basic displacement functions (bdfs)

In order to obtain accurate results from displacement-based Finite Element Method (FEM), it is crucial to introduce accurate shape functions that interpolate the displacement field within an element. This paper attempts to provide such a new component by using Finite Element method using Basic Displacement Function (BDFs) for the free vibration analysis of plates with in-plane Functionally Graded Material (FGM). The first step is to introduce displacement functions and compute them using the energy method. Later, new shape functions are developed based on stiffness and force methods used to model the mechanical behavior of the element, wherein the shape functions benefit from the generality and accuracy of the stiffness and force methods. Last, the plate is analyzed using Finite Element method to derive the structural matrices from new shape functions. Several numerical examples demonstrate the accuracy and efficiency of the method, and a special material graded index named Ns is introduced.