Nanofibers Research Papers - Academia.edu (original) (raw)

Most of the phenomena in life, such as heat transfer, wave propagation, thermoelectricity, sheet materials, multifunctional material properties, etc., can be expressed through mathematical equations or partial differential equations (PDEs). However, with complex differential equations, it is difficult or impossible to find solutions, especially differential equations for complex problems such as solid-liquid interactions, mechanical-thermal-electrical environments, and functional material plate environments in the multiphysics environment, etc. Since then, many numerical methods have been researched and developed to find approximate solutions to partial differential equations. Today, the finite element method (FEM) is the most widely used and effective among the commonly used numerical methods. However, with the continuous emergence of new complex problems in science and technology, especially problems in the multiphysics environment in sheet-material structures, the finite element method has revealed new challenges. There are certain limitations related to the element technique and the weak form discretization of the problem of sheet structure with many different degrees of freedom, significantly affecting the accuracy and efficiency of calculations. Therefore, it is always important to propose improvements to the traditional finite element method and the optimal method algorithm to meet the increasing requirements in the behavior analysis of sheet materials. This research direction is always topical and has received the attention of scientists around the world for many decades.