無元素葛勒金法

Element Free Galerkin Method

謝宜典(I-Tien Shueh)

指導教授 ： 鄔蜀威

國立中央大學/工學院/機械工程學系/碩士(2006年)

摘要

本文將介紹無元素葛勒金法，此無元素法為利用變動最小二乘法所求的近似函數引入葛勒金弱式推導。可克服有限元素在工程上的限制。例如：鎖死、大變形問題精確度降低及裂縫成長等問題。本文將以靜彈性力學為例，說明標準補丁測試、懸臂梁和中間挖孔平板，並討論精確度與收斂性。也提供了Fortran程式碼，可供發展應用軟體或為撰寫其他無元素法程式參考。

本文包括無元素葛勒金法、變動最小二乘法基本原理及三個數值範例與無元素葛勒金法懲罰法Fortran程式碼。

關鍵字

無網格法 ； 無元素法 ； 變動最小二乘法 ； 無元素葛勒金法

並列摘要

An element-free Galerkin(EFG) method is introduced in this paper. It is an meshfree method. In this method, moving least-square interpolates are used to construct the approximate function for the Galerkin weak-form. EFG can overcome finite element method(FEM) several limitations in the engineering. For example, locking, large deformation problems accuracy losing, and crack growth problems. In this study, EFG is applied to elastostatics analysis. Path test, cantilevered beam, and plate with a central circular hole will be computed in this paper. Accuracy and convergence are also discussed in this paper. In addition, EFG method Fortran code also is offered in this paper. This Fortran code can be developed to meshfree application software or other meshfree method in the further.

並列關鍵字

MLS ； Meshfree ； Meshless ； EFG

參考文獻

1. Lucy L. B. (1977) “A numerical approach to the testing of the fission hypothesis,” The Astron. J, 8(12), pp. 1013-1024

2. Nayroles B., Touzot G., Villon P. (1992) “Generalizing the finite element method: diffuse approximation and diffuse elements,” Comput. Mech, Vol. 10 pp. 307-318

3. Belytschko T., Lu Y. Y. (1994) “Element free Galerkin method,” Int. J. Num. Meth, Vol. 37, pp. 229-256

4. Chung H. J., Belytschko T. (1998) “An error estimate in the EFG method,” Comput. Mech, Vol. 21, pp. 91-100

5. Dolbow J., Belytschko T. (1999) “Numerical integration of the Galerkin weak form in meshfree methods,” Comput. Mech, Vol. 23, pp. 219-230