1. The Finite Element Method Prof. Su-Jin Kim Gyeongsang National University

2. Applications of FEM Structural analysis Heat transfer Fluid mechanics Acoustics Electromagnetic

3. Overview of FEM The FEM is a numerical method for solving a system of governing equations over the domain of a continuous physical system. 구조물을 유한 개의 작은 요소 (Element) 들로 나누고 요소들을 연결하는 절점 (Node) 들의 변위를 미지수로 하는 연립방정식을 계산 함으로써 변위, 변형률, 응력 등을 구하는 수치해법

4. Steps 1.Small elements subdivide the solid 2.Elements assemble through points on each elements called nodes 3.Equations for each element are the function of the unknown nodal values 4.Equations are combined and solved by numerical method

5. 1D Spring Structure Elements, E Nodes, N Displacements of each node, u Applied force, F N1N1 N2N2 N3N3 E2E2 E1E1 F

6. 1D Spring Element Equations for each element NiNi NjNj EpEp f pj f pi

7. Combined Equation Internal force, f External force, F Combined Equation

8. Solution Node 1 is fixed, u 1 =0 External force of node 2 is 0 External force of node 3 is F

9. 3D Solids Stiffness matrix k

10. 3D Solids A linear tetrahedron elements The assumed displacement interpolation

11. 3D Solids A quadratic tetrahedron The assumed displacement interpolation

12. 3D Solids A linear and quadratic hexahedron elements

13. The Analysis Step