Question

In a force-displacement framework, why is stiffness of an element represented in matrix form?

Answer 1

Stiffness is the force required to cause a unit displacement or deformation in a body. If body is considered in actual condition then it has multiple degree of freedom. So it will give as many stiffness terms as of degree of freedom. So during nodal analysis of any structure with multi degree of freedom , stiffness In terms of matrix is required to establish a relationship between applied force and deformation.

So in FEM, during nodal analysis we need a stiffness matrix to find deformation I'm body.