Register

#### 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.

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