Propose Theoretical Foundations for Analyzing the Dynamic Control and Optimizing the Structure of Multifunctional Carbon Fiber-Reinforced Material Plate Integrated Piezoelectric

Abstract

In the fields of aviation, energy, construction, biomedicine, chemical technology, and some other fields, the use of functionally graded materials (FGMs) plates, multifunctional carbon nanofibers reinforced material plates, piezoelectric plates, and several others are increasingly popular. The behavior of material plates can be analyzed through partial differential equations (PDEs). However, the PDEs are for complex problems such as solid-liquid interactions, thermoelectric mechanical environments, functional material plates in multi-physics environments, and others that are very difficult or impossible to find a solution. In many numerical methods have been researched and developed, the finite element method (FEM) is a widely used and effective method to find approximate solutions of the PDEs. But the FEM has certain limitations in element techniques, discretizing the weak form for the plate structure problems with many degrees of freedom significantly, and affects the accuracy and efficiency of calculation. Proposing improvements to traditional FEM combines dynamic control analysis in the presence of piezoelectric crystals and optimization method algorithms, meeting the increasing requirements in analyzing the behavior of carbon nanofiber material plates used in many fields. On this basis, the article presents some theoretical foundations to solve the problem of dynamic control and optimizing the structure of multifunctional carbon nanofiber-reinforced material plates with integrated piezoelectric crystal.