5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 163
© C.G. Daley
Topic 16 Overview of Finite Element Theory
Introduction
In this chapter we will
• introduce the 2D finite element called the constant stress triangle
(cst)
• show how to derive the element stiffness and all output values from
energy considerations
~~~~~~~~~~~~~~~~~~~~
Finite element method
Recall that for a beam, we can relate the end loads
by a stiffness equation in matrix form;
{ F } = [ K ]{ x}
We can find the K terms for a beam by solving the
beam bending equation for various end
movements. To find the displacement of some
point along the beam (at x ) we could solve the
system for the displaced shape. We would find that
the displacements would be;
dx = d + x d − d )
(why so simple?)
and
1
( 4 1