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. – (Б-ка гидротехника и гидроэнергетика; Вып. 70). Стр. 115-121.
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 beam-wall (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 single-noded, one-sided 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 |
uE, mm |
23.473 |
23.473 |
0.00 |
wE, mm |
2.2222 |
2.2222 |
0.00 |
|
2 |
uE, mm |
23.473 |
23.460 |
0.055 |
wE, mm |
2.2222 |
2.2204 |
0.081 |