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3-D shell components are used intensively in the automotive industry. Many structural topology optimization techniques were developed to reduced the total weight of shell structures while retaining its structural performance. One common approach is to utilize the concept of the design domain, such as the homogenization method and the density function approach. In this paper, a new micro-structure based design domain method is introduced to solve 3-D shell topology optimization problems. Based on physical micro-structure model, simple closed-form expressions for effective Young's modulus and effective shear modulus are rigorously derived. Using these simple relations, topology optimization problems can be formulated and solved with sequential convex approximation algorithms. Two design examples obtained from the new method are presented.

In search of improved design, Reliability Based Design Optimization using probabilistic constraints has evolved as a powerful tool, however extensive computational efforts necessary for RBDO being one of the biggest challenges in this field. In order to evaluate probabilistic constraints, single loop and double loop strategies have been successfully used, the number of function evaluations being a decisive comparison criteria. However, when applied to complicated functions, above techniques lead to much higher number of function evaluations. Efforts to make RBDO technique computationally feasible have generated superior single loop strategy presented in this paper, dealing with the approximated form of the original functions. At the same time, improved Most Probable Point search algorithm has been used providing modified gradient information for fast convergence of the constraints.

To reduce the low frequency noise, a new method in optimal stiffener design is presented in this paper. A Microstructure-based Design Domain Method is employed to formulate a topology optimization problem. Using the MDDM, sensitivity of coupled system can be easily derived. The optimal stiffener design is solved using a sequential convex approximation method called Generalized Convex Approximation (GCA). Examples from this approach are presented to demonstrate its effectiveness.

It is common to give assurance in terms of the probability of success in satisfying some performance criteria and the probability of success is estimated from the mean value and variance of the performance function. The mean value and variance of the performance function is further estimated from the propagation of the input uncertainties. Therefore, it becomes a fundamental challenge to accurately estimate the uncertainty propagations from given input randomness in the probabilistic design process. Better approximation of the performance function is a key factor in enhancing the approximation quality of the mean value and the standard deviation. However, higher order approximations for the performance increase the computational cost associated. This paper presents an improved approximation method for the prediction of the mean and variance without increasing the number of function evaluations.