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| Study on semi-analytic numerical method for structure analysis of functionally graded materials |
| Received:January 15, 2009 Revised:June 02, 2009 |
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| DOI：10.7511/jslx20106003 |
| KeyWord:method of lines functionally graded materials finite difference B spline collocation method at Gaussian points semi-analytical method |
| Author | Institution |
| 燕秀发 |
解放军理工大学 工程兵工程学院, 南京 ;解放军91550部队, 大连 |
| 钱七虎 |
解放军理工大学 工程兵工程学院, 南京 |
| 王玮 |
解放军91550部队, 大连 |
| 孙翱 |
解放军91550部队, 大连 |
| 戴耀 |
解放军装甲兵工程学院, 北京 |
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| Abstract: |
| A representative semi-analytical numerical method, method of lines(MOLs), was introduced into structure analysis of functionally graded materials(FGMs). Equilibrium equations and boundary conditions for FGM problems were derived with respect to displacement variables. Then, solution process and numerical fundamental of the approach were expounded. The basic idea of the method is to semi-discretizing the governing equations into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. Solving the ODEs by using B spline collocation method at Gaussian points, solutions of the problem can be obtained. The examples of the FGM plate with exponential or linear gradation under constant displacement, tensile loading or bending loading were presented to demonstrate how to use the method for structure analysis of FGMs. Computational results of MOLs are quite accurate by comparison with ones of analytical solutions of corresponding problems and other numerical approaches. Moreover, it was confirmed that the method can effectively simulate continuous variation of material property parameters without any especial considerations and the approximate field function satisfying special conditions need not be chosen in advance. Therefore, it is an effective semi-analytical numerical method suitable to the structure format and material characteristic of FGMs. |
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