FINITE ELEMENT METHODS IN ENGINEERING-1 036015 Pinhas Z. Bar-Yoseph Computational Mechanics Lab. Mechanical Engineering, Technion Winter Semester Tutorial.

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Presentation transcript:

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

Finite Element mesh- 1 quadratic element Quadratic Lagrangian element

Imposing B.C.’s

Postprocessing

Finite element mesh- 2 quadratic elements

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

Static condensation Given a higher order element:

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

Finite Element mesh- 2 cubic elements

Higher order Lagrangian elements Lagrange polynomials:

cubic element

Finite Element mesh- 2 cubic elements