A Polynomial Chaos Expansion Method for Mechanical Properties of Flexoelectric Materials Based on the Isogeometric Finite Element Method

Abstract

The paper proposes a method for analyzing the mechanical properties of flexoelectric materials based on the isogeometric finite element method (IGA-FEM) and polynomial chaos expansion (PCE). The method discretizes the flexoelectric governing equations utilizing the B-spline shape functions that satisfy the continuity requirement to obtain the mechanical properties (electric potential) of the material. To obtain a mechanical property with different input parameters, we choose the truncated pyramid model as the object of study, and use IGA-FEM and PCE to solve different single uncertain parameters, including independent Young’s modulus and uniformly distributed force, and two kinds of flexoelectric constants, respectively. Numerical examples are presented to bear out the accuracy and viability of the proposed methodology.

FEM/Wideband FMBEM coupling based on subdivision isogeometry for structural-acoustic design sensitivity analysis

“…This advanced technique combines the original FMM with the diagonal form FMM, leading to more efficient solutions. Therefore, the challenges related to large-scale fluid-structure interaction problems can be effectively resolved through the utilization of the coupling approach based on FEM/fast multipole boundary element method (FEM/FMBEM) [19][20][21][22][23]. Furthermore, this study proposes the utilization of the FEM/Wideband FMBEM coupling method to tackle the intricate problems associated with fluid-structure interactions.…”