ASME_regional_student_conference

ASME_regional_student_conference - Finite Element Modeling...

This preview shows pages 1–10. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
FEM: Element types 1-dimensional Rod elements Beam elements 2-dimensional Shell elements 3-dimensional Tetrahedral elements Hexahedral elements

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/10/2011 for the course EML 4500 taught by Professor Schonning during the Spring '11 term at UNF.

Page1 / 39

ASME_regional_student_conference - Finite Element Modeling...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online