MECh300H Introduction to Finite Element Methods Finite Element Analysis (F.E.A.) of 1-D Problems – Applications

Plane Truss Problems Example 1: Find forces inside each member. All members have the same length. F

Arbitrarily Oriented 1-D Bar Element on 2-D Plane Q 2, v 2  P 2, u 2 Q 1, v 1 P 1, u 1

Relationship Between Local Coordinates and Global Coordinates

Stiffness Matrix of 1-D Bar Element on 2-D Plane Q 2, v 2  P 2, u 2 Q 1, v 1 P 1, u 1

Arbitrarily Oriented 1-D Bar Element in 3-D Space  x,  x,  x are the Direction Cosines of the bar in the x-y-z coordinate system xx x xx xx y z

Stiffness Matrix of 1-D Bar Element in 3-D Space xx x xx xx y z

Matrix Assembly of Multiple Bar Elements Element I I I

Matrix Assembly of Multiple Bar Elements Element I I I

Matrix Assembly of Multiple Bar Elements Apply known boundary conditions

Solution Procedures u 2 = 4FL/5AE, v 1 = 0

Recovery of Axial Forces Element I I I

Stresses inside members Element I I I