TEST CASE 6.6 SYSTEM WITH TWO DEGREES OF FREEDOM IN THE PRESENCE OF FRICTION
Reference:
Вовкушевский А.В., Шойхет Б.А., Расчёт массивных гидротехнических сооружений с учётом раскрытия швов. – М.: Энергия, 1981. – (Бка гидротехника и гидроэнергетика; Вып. 70). Стр. 115121.
Problem description:
Bar system is loaded by two mutually perpendicular concentrated forces at point E. In this point is applied a supporting spring, which can slide in horizontal plane. Determine horizontal and vertical displacements at point E u and w respectively at follow variants:
 at first system is loaded by vertical force and after by horizontal load;
 at first system is loaded by horizontal force and after by vertical load.
Problem sketch:
Type of created problem:
Plane truss or beamwall (X, Z).
Geometric characteristics:
Rod length AE and BE: L = 1 m.
Rigid and dissipative properties:
Relative stiffness of bar АЕ: EA/L = 955 tf;
Relative stiffness of bar ВЕ: EA/L = 2.5 tf;
Axial spring stiffness: k = 10000 tf/m;
Friction coefficient: f = 0.15.
Boundary conditions:
Points A and B: X = Z = 0.
Loads:
F = 1 tf.
Model description:
The system is modeled by 2 general finite elements of spatial bar (FE type is 10) and 1 physically nonlinear singlenoded, onesided friction element (FE type is 263). For nonlinear solution, iterative process is used (number of steps is 50, minimum number of iterations is 15000).
Calculation results:
Variant 
Target value 
Analytical solution 
LIRA 10 
Deviation, % 
1 
u_{E}, mm 
23.473 
23.473 
0.00 
w_{E}, mm 
2.2222 
2.2222 
0.00 

2 
u_{E}, mm 
23.473 
23.460 
0.055 
w_{E}, mm 
2.2222 
2.2204 
0.081 