All courses › Finite Element Method › Assembly

Assembly

A structure is built from several elements that share nodes. Assembly places the element matrices into one global stiffness matrix, where contributions from elements sharing a node are summed at that position. The result, $K\vec u = \vec f$ , is solved for the nodal displacements.

K_{ii} = \sum_e k_{ii}^{(e)}

diagonal entry: sum of contributions from all elements at node

i

Symbols

$K$	global stiffness matrix	N/m
$k^{(e)}$	element stiffness matrix	N/m

Example

Two bar elements with $k_1 = 200$ and $k_2 = 300$ N/mm share node 2:

$K_{22} = k_1 + k_2 = 500$ N/mm.

Only elements that actually share a node contribute to the same row/column in

K

Practise bar elements and stiffness matrices for free →

← Bar element stiffness matrix · Boundary conditions and Ku = f →

Part of Finite Element Method: Bar elements and stiffness matrices.