Finite Element Modelling for Static and Free Vibration Response of Functionally Graded Beam

Abstract

A 1D Finite Element model for static response and free vibration analysis of functionally graded material (FGM) beam is presented in this work. The FE model is based on efficient zig-zag theory (ZIGT) with two noded beam element having four degrees of freedom at each node. Linear interpolation is used for the axial displacement and cubic hermite interpolation is used for the deflection. Out of a large variety of FGM systems available, Al/SiC and Ni/Al2O3 metal/ceramic FGM system has been chosen. Modified rule of mixture (MROM) is used to calculate the young's modulus and rule of mixture (ROM) is used to calculate density and poisson's ratio of FGM beam at any point. The MATLAB code based on 1D FE zigzag theory for FGM elastic beams is developed. A 2D FE model for the same elastic FGM beam has been developed using ABAQUS software. An 8-node biquadratic plane stress quadrilateral type element is used for modeling in ABAQUS. Three different end conditions namely simply-supported, cantilever and clamped-clamped are considered. The deflection, normal stress and shear stress has been reported for various models used. Eigen Value problem using subspace iteration method is solved to obtain un-damped natural frequencies and the corresponding mode shapes. The results predicted by the 1D FE model have been compared with the 2D FE results and the results present in open literature. This proves the correctness of the model. Finally, mode shapes have also been plotted for various FGM systems.

Finite element modelling to assess the effect of position and size of the piezoelectric layer of a hybrid beam

“…To show the accuracy and efficiency of the present formulation, the results of 1D-FE model are compared with the converged 2D-FE ABAQUS results Khan et al, 2016 . The hybrid beams are modelled in 2D planar modelling space as a deformable shell using FE package ABAQUS 2010 wherein the layup with different material properties are defined across the beam thickness and suitable element types for elastic substrate and piezoelectric layers are assigned.…”

Finite element forced vibration analysis of refined shear deformable nanocomposite graphene platelet-reinforced beams

“…The finite element approach is a well-known solution technique which is broadly applied in analyzing static and dynamic characteristics of beams. Most of the investigations are based upon Euler-Bernoulli and Timoshenko beam models, and the master element according to these beam models can be found in the literature [18][19][20]. The classical or Euler-Bernoulli beam element is not applicable for thick beams with small values of slenderness ratios.…”

New hybrid approach for free vibration and stability analyses of axially functionally graded Euler-Bernoulli beams with variable cross-section resting on uniform Winkler-Pasternak foundation

“…Arefi (2015) studied electromechanical stability of a functionally graded circular plate integrated with two functionally graded piezoelectric layers under radial compressive. Khan et al (2016) proposed a finite element solution for free vibration and static analyses of beam made up of functionally graded materials (FGMs), based on efficient zig-zag theory (ZIGT). Based on the modified couple stress theory, mechanical behavior of non-uniform bi-directional functionally graded beam sensors was studied in detail by Khaniki and Rajasekaran (2018).…”