1. FINITE ELEMENT METHODS IN ENGINEERING-1 036015 Pinhas Z. Bar-Yoseph Computational Mechanics Lab. Mechanical Engineering, Technion Winter Semester Tutorial # 4 Copyright by PZ Bar-Yoseph ©

2. Finite Element mesh- 1 quadratic element Quadratic Lagrangian element

5. Imposing B.C.’s

6. Postprocessing

8. Finite element mesh- 2 quadratic elements

10. The higher the element order the higher is the bandwidth How the problem size can be significantly reduced?

11. Static condensation Given a higher order element:

14. At this point, element matrix assembly is proceeded as if the element is a linear element:

15. Finite Element mesh- 2 cubic elements

16. Higher order Lagrangian elements Lagrange polynomials:

17. cubic element

22. Finite Element mesh- 2 cubic elements