Strip under the Action of Two Tensile Forces

Let us consider a strip of length L, loaded with two forces F, applied by normal to either of the ends. The cross-section of the strip is a rectangle of width b and height h.

Beam under the action of two tensile forces

Sought is the maximum extension.
Assume F = 1000 N, L = 0.5 m, b = 0.05 m, h = 0.02 m.
Characteristics of material have values: Young's modulus E = 2.1E+011 Pa, Poisson's ratio ν = 0.28.
Both ends of the beam are assumed free and subjected to the load F, directed normally to their faces.
To solve this study in AutoFEM Analysis, it is necessary to turn on the option "Stabilize the unfixed model" with additional stiffness equal 1.
You should check this box at the Properties dialog of Static Analysis on the page "Solving".

Beam under the action of two tensile forces, the finite element model with applied loads and restraints

The finite element model with applied loads and restraints

The analytical solution appears as:

w = ( F . L ) / ( A . E ) = 2.381E-006 m

where P – is the force, L – the beam length, E – the material Young's modulus, A = b . h - the area of the beam section.

After carrying out calculation with the help of AutoFEM, the following results are obtained:

(extension of the beam is equal to (1.1888E-006)+(1.1884E-006)=2.3755E-006 m)

Table 1.Parameters of the finite element mesh

Finite Element Type	Number of Nodes	Number of Finite Elements
linear triangle	258	420

Table 2. Result "Displacement, 0X"*

Numerical Solution Displacement 0X*, m	Analytical Solution Displacement 0X, m	Error δ =100%* \|0X* - 0X\| / \|0X\|
2.3772E-006	2.381E-006	0.16

Beam under the action of two tensile forces, Result "Displacement, 0X

*The results of numerical tests depend on the finite element mesh and may differ slightly from those given in the table.