FINITE ELEMENT MODELLING FOR STATIC AND FREE VIBRATION RESPONSE OF FUNCTIONALLY GRADED BEAM

Authors

  • ATEEB AHMAD KHAN ALIGARH MUSLIM UNIVERSITY
  • M. NAUSHAD ALAM ALIGARH MUSLIM UNIVERSITY
  • NAJEEB-UR RAHMAN ALIGARH MUSLIM UNIVERSITY
  • MUSTAFA WAJID ALIGARH MUSLIM UNIVERSITY

Keywords:

FINITE ELEMENT, MROM, ZIG-ZAG THEORY, FUNCTIONALLY GRADED BEAM, ABAQUS

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 MET-AL/CERAMIC FGM SYSTEM HAS BEEN CHOSEN. MODIFIED RULE OF MIXTURE (MROM) IS USED TO CALCULATE THE YOUNGÂS MODULUS AND RULE OF MIX-TURE (ROM) IS USED TO CALCULATE DENSITY AND POISSONÂS 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 ITERA-TION 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 SYS-TEMS.

Author Biographies

ATEEB AHMAD KHAN, ALIGARH MUSLIM UNIVERSITY

MASTER'S STUDENT

DEPARTMENT OF MECHANICAL ENGINEERING

ALIGARH MUSLIM UNIVERSITY, ALIGARH

M. NAUSHAD ALAM, ALIGARH MUSLIM UNIVERSITY

PROFESSOR

DEPARTMENT OF MECHANICAL ENGINEERING

ALIGARH MUSLIM UNIVERSITY, ALIGARH

NAJEEB-UR RAHMAN, ALIGARH MUSLIM UNIVERSITY

ASSISTANT PROFESSOR

DEPARTMENT OF MECHANICAL ENGINEERING

ALIGARH MUSLIM UNIVERSITY, ALIGARH

MUSTAFA WAJID, ALIGARH MUSLIM UNIVERSITY

MASTER'S STUDENT

DEPARTMENT OF MECHANICAL ENGINEERING

ALIGARH MUSLIM UNIVERSITY, ALIGARH

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Published

2016-02-17

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Section

Articles