This chapter deals with bar elements. Using these simple elements, an introduction to interpolation functions and their use for stiffness matrix derivation is presented. The developed stiffness matrices are modified to perform FEM modeling of piping networks. Integrated analytical solutions on how to derive the local stiffness matrices, how to expand them into the degrees of freedom of the whole structure, how to assemble the expanded stiffness matrices, and how to compose the structural matrix equation incorporating both the global stiffness matrix and the submatrices containing the boundary conditions, are provided. In addition to the above analytical procedures, an implementation of the CALFEM/MATLAB on the analysis of a hydraulic network is also presented.
[1]
O. C. Zienkiewicz,et al.
The Finite Element Method for Solid and Structural Mechanics
,
2013
.
[2]
R. Cook,et al.
Concepts and Applications of Finite Element Analysis
,
1974
.
[3]
D. Logan.
A First Course in the Finite Element Method
,
2001
.
[4]
Göran Sandberg,et al.
CALFEM - A finite element toolbox, version 3.4
,
2004
.
[5]
Assem S. Deif,et al.
Advanced matrix theory for scientists and engineers
,
1990
.
[6]
T. Belytschko,et al.
A first course in finite elements
,
2007
.