Plate with holes

This test case represents a multiply connected 2D domain subjected to a time- and space-dependent heat source (Hematiyan et al., 2011). Domain and boundary conditions are depicted in Figure.

The following time- and space-dependent heat source function is adopted:

g(x,y,t) = 5\times10^7xy\sin(\pi x/0.5)[1-\exp(-0.01t)]

The initial temperature is equal to zero. Plane strain assumption is taken. Material properties are: E = 210 GPa, ν = 0.3, ρ = 7850, α = 11.7·10−6 , k = 64, and c = 434.

The computational mesh has average element size of 5 · 10⁻² , for a total of 4238 nodes and 8070 elements. The time step is 0.01.

Results at the boundary point A = (0.4, 0.2) and the internal point B = (0.25, 0.1) are compared with Hematiyan et al. (2011). Time evolution of temperature and evolution of x-deformation are reported below.

Reference

Hematiyan, M., Mohammadi, M., Marin, L., & Khosravifard, A. (2011). Boundary element analysis of uncoupled transient thermo-elastic problems with time- and space-dependent heat sources. Applied Mathematics and Computation, 218 (5), 1862-1882.