Тест 7.7 Dynamic one-sided contact problem for a square plate

Numerical solution: П. Panagiotopoulos Inequalities in Mechanics and their Applications, Moscow: Mir, 1989, pp. 408 - 415.

Geometry::

а = 1 м b = 4 м; h = 0.05 м.

Material characteristics: Е=4 х 10⁷ т/м², ν = 0.16, ρg = 2.5 т/м²,g=9.81 м/с², coefficient of elasticity of a one-sided base k = 3 x 10⁴ т/м³.

Boundary conditions: By square RSPQ - one-sided elastic base (compression)

Loads: Along the contour of the plate - instantly applied constant force distributed along the line P = 5 т/м;
в точке А – Р₁ = 200 т; м
в точке Е (и симметричных) – сила P


The structure was modeled with slab finite elements (FE 41) on a one-sided elastic base, 50 x 50 FE breakdown.

CALCULATION RESULTS:

Point	The desired value	Numerical solution	Calculation results (LIRA)	Uncertainty,%
A	wmax, м	3,95 х 10-2 (t = 4,9 x 10-3 c)	4,1 х 10-2 (t = 4,92 x 10-3 c)	3,8 (0,4)
D (5;5)	wmax, м	5,55 х 10-2 (t = 2 x 10-2 c)	5,99 х 10-2 (t = 2 x 10-2 c)	7,93 (0)
L (1;1)	wmax, м	6,75 х 10-3 (t = 1,5 x 10-2 c)	6,84 х 10-3 (t = 1,45 x 10-2 c)	1,33 (3,33)

Preview image: Array

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