Plate with hole

In this example, a square plate with a hole under a tensile load is analyzed. The plate is subject to a time-dependent tensile force T(t), which is uniform in space. The geometry, boundary conditions, and the time dependency of the load are all shown in Figures below.

The problem is analyzed under the plane stress condition with E = 100 kPa, 𝜈 = 0.3, and 𝜌 = 1kg/m³ (props.txt). The tensile load is increased from zero to T_max during a time interval of t₁ = 0.1 s. Top and bottom boundaries, along with the hole are traction-free (solid_ic_bc.hpp).

The grid has triangular elements with size 0.02 m around the hole and 0.05 m at the external boundaries (mesh.geo).

Time step is 1e-4 s, with generalized alpha method employing 0.75 of rho inf and zero acceleration (setup.txt).

Gales results and reference solution are reported below.

References

Khoshroo et al. “Two-dimensional elastodynamic and free vibration analysis by the method of fundamental solutions” (2020) Engineering Analysis with Boundary Elements