Shape optimization of GFRP elastic gridshells by the weighted Lagrange ε-twin support vector machine and multi-objective particle swarm optimization algorithm considering structural weight

Abstract

Elastic gridshell is a type of free-form structure usually with double-curved shape and it is constructed by deforming an initially flat grid to achieve the final structural form. Determining a reasonable structural shape considering structural performance is an essential task in the design of such structures. This paper presents a shape optimization method for elastic gridshells considering structural weight, aiming to minimize the structural stress and deformation. Support vector machine is utilized to predict the structural performance in the optimization process in order to avoid the time-consuming structural analysis. The least square support vector machine (LSSVM), weighted least square support vector machine (WLSSVM), a combination of particle swarm optimization and least square support vector machine (PSO-LSSVM), and weighted Lagrange ε-twin support vector machine (WL-ε-TSVM) are first compared for predicting the structural analysis results. The WL-ε-TSVM algorithm shows superior performance and is further adopted in the optimization method. The k-fold cross validation is implemented during the validation process of this algorithm to improve the predictive performance. Based on predicted structural performance, the optimal shape of gridshell is provided by using the multi-objective particle swarm optimization (MOPSO) algorithm. The Taguchi technique is applied to tune the parameters of the MOPSO algorithm. Afterwards, the technique for order preference by similarity to ideal solution (TOPSIS) is implemented to determine the most desirable solution from the Pareto optimal set. The presented method is validated through an example and the structural behavior of the optimized structure is further assessed by finite element analysis. Results demonstrate that the presented method is applicable for finding the optimum shape of gridshells with high structural performance.