文档介绍：MSC/PATRAN TUTORIAL # 1
MODELING A BAR PROBLEM
I. THE PHYSICAL PROBLEM
In the simple bar problem below, there are three separate sections of the bar.
Each section has different properties. The following properties apply, Al
àAluminum, St à Steel, E for Steel = 200 E9 Pa, E for Al = 70 E9 Pa
All Bars have square cross section and the right and left ends of the bar are
built in. The force "F" = 9000 Newtons
F
Al Al
St
The 2-d model of the problem is shown below.
Al F
St 1 cm
Al
2 cm
5cm
F
5 cm 5 cm 10cm
2
II. THINKING ABOUT THE MECHANICS
The analytic solution for stresses and displacements for this problem is readily available.
Any Mechanics of Materials text will provide equations for the displacements and
stresses throughout the bar. The problem is indeterminant because there are two
reactions (one at each wall) and only one relevant equilibrium equation ( å Fx = 0).
Therefore, it is necessary to use the Mechanics of materials (stress and or displacement)
equations as well as the force equilibrium equations to solve the problem.
The normal stress due to axial loading is given by :
σ= P , where P is the internal force in the axial direction and A is the cross sectional
xx A
PL
area of the bar. The displacements puted from u = here L is the bar’s length
AE
and E is the Elastic (Young’s) modulus.
Some basic questions to consider before creating putational model are:
1. Where will the stresses be tensile and where will they pressive?
2. What will be the magnitude and direction of the reaction forces?
3. Where will the displacements be greatest?
4. How do the displacements vary along the length (linear, quadratic etc.)?
5. What will the local effect of the concentrated load be on the stresses?
6. Is the model fully constrained from rigid body rotations and displacements?
Answering these questions qualitatively, along with the quantitative analytical solutions
for the stresses and displacements, will provid