VM80

VM80
Plastic Response to a Suddenly Applied Constant Force

Overview

Reference:

J. M. Biggs, Introduction to Structural Dynamics, McGraw-Hill Book Co., Inc., New York, NY, 1964, pg. 69, article 2.7.

Analysis Type(s):

Full Transient Dynamic, Plastic Analysis (ANTYPE = 4)

Element Type(s):

3D Spar (or Truss) Elements (LINK180)

Structural Mass Elements (MASS21)

Input Listing:

vm80.dat

Test Case

A mass m supported on a thin rod of area A and length is subjected to the action of a suddenly applied constant force F₁. The stress-strain curve for the rod material is shown below. Determine the maximum deflection y_max and minimum deflection y_min of the mass, neglecting the mass of the rod.

Figure 111: Plastic Response Problem Sketch

Material Properties

Geometric Properties

m = 0.0259 kips-sec²/in

E = 30 x 10³ ksi

σ_yp = 162.9 ksi

= 100 in

A = 0.278 in²

F₁ = 30 kips

(see time history in Figure 111: Plastic Response Problem Sketch)

Analysis Assumptions and Modeling Notes

The initial integration time step (0.004/10 = 0.0004 sec) is chosen small enough to allow the initial step change in acceleration to be followed reasonably well. The final integration time step ((0.14-.004)/68 = 0.002 sec) is based on 1/60 of the period to produce sufficient printout for the theoretical comparison. The final time of 0.14 sec allows slightly more than 1 cycle of vibration to be followed. POST26 is used to extract results from the solution phase.

Results Comparison

	Target	Mechanical APDL [1]	Ratio
y_max, in	0.806	0.804	0.998
Time, sec	0.0669	0.0680	1.016
y_min, in	0.438 [2]	0.438	0.999
Time, sec	0.122 [2]	0.122	1.000

Mechanical APDL printout does not occur at theoretical time point given. Comparison (ratio) is therefore made with closest Mechanical APDL time and theoretical time point given.
Based on graphical values.

Figure 112: Displacement vs. Time Display