Why learn FEM ? FEM literacy Not as a black box Expensive commercial package New phenomena, material, process FEM, DEM, BEM

EA Pl = d P Ax=b K U = F p u1 u2

C, Fortran, Basic, Pascal MATLAB COSMOS/M, Nastran, LUSAS, Abacus etc.

Exact Solution Experiment Approximate Solution TITLE OF PROBLEM <Beam Analysis> EXAMPLE 1 NN NE NM NDIM NEN NDN 8 7 1 1 2 2 ND NL NCH NPR NMPC 2 1 1 1 0 Node# Coordinates 1 0 2 .1 3 .2 4 .3 5 .4 6 .5 7 .6 8 .626 Elem# N1 N2 Mat# Mom_Inertia) 1 1 2 1 4.5e-11 2 2 3 1 4.5e-11 3 3 4 1 4.5e-11 4 4 5 1 4.5e-11 5 5 6 1 4.5e-11 6 6 7 1 4.5e-11 7 7 8 1 4.5e-11 DOF# Displacement 1 0 15 0 DOF# Load 7 -10 MAT# PROP1 1 200e9 Approximate Solution Experiment

Results from the analysis Activity Deflection at loading (mm) Exact solution 4.83 Experiment 4.55 (6 % error) Approximate solution 5.03 (4 % error) Data: P = 1 kg, E = 200 GPa, L = 226 mm, a = 400 mm

Finite Element for Adaptive Crack Propagation Using Parallel Processing Worker Worker Master Worker Server-client Architecture Parallel Processing for Adaptive Crack Propagation using three processor

Master Worker