01+02 - Introduction - FEM & FDM Flashcards
1
Q
Clinical Motivation
A
- screening for hip fracture risks in osteoporosis
- today: aBMD (areal bone mineral density) with DXA (dual-energy x-ray absorptiometry) scan
- limitations: high variability, low sensitivity and specificity => poor screening accuracy + ineffective preventive treatment
2
Q
Preventive care of osteoporosis
A
- pharmacological therapy
- hip protectors (low compliance)
- exercise (strength)
3
Q
Building organ level FEM
A
- CT image segm° -> meshing -> material mapping -> BC -> FE solution
=> discretize the solution domain + simple approx solution for each element
4
Q
How to better screen for hip fracture risk?
A
- improve FEM-based hip fracture classification performance -> models that dynamically sim sideaway fall impact
- develop accurate fall risk assessment
- improve preventive treatments
5
Q
Description of a mechanical loading problem
A
- force balance: A.rho.ü = q + dF/dx
- Hooke’s law: F = A.sigma = A.E.epsilon
- BCs + initial conditions
6
Q
Galerkin method
A
- ODE solution has polynomial form u
- def error function e = ODE(u) != 0
- residual = integr(e), total error = integr(e2)
- weighing functions w_i gives ODE weak form: integr(e.w_i) with w_i = least square weighing function de/da_i /OR/ Galerkin weighing function du/da_i
- integration by parts + NBCs and EBCs to calc displacements
7
Q
Rayleigh-Ritz method
A
use minimization of potential energy Pi = U - W
=> equivalent energy form
8
Q
Finite Element Method
A
- discretize the solution domain
- coefficients of the polynomials in the assumed solution are defined in terms of the unkn. solution at some predetermined locations = nodes
- u_i = displacement at node i; u = sum(N_i(x).u_i) = N^T.d
- N_i = interpolation/shape function = du/du_i = w_i
- k.d = r_q + r_p (stiffness, displacement, loads)
9
Q
Finite Difference Method
A
- discretize the PDE
- split the bar into N sequentially connected bars => approx 2nd derivative of ODE + BCs
- solve N+1 coupled equations
10
Q
Comparison FEM/FDM
A
- FEM discretize solution domain, good for general problems
- FDM discretize PDE, for simple regular shapes
