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The Finite Element Method

The Finite Element Method. Prof. Su-Jin Kim Gyeongsang National University. Applications of FEM. Structural analysis Heat transfer Fluid mechanics Acoustics Electromagnetic. Overview of FEM.

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The Finite Element Method

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  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 계산함으로써 변위, 변형률, 응력 등을 구하는 수치해법

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

  5. 1D Spring Structure Elements, E Nodes, N Displacements of each node, u Applied force, F E2 E1 F N3 N2 N1

  6. 1D Spring Element Equations for each element Ep Ni Nj fpj fpi

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

  8. Solution Node 1 is fixed, u1=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

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