Modified Fixed Grid Finite Element Method to Solve 3D Elasticity Problems of Functionally Graded Materials

Document Type : Persian

Authors

1 Assistant Professor, Mechanical Engineering Department, Islamic Azad University, Shiraz Branch

2 Associate Professor, Mechanical Engineering Department, Shiraz University

Abstract

In the present paper, applicability of the modified fixed grid finite element method in solution of three dimensional elasticity problems of functionally graded materials is investigated. In the non-boundary-fitted meshes, the elements are not conforming to the domain boundaries and the boundary nodes which are used in the traditional finite element method for the application of boundary conditions no longer exist. Therefore, special techniques are needed for computation of the stiffness matrix of boundary intersecting elements and application of boundary conditions.The stiffness matrix of boundary intersecting elements are calculated via integration of strain energy over the internal parts of these elements. Essential boundary conditions are applied using penalty function method. To examine the effectiveness of the proposed method, some numerical examples are solved and results are compared with those obtained using the standard finite element method.

Keywords

References

[1] Reddy J.N., An introduction to the finite
  element method, 2nd Ed., McGraw-Hill, New
  York, 1993.
[2]  Thompson J.F., Soni B.K. and Weatherill N.P., Handbook of grid generation, CRC press, New York, 1999.
[3]  Belytschko T., Krongauz Y., Organ D., Fleming M. and Krysl P., Meshless methods: An overview and recent developments, Computer Methods in Applied Mechanics and Engineering, Vol. 139, 1996, pp. 3-47.
 
[4]  Liu G.R., Mesh free methods: moving beyond the finite element method, CRC Press, New York, 2003.
[5]  Garcia M.J. and Steven G.P., Fixed grid finite elements in elasticity problems, Engineering Computations, Vol. 16, 1999, pp. 145-164.
[6]  Garcia M.J., Ruiz O.E. and Henao M.A., Fixed grid finite element analysis for 3D structural problems, International Journal of Computational Methods, Vol. 22, 2004.
[7]   Kim H., Garcia M.J., Querin O.M., Steven G.P. and Xie Y.M., Fixed grid finite element analysis in evolutionary structural optimization, Engineering Computations, Vol. 17, 2000, pp. 427-439.
[8] Garcia M.J. and Gonzalez C.A., Shape optimization of continuum structures via evolution strategies and fixed grid finite element analysis, Journal of structural and multidisciplinary optimization, Vol. 26, 2004, pp. 92-98.
[9] Birman V. and Byrd L.W., Modeling and Analysis of Functionally Graded Materials and Structures, Applied Mechanics Reviews, Vol. 160, 2007, pp. 195-216.
[10]   دانشمند ف.، فرید م. و کاظم زاده پارسی م.ج.، روش اصلاح شده المان محدود شبکه ثابت در تحلیل مسائل دو بعدی ارتجاعی خطی، مجله علمی پژوهشی استقلال، دانشگاه صنعتی اصفهان، سال 27، شماره 2، اسفند 1387، صص103 – 122.
[11]  کاظم زاده پارسی م.ج.، دانشمند ف. و فرید م.، روش اصلاح شده المان محدود شبکه ثابت و کاربرد آن در حل مسائل سه بعدی ارتجاعی خطی، مجموعه مقالات سیزدهمین کنفرانس مهندسی مکانیک ایران، دانشگاه صنعتی اصفهان، اصفهان، 1384.
[12]  Daneshmand F. and Kazemzadeh-Parsi M.J., Static and dynamic analysis of 2D and 3D elastic solids using the modified FGFEM, Finite Elements in Analysis and Design, Vol. 45, 2009, pp. 755-765.
[13]  Bensoe M. and Kikuchi N., Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, Vol. 71, 1988, pp. 197-224.

Files

Share

How to cite

Statistics