Stochastic Wave Finite Element Method in Uncertain Function Gradient Material Structure

This chapter delves into the application of the Stochastic Wave Finite Element Method (WFE) to analyze wave propagation in Functionally Graded Materials (FGMs) with uncertain properties. It begins by introducing FGMs and their diverse applications, highlighting the need for robust predictive tools like the WFE method. The chapter then compares the WFE method with traditional Finite Element Method (FEM) and analytical approaches, emphasizing its efficiency and accuracy in wave propagation analysis. The modeling of FGM beams using the finite element approach is detailed, including the formulation of mass and stiffness matrices. The chapter also explores the use of probabilistic tools, such as the Monte Carlo method, to model uncertainties in geometric and mechanical parameters. Numerical results and discussions are presented, showcasing the method's ability to simulate bending wave propagation and the impact of uncertainties on dispersion curves. The chapter concludes with insights into the method's limitations and potential future research directions, such as the use of artificial intelligence techniques for uncertainty quantification and fault detection in composite materials.