Rigidly fixed semi-plane – gales.pi.ingv.it

Rigidily fixed semi-plane

This 2D benchmark consists in a semi-plane with fixed deformations at infinity and at the boundary, that is exposed to a stationary local smooth perturbation on the boundary itself (Rychahivskyy & Tokovyy, 2008). The imposed temperature is a combination of parabolic and exponential functions:

T|_{y=0} = 10(x^2-0.5)\exp(-x^2)

The thermal and mechanical evolutions are computed until the steady state, over which the comparison with the analytical solution is performed.

The domain is a rectangle of width 100 and height 50, meshed with triangular elements of average size 5, with 0.01 size refinement at the boundary. The mesh is composed of 34293 nodes and 66278 elements. Temporal evolution is computed with a time step of 0.1 s.

Plain strain conditions are prescribed. Mechanical properties of the medium are Young modulus E = 10 GPa, Poisson’s ratio ν = 0.25, thermal expansion coefficient α = 0.01, with zero reference temperature. Thermal properties are thermal conductivity k = 1, specific heat c = 1 and density ρ = 1.

Contours of temperature at steady state from the present computations and from the reference solution (Rychahivskyy & Tokovyy, 2008) are compared in Figure:

Horizontal and vertical deformations are depicted against the reference solution:

Finally, stresses are compared:

Reference

Andriy V. Rychahivskyy & Yuriy V. Tokovyy (2008) Correct Analytical Solutions to the Thermoelasticity Problems in a Semi-Plane, Journal of Thermal Stresses, 31:11, 1125-1145, DOI: 10.1080/01495730802250854