摘 要 本文探討一種無網格的數值分析方法－力場疊加法，並應用於股骨近端的二維彈性力學的分析。 力場疊加法的原理是將邊界選取數個與虛擬源點相同數量且具代表性的場點，而虛擬源點為在分析區域外設定的假想源點，這些虛擬源會產生和實體邊界相同的邊界條件，再使用基本解與邊界場點的關係，可求得分析區域內各點的受力情況。此法相較於有網格數值分析法來說是相當的簡單便利，故值得推廣使用。 本文使用兩個實例來測試力場疊加法的正確性，並將其分析股骨近端的結果與有限元素法做比較，來驗證力場疊加法的可行性。 ABSTRACT The study investigates a meshless numerical analysis method－Force Field Superposition (FFS) method. The method applys to the two- dimensional proximal femur’s elastostatics analysis. The basic theorem of Force field superposition method is taking a few representative force points in solution domain boundary which amount are the same with the virtual points. The virtual points are locate outside the solution domain, these points will generate boundary conditions equal to the solution domain. We use the relationship between fundamental solution and force points and virtual points, we can get the fore field situation inside the solution domain. The method is simpler and more convenient than meshing numerical analysis method, so it is worth popularizing. The study uses two cases to test the accuracy of the force field superposition method, and comparing the proximal femur analysis result with the result of using finite element method. It can prove the practicality of the force field superposition method.
