Derivation of Stiffness Matrix and finite Element Equation for One Dimensional Linear bar Element

Lesson 7 of 10 • 3 upvotes • 11:57mins

Joel George

One dimensional problems are problems related to beam or bar element. A general discussion of such a kind of problem is done in this lesson. A general description of stiffness matrix, its properties and the derivation of this very stiffness matrix is done in this lesson. Apart from stiffness matrix a simplified method of derivation for finite element equation is also considered in this lesson. Determining the displacement at any point on a one dimensional element is done easily with the technique defined in this lesson Significance of shape function in deriving the stiffness matrix is defined properly in this lesson. Relation between shape function and derivative of displacement is also discussed in this lesson. This relation finds large application in solving problems when any one of the above is unknown parameter.