Page 28 - Finite Element Modeling and Simulations with ANSYS Workbench

Introduction 13

Then we write the element stiffness matrix for each element

u 4 u 2
 k 1 − k 1
1 k =   ,
 − k 1 k 1 
u 2 u 3
 k 2 − k 2 
2 k =   ,
 − k 2 k 2 
u 3 u 5
k
 k 3 −k 3 
3 k =   ,
 − k 3 k 3 
u 2 u 1
 k 4 − k 4 
k 4 =  − 
 k 4 k 4 

Finally, applying the superposition method, we obtain the global stiffness matrix as
follows:

u 1 u 2 u 3 u 4 u 5
 k 4 − k 4 0 0 0 
 
 − k 4 k 1 + k 2 + k 4 − k 2 − k 1 0 
K =  0 − k 2 k 2 + k 3 0 − 
k 3
 
 0 − k 1 0 k 1 0 0 
 0 0 −k 0 k 
 3 3 
The matrix is symmetric, banded, but singular, as it should be.
After introducing the basic concepts, the section below introduces you to one of the
general-purpose finite element software tools—ANSYS Workbench.

1.3 Overview of ANSYS Workbench
ANSYS Workbench is a simulation platform that enables users to model and solve a wide
range of engineering problems using the FEA. It provides access to the ANSYS family
of design and analysis modules in an integrated simulation environment. This section
gives a brief overview of the different elements in the ANSYS Workbench simulation envi-
ronment or the graphical-user interface (GUI). Readers are referred to ANSYS Workbench
user’s guide [2] for more detailed information.

1.3.1 The User Interface

The Workbench interface is composed primarily of a Toolbox region and a Project Schematic
region (Figure 1.8). The main use of the two regions is described next.