In this study, the isogeometric boundary element method (IGBEM) based on non-uniform rational basis spline (NURBS) is used to perform shape design sensitivity and optimization of rotating three-temperature (3T) thermoelastic structures. During the optimization process, the shape design sensitivity within the IGBEM formulation was derived to include precise geometries and greater continuities. It was found through the application of the IGBEM that the shape design velocity has a significant effect on accuracy of the obtained shape design sensitivity. As a result, the developed shape design sensitivity analysis (SDSA) technique based on the considered IGBEM formulation outperforms the computational solution based on the traditional SDSA method. The isogeometric shape sensitivity and optimal design for a complicated three-temperature thermoelastic problem in rotating structures are investigated. The impact of rotation on the thermal stress sensitivity, optimal three-temperature, optimal displacement and optimal three temperature thermal stress distributions are established. It is shown that the SDSA derived using IGBEM is efficient and applicable for most three-temperature thermoelastic optimization problems.

The primary goal of this study is to create a novel mathematical model based on the time-stepping boundary element method (BEM) scheme for solving three-dimensional coupled dynamic thermoelastic fracture issues in anisotropic functionally graded materials (FGMs). The crack tip opening displacement determines the dynamic stress intensity factor (SIF). The effects of anisotropy, graded parameters, and angle locations on the SIF were studied for three-dimensional coupled dynamic thermoelastic fracture situations. The results show that the novel method is exceptionally exact and efficient at assessing the fracture mechanics of fractured thermoelastic anisotropic FGMs. In addition, this paper provides a theoretical framework for analyzing a wide range of real engineering applications.