a higher order approximation scheme in the framework of adjoint variable method

In the design sensitivity analysis, the adjoint variable method has been widely used for the sensitivity calculation. The adjoint variable method can reduce computation time and save computer resources because it can provide the sensitivity values only at the positions in which designers are willing to obtain. However, exact analytical differentiation with respect to the design variables is commonly employed in adjoint variable method. Although the exact derivative assures the accurate sensitivity, it is cumbersome to take differentiation in an exact manner for every given type of finite element. Therefore, in the present study, a new improved semi-analytic design sensitivity method is proposed in the framework of adjoint variable method. Recently, a numerical inaccuracy trouble in the traditional semi-analytic method has been settled by the rigid body mode separation technique and high order approximation scheme. Combining the adjoint variable method with improved semi-analytic design sensitivity scheme, the design sensitivity value can be calculated accurately and efficiently. Through numerical examples, the efficiency and accuracy of the proposed semi-analytic sensitivity scheme in the adjoint variable method are demonstrated.

Identification of the piezoelectric material coefficients using the finite element method with an asymptotic waveform evaluation

A rapid identification of the piezoelectric material constants for a piezoelectric transducer is proposed. The validity of a three-dimensional finite element routine was confirmed experimentally. The asymptotic waveform evaluation (AWE) was adopted for a fast frequency sweep of the finite element analysis. The three-dimensional finite element method with an AWE and a design sensitivity method was used for a material inversion scheme of piezoelectric transducers. In order to confirm the inversion routine of the material constants, the mechanical displacements, which mean the mode shape, were calculated along the vertical and lateral position of the sample transducer.

Identification of material constants for piezoelectric transformers by three-dimensional, finite-element method and a design-sensitivity method.

In this paper, an inversion scheme for piezoelectric constants of piezoelectric transformers is proposed. The impedance of piezoelectric transducers is calculated using a three-dimensional finite element method. The validity of this is confirmed experimentally. The effects of material coefficients on piezoelectric transformers are investigated numerically. Six material coefficient variables for piezoelectric transformers were selected, and a design sensitivity method was adopted as an inversion scheme. The validity of the proposed method was confirmed by step-up ratio calculations. The proposed method is applied to the analysis of a sample piezoelectric transformer, and its resonance characteristics are obtained by numerically combined equivalent circuit method.

Optimal curing for thermoset matrix composites: Thermochemical and consolidation considerations

AbstractA design sensitivity method is used to find optimal autoclave temperature and pressure histories for curing of thermoset‐matrix composite laminates. The method uses a finite element simulation of the heat transfer, curing reaction, and consolidation in the laminate. Analytical sensitivities, based on the direct differentiation method, are used within the finite element simulation to find the design sensitivities, i.e., the derivatives of the objectives function and the constraints with respect to the design variables. Standard gradient‐based optimization techniques are then used to systematically improve the design, until an optimal process design is reached. In this study the objective is to minimize the total time of the cure cycle, while the constraints include a maximum temperature in the laminate (to avoid thermal degradation) and a maximum deviation of the final fiber volume fraction from its target value (to achieve proper consolidation). The simulations of curing process are performed for EPON 862/W epoxy under a conventional cure cycle, for both thin and thick parts. Time‐optimal cure cycles are found using the optimization program. Simulations of fast‐curing cycles are also examined. The optimal cycles are similar in form to conventional cure cycles, but give substantially shorter cure times. The entire scheme works automatically and efficiently, simultaneously adjusting multiple design variables at each iteration.

B-spline parametrization of finite element models for optimal design of electromagnetic devices

This paper presents B-spline parametrization method for the optimal shape design of electromagnetic devices. As an optimal design technique, the design sensitivity method based on the finite element method is used. Since the design variables of one-to-one correspondence with node points of finite element model can cause saw-tooth shape and serious accuracy problem, the design interface is parameterized into smooth curves using geometrical relation of design variables and node points of finite element model. B-spline technique used widely in computer graphics is capable of representing smooth curves and surfaces and can generate a wide variety of shapes. In addition, its geometry data can be easily connected to many commercial CAD tools. To show validity of the presented technique, we test two numerical examples: a magnet shape design problem for uniform magnetic field and a electrode shape design problem for uniform electric field.