Linear strain triangular Tieme Willems Finite element method Linear strain triangular Tieme Willems

introduction Plane stress situation Normal stress and shear stress directed perpendicular to the plane (assumed to be 0) Loads act only in x-y plane In this presentation: Investigate amount of elements/ nodes Investigate aspect ration

Chapter 1, Aspect ratio Changing the aspect ratio, by increasing the amount of elements. 4 elements 8 elements 10 elements 20 elements

1.2 conclusion Exact = PL = 10000*20 EA 10*(30*10^6) Case Aspect ratio # nodes # elements FEM e-004 Exact % error 1 6 4 674.68 670 0.69 2 10 8 670.41 0.06 3 2.5 12 668.44 0.23 5 22 20 663.45 0.98 Exact = PL = 10000*20 EA 10*(30*10^6)

Chapter 2, elements Increase the amount of elements, but maintain the aspect ratio Aspect ratio 1 4 elements 16 elements 64 elements Aspect ratio 2 2 elements 8elements

Chapter 2, number of elements Increase the amount of elements, but maintain the aspect ratio More elements gives in this case at first a more accurate solution, but with 64 nodes a less accurate solution due to the distribution of force on the nodes Case Aspect ratio # nodes # elements FEM e-004 Exact % error 1 6 4 674.68 670 0.69 2 15 16 671.93 0.29 3 45 64 722.48 7.27 Case Aspect ratio # nodes # elements FEM e-004 Exact % error 1 2 4 663.70 670 0.95 10 8 670.41 0.06

Chapter 2, conclusion Increasing the amount of elements results into a more exact solution; If can distribute the forces appropriate over more notes, the result becomes more accurate; If can keep the aspect ratio close to 1 the result comes closest to the exact result; Amount of elements is situation related (meaning we should run the program with different aspect ratio to see which result comes closest to the exact)