Finite Element Methods in Engineering-1 036015 Winter Semester Lecture 8 Copyright by PZ Bar-Yoseph ©

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Finite Element Methods in Engineering Winter Semester Lecture 8 Copyright by PZ Bar-Yoseph ©

Bilinear (4-node) rectangular element FE Model for 2-D Boundary Value Problems

Assuming that the problem is symmetric w.r.t. x & y :

Uniform mesh refinement with 4-node rectangular elements

Non-uniform mesh refinement with 4-node rectangular elements

Bilinear 4-node rectangular element Bilinear interpolation on the eth rectangular element

Real element Master element

Bilinear Lagrangian Element

where

Various types of incompatible connections of finite elements. (Interelement continuity is violated along the connecting sides)

Along side 3-4:

Pascal’s triangle for bilinear and biquadratic elements

Gauss points and weights for 2-D product type Gauss-Legendre quadrature rule.