Shape Functions in FEM — From 4 Nodes to 9 Nodes (Step-by-Step)
Learn how to derive the shape functions for quadrilateral elements with 4 to 9 nodes in this step-by-step Finite Element Method (FEM) tutorial.
We start with the simplest 4-node bilinear element and build up systematically to the 9-node quadratic element. Along the way, you’ll see how each additional node modifies the existing shape functions and why adjustments are needed to satisfy interpolation rules.
🔹 Topics covered:
Shape functions for 4-node quadrilateral (bilinear element)
Adding mid-side nodes (5, 6, 7, 8) and modifying shape functions
Introducing the center node (node 9)
Ensuring shape function properties: unity and zero conditions
Complete set of shape functions for 4 to 9 nodes
This video is perfect for students, engineers, and professionals who want a clear and detailed explanation of isoparametric quadrilateral elements in FEM.
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