Optimization of a higher-order sandwich composite beam under uncertainties
Optimization under uncertainties of structures is a challenging field due to the requirements of high computational resources. The typical approaches include reliability-based design optimization (RBDO) and robust design optimization (RDO), which provide more realistic optimal designs than the conventional deterministic optimization approaches. For complex engineering structures, performing RBDO and RDO becomes computationally intractable or even infeasible. Thus, there is a requirement to employ efficient uncertainty quantification methods to perform the optimization under uncertainty of advanced structures. This thesis investigates the reliable and robust optimum design of a higher-order sandwich composite beam under the effect of uncertainty in material properties. Sandwich composites are a unique class of composite materials that are quite popular in the aerospace, marine, and automobile industries, mainly due to their superior properties such as high stiffness, low weight to strength ratio, high corrosion resistance, and high energy absorption capabilities. The sandwich composite beam is modeled using the extended higher-order sandwich panel theory. The optimization procedure is performed using an accelerated particle swarm optimization. The efficiency of the optimization process is enhanced by using a novel time-domain spectral element method-based polynomial chaos surrogate model. The proposed surrogate model is based on the highly efficient hybrid stochastic time domain spectral element method (STSEM). STSEM couples the computational efficiencies of the spectral stochastic finite element method and the time-domain spectral element method. The uncertainty analysis of a higher-order sandwich composite beam using STSEM is performed to compare the numerical accuracy and the computational efficiency of the proposed method with the Monte Carlo simulation (MCS). Sobol indices-based global sensitivity analysis is also performed to identify the sensitive random parameters. The numerical results indicate the superior computational efficiency and excellent numerical accuracy of STSEM in comparison with MCS. Thus, a surrogate model is built using STSEM to perform the optimization of a higher-order sandwich composite beam under uncertainty. The proposed surrogate model alleviates the high computational requirements of RBDO and RDO procedures for sandwich composite. The numerical results of the reliable and robust optimal design are presented and discussed. Furthermore, the effect of load density and allowable deflection on the optimal design is also examined.