Optimization of multi-directional functionally graded plates in thermal environment based on 3D isogeometric analysis and adaptive-hybrid evolutionary firefly algorithm

Abstract

In this study, a numerical model based on three-dimensional isogeometric analysis and adaptive hybrid evolutionary firefly algorithm is developed to concurrently optimize the shape and material distribution of multi-directional functionally graded plates. The optimization problems focus on maximizing the fundamental frequency of the plates subjected to thermal effects, while the volume fraction of ceramic constituent material and volume of the plates are considered as side constraints. Isogeometric multi-mesh design approach is employed to generate design and analysis domain. The free vibration analysis of multi-directional functionally graded plates with variable thickness is conducted within the framework of three-dimensional elasticity theory and isogeometric analysis. The generalized numerical framework developed in this study could accurately capture the thermal effects on the behavior of nonhomogeneous plates with variable thickness. Various numerical examples are conducted to illustrate the optimal shapes and material distributions within square, rectangular, and circular plates. Influences of temperature field, boundary conditions, and geometries of the plates on the optimal results are also addressed.