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Part 1_Recap and background.pdf
- 1. FEA/CFD for Biomedical Engineering Week 3: Trusses Book: Saeed Moaveni Finite Element Analysis Theory and application with ANSYS Chapter 3
- 2. Recap
- 3. Develop Equations – FEA Analysis 1 2 k u1 u2 F1 F2 Consider equilibrium of each node Stiffness Matrix Element Force vector Element displacement vector In Matrix form 𝐴𝐴𝐴𝐴 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 1 ⇒ 𝐹𝐹1 = 𝑘𝑘𝑢𝑢1 − 𝑘𝑘𝑢𝑢2 𝐴𝐴𝐴𝐴 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 2 ⇒ 𝐹𝐹1 = −𝑘𝑘𝑢𝑢1 + 𝑘𝑘𝑢𝑢2 𝑘𝑘1 −𝑘𝑘1 −𝑘𝑘1 𝑘𝑘1 𝑢𝑢1 𝑢𝑢2 = 𝐹𝐹1 𝐹𝐹2 𝐾𝐾 𝑢𝑢 = 𝐹𝐹
- 4. Stiffness matrix is defined as the element stiffness matrix in the element coordinate system (or local system), {u} is the column matrix (vector) of nodal displacements, and { F } is the column matrix (vector) of element nodal forces. 𝐾𝐾 𝑢𝑢 = 𝐹𝐹
- 5. Processing -Define the Calculation • Using this form allows the elements forming the structure to be easily combined. • The basic form can be adapted for different physical conditions
- 6. Combine elements to form global system 𝑘𝑘1 −𝑘𝑘1 0 0 0 −𝑘𝑘1 𝑘𝑘1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 + 0 0 0 0 0 0 𝑘𝑘2 −𝑘𝑘2 0 0 0 −𝑘𝑘2 𝑘𝑘2 0 0 0 0 0 0 0 0 0 0 0 0 + 0 0 0 0 0 0 0 0 0 0 0 0 𝑘𝑘3 −𝑘𝑘3 0 0 0 −𝑘𝑘3 𝑘𝑘3 0 0 0 0 0 0 + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 𝑘𝑘4 −𝑘𝑘4 0 0 0 −𝑘𝑘4 𝑘𝑘4 𝑢𝑢1 𝑢𝑢2 𝑢𝑢3 𝑢𝑢4 𝑢𝑢5 = 𝐹𝐹1 𝐹𝐹2 𝐹𝐹3 𝐹𝐹4 𝐹𝐹5 𝑘𝑘1 −𝑘𝑘1 0 0 0 −𝑘𝑘1 𝑘𝑘1 + 𝑘𝑘2 −𝑘𝑘2 0 0 0 −𝑘𝑘2 𝑘𝑘2 + 𝑘𝑘3 −𝑘𝑘3 0 0 0 −𝑘𝑘3 𝑘𝑘3 + 𝑘𝑘4 −𝑘𝑘4 0 0 0 −𝑘𝑘4 𝑘𝑘4 𝑢𝑢1 𝑢𝑢2 𝑢𝑢3 𝑢𝑢4 𝑢𝑢5 = 𝐹𝐹1 𝐹𝐹2 𝐹𝐹3 𝐹𝐹4 𝐹𝐹5
- 7. Partition System × 107 3360 −3360 0 0 0 −3360 5880 −2520 0 0 0 −2520 4200 −1680 0 0 0 −1680 2520 −840 0 0 0 −840 840 0 𝑢𝑢2 𝑢𝑢3 𝑢𝑢4 𝑢𝑢5 = 𝑅𝑅 0 0 0 100 × 107 5880 −2520 0 0 −2520 4200 −1680 0 0 −1680 2520 −840 0 0 −840 840 𝑢𝑢2 𝑢𝑢3 𝑢𝑢4 𝑢𝑢5 = 0 0 0 100
- 8. Trusses
- 9. Truss v Beam Truss (Bar) • Axial load and motion only • Carry no moment Beam • Carry moment and rotation • Can have shear motion out of or not along length of element
- 10. Truss • An Engineering structure consisting of straight members • Connected at their ends by means of bolts, rivets, pins or welds • Trusses offer practical solutions to many engineering problems – Power transmission towers, bridges, roofs • A plane truss is defined as a truss whose members lie in a single plane • Forces must also lie in this plane • Trusses generally considered 2-force members – Internal forces act in equal and opposite directions
- 11. Trusses in Biomedical Engineering • 4WEB® patient specific segmental bone defect procedure • Ability to customize the truss implant to match the unique anatomy of an individual patient is a significant advancement in orthopaedics • The open architecture truss implant technology provides a robust scaffolding for structural support