# Tutorial 4b – FE-plate problem

In this tutorial we use Fesslix to analyze a finite element plate (using finite elements with linear shape functions).

## 1   Mechanical model

We investigate the problem of the following linear elastic finite element plate with a hole:

Figure 1: Linear elastic finite element plate with a hole investigated in this tutorial.

where the distributed load q is 5kN/m. The Young's modulus of the plate is , and the thickness of the plate is 0.1m.

Figure 2: Finite element mesh employed in this tutorial.

## 2   Step by Step Instruction

Fesslix parameter file
#! ===============================
#! Load the FE module
#! ===============================
loadlib "fem";

#! ===============================
#! Load the FE mesh
#! ===============================
# The mesh is imported from a file.
# Different input meshes with varying resolutions are available in the sub-folder 'meshes'.

#! –––––––––––––––-
#! preliminary definitions
#! –––––––––––––––-

# Material that has Young's modulus E
isomat 0 E 21e4 nu 0;

# Load case with a multiplier of 5
loadcase 0 { factor = 5; };
# The mesh to import specifies q as 1.
# Thus, we should view the multiplier as the distributed load q; i.e., 5kN/m.

#! –––––––––––––––-
#! import the mesh
#! –––––––––––––––-

# Define constant that specifies the mesh resolution
const MESH = 2; # integer between 1 and 10 (larger integer result in a finer mesh)

# Import the mesh
# we import the file "meshes/plate_hole_2.dat", where the file-format is 'ps2Ddomesh'.
data_import("meshes/plate_hole_" & {MESH} & ".dat",ps2Ddomesh) {
material = 0; # the material-number to assign to the elements of the mesh
t = 0.1; # the thickness of the plate elements
planestress = true;
loadcase = 0; # the number of the load-case to utilize
};
# Using the format 'SOFiSTiK', we could alternatively import a SOFiSTiK mesh.

#! ===============================
#! Solve the FE-system
#! ===============================

fem assdof; # assemble degrees of freedom
fem assstf; # assemble stiffness matrix
fem assforces; # assemble forces
fem solve; # solve the system

#! ===============================
#! Post-processing
#! ===============================

# Output the vertical (wy) and horizontal (wx) displacement
# at the left (node 4) and right (node 3) upper corner of the plate:
funplot nodeu([4,wy]), nodeu([3,wy]), nodeu([4,wx]), nodeu([3,wx]);

This should return a displacement of 1.16mm in vertical direction and 0.35mm in horizontal direction.

## 3   The complete input files of this tutorial

fesslix.org – Home  |  Contact  |  Impressum  |  © 2015-2017 Wolfgang Betz