演講者：蕭錫源

1. A new BEM formulation for transient axisymmetricporoelasticity via particular integralsK.H. Park a, P.K. Banerjee b,* 演講者：蕭錫源

2. Abstract • A simple particular integral formulation is presented for the first time in a purely axisymmetric poroelastic analysis. • The axisymmetric elastostatic and steady-state potential flow equations are used as the complementary solution. • The particular integrals for displacement, traction, pore pressure and flux are derived by integrating three-dimensional formulation alongthe circumferential direction leading to elliptic integrals.

3. 1. Introduction • The general theory of poroelasticity is governed by two coupled differential equations: the Navier equation with pore pressure body force and the pore fluid flow equation as (Banerjee, 1994)

4. 是位移 是有效滲透率 是孔隙壓力和 Lame’s的常數 the undrained不透水的 該排水體積彈性模量是在對堅實組成部分的BULK模數某些情況經驗得知的常數 是body force和source（如果存在的話）for 2D (3D)

5. 常數　和　也可以表示在不排水體積的 彈性模數 　(Rice and Cleary, 1976) 　　是著名的skempton係數的孔隙壓力。

6. Park and Banerjee (2002a) first proposed the particular integral formulation

7. 左為２００６下為２００２

8. 2.Three-dimensional particular integral formulation 位移 曳引力孔隙壓力流量

9. 將右式global shape function代入

11. 將上三頁的式子代入２００６的非均值式子中得下列係數將上三頁的式子代入２００６的非均值式子中得下列係數

12. 3. Axisymmetric particular integral formulation • For axisymmetric problems, use of such polynomial functions as functions of r and z coordinates have been discussed in Henry et al. (1987). • It is of considerable interest to note that Wang and Banerjee (1988, 1990) in their developments of particular integrals in free-vibration analysis of axisymmetric solids also observed the same to be true.

13. 為方便起見，所界定的軸對稱case

14. 考慮到在圓柱坐標系的純粹的軸對稱體

15. then 分別為在X點在R和Z -方向 的normal vector。

16. 4. Numerical implementation 軸對稱彈性力學和穩定狀態勢流方程的根本解 和 分別代表jump terms resulting 所產生的奇異性質的 和

17. 離散↓ ↓

18. 因考慮而加入有限的數量、時間、位移、牽引、孔隙壓力和流量因考慮而加入有限的數量、時間、位移、牽引、孔隙壓力和流量

19. 5. Numerical examplesExample 1

23. Example 2

24. 其中　　是　　　　　　　　　　　　的根

27. Example 3

29. 6. Conclusions • The simple particular integral formulation has been developed for axisymmetric coupled poroelastic analysis. • The equations of axisymmetric elastostatic and steady-state potential flow have been used as the complementary functions. • The particular integrals of displacement, traction, pore pressure and flux are obtained by integrating three-dimensional BEM formulation along the circumferential direction and converting them into elliptic integrals.