ADVANCES IN THE FINITE ELEMENT METHOD BASED ON THE ANALYTICAL TRIAL FUNCTIONS

The finite element method based on the analytical trial functions is an organic integration of the analytical method with the discrete method. This method has overcome some challenges to the tradition finite element method. This paper introduces some newest advances in the research of shear locking problems and the sensitivity of mesh distortions. According to the variational principle containing stress functions, the study of the high-performance and high-order element models shows the way to obtain the high-order exact element models which are not sensitive to the mesh distortion. According to “Operator matrix” theory of partial differential equations, the solving of characteristic differential equations is proposed as a general mehod for constructing complete and independent analytical trial functions.