ASME_regional_student_conference

ASME_regional_student_conference - Finite Element Modeling...

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Finite Element Modeling and Analysis with a Biomechanical Application Alexandra Schönning, Ph.D. Mechanical Engineering University of North Florida ASME Southeast Regional XI Jacksonville, FL April 8, 2005
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Presentation overview Finite Element Modeling The process Elements and meshing Materials Boundary conditions and loads Solution process Analyzing results Biomechanical Application Objective Need for modeling the human femur Data acquisition Development of a 3- Dimensional model Data smoothing NURBS Finite element modeling Initial analysis Discussion and future efforts
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Finite Element Modeling (FEM) What is finite element modeling? It involves taking a continuous structure and “cutting” it into several smaller elements and describing each of these small elements by simple algebraic equations. These equations are then assembled for the structure and the field quantity (displacement) is solved. In which fields can it be used? Stresses Heat transfer Fluid flow Electromagnetics
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FEM: The process Determine the displacement at the material interfaces Simplify by modeling the material as springs. Co F3 = 30kN F2 = 20kN St k1 k2 F3 = 30kN F2 = 20kN n1 n2 n3
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FEM: The process Draw a FBD for each node, sum the forces, and equate to zero k1 k2 F3 = 30kN F2 = 20kN n1 n2 n3 n3 F3 Spring force2 = k2(x3-x2) ΣF = 0: -k2(x3-x2)+F3 = 0 k2*x2-k2*x3+F3 = 0 -k2*x2+k2*x3 = F3 Spring force1 = k1(x2-x1) n2 F2 Spring force2 = k2(x3-x2) ΣF = 0: -k1(x2-x1)+k2(x3-x2)+F2 = 0 -k1*x1+(k1+k2)*x2-k2*x3 = F2 n1 Spring force1 = k1(x2-x1) R ΣF = 0: R+k1(x2-x1)= 0 k1*x1-k1*x2 = R
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FEM: The process Re-write equations in matrix form k1*x1-k1*x2 = R (node 1) -k1*x1+(k1+k2)*x2-k2*x3 = F2 (node 2) -k2*x2+k2*x3 = F3 (node 3) k1 k1 - 0 k1 - k1 k2 + k2 - 0 k2 - k2 x1 x2 x3 R F2 F3 Stiffness matrix [K] Displacement vector {δ} Load vector {F} k1 k2 F3 = 30kN F2 = 20kN n1 n2 n3
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FEM: The process Apply boundary conditions and solve At left boundary Zero displacement (x1=0) Simplify matrix equation Plug in values and solve k1 k2 + k2 - k2 - k2 x2 x1 F2 F3 k1 k2 F3 = 30kN F2 = 20kN n1 n2 n3 k1=40 MN/m k2 = 60 MN/m x2 x1 40 60 + 60 - 60 - 60 1 - 20 30 = x2 x1 1.25 1.75 = x3 x3 x3
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FEM: The process The continuous model was cut into 2 smaller elements An algebraic stiffness equation was developed at each node The algebraic equations were assembled and solved This process can be applied for complicated system with the help of a finite element software
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FEM: Element types 1-dimensional Rod elements Beam elements 2-dimensional Shell elements 3-dimensional Tetrahedral elements Hexahedral elements
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This note was uploaded on 07/10/2011 for the course EML 4500 taught by Professor Schonning during the Spring '11 term at UNF.

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ASME_regional_student_conference - Finite Element Modeling...

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