2. Benchmark solution#

2.1. Method used to calculate the reference solution#

This gantry was studied for the first time in 1968 by Lee [1], who proposed an analytical solution in the elastic case and neglecting the deformation energy due to normal force. Since then, several other authors have in turn studied the structure, in particular in 1984, Cichon [2] was the first to propose a solution by considering elasto-plastic behavior.

2.2. Benchmark results#

We are interested in horizontal and vertical displacements in the global coordinate system of point \(X\) for various values of the force applied.

Below is a summary table of the results obtained by Cichon as well as by Waszczyszyn and Janus-Michalska [3]. As a reference, we choose the average of these two results shown in bold.

Displacement (\(\mathrm{cm}\))

\(U\) (horizontal)

\(V\) (vertical)

\(F(N)\)

Waszczyszyn

Cichon

Average

Waszczyszyn

Cichon

Average

0.968

1,812

1,734

1,773

10,414

10,078

10,246

1,242

3,482

3,913

3.6975

15.61

16,639

16,1245

1.4153

6,281

6,711

6,496

22,305

23,344

22,8245

1,507

12,516

13,836

13,176

38,804

36,501

37.6525

1,4605

19,025

18,148

18.5865

44,18

42,543

43,3615

1,4006

23,104

23,073

23,0885

49,262

47,374

48,318

1,3151

28,998

28,303

28,6505

53,012

51,102

52,057

1,1062

39,266

37,765

38,5155

58,904

56,181

57,5425

0.9275

46,871

44,831

45,851

61,775

58,442

60,1085

2.3. Uncertainty about the solution#

Between 1 and 5% (maximum relative difference to the mean of the results).

2.4. Bibliographical references#

  1. Lee S., Manuel F.S., and Rossow E.C., « Large deflections and stability of elastic frames. » J. Engrg. Mech. Div., ASCE, 1968; EM2, 521-547.

  2. Cz cichon. « Large displacements in-plane analysis of elasto-plastic frames ». Comp Struct 1984; 19,737-45.

  3. Waszczyszyn Z., Janus-Michalska M. « Numerical approach to the “exact’finite element analysis of in-plane finite displacements of framed structures ». Compute. Struct. 1998; 69, 525-535.