Question

What is the total size of the assembled stiffness matrix of a plane elastic structure such that its finite element mesh has eight nodes and two degrees of freedom at each node?

(a) 16×16

(b) 8×8

(c) 2×2

(d) 4×4

This question was addressed to me in semester exam.

My enquiry is from Plane Elasticity in division Plane Elasticity of Finite Element Method

Answer 1

The correct choice is (a) 16×16

For explanation I would say: The size of the assembled stiffness matrix is equal to the total DOF of a structure. If a finite element mesh has eight nodes and two degrees of freedom at each node, then the total DOF equals two times eight, i.e., sixteen. Thus the order of the assembled stiffness matrix is 16×16.