ADVANCES IN NEW NATURAL COORDINATE METHODS FOR FINITE ELEMENT METHOD

The sensitivity problem to mesh distortion is a challenging difficulty in the field of the finite element method. Recently, some new natural coordinate methods have been successfully established for developing robust finite element models. They provide possible ways to overcome the problem. This paper introduces some newest advances in the research on this area, including the quadrilateral area coordinate method of type I and its applications (construction of finite element model, establishment of analytical element stiffness matrix, and application in geometrically nonlinear problem); the quadrilateral area coordinate method of type II and its application; and the hexahedral volume coordinate method and its applications. Numerical examples show that element models formulated by these new natural coordinate systems are quite insensitive to various mesh distortions. It demonstrates that these new natural coordinate methods are powerful tools for constructing high-performance hexahedral finite element models.