Rectangle with transverse loading

In this 2D wave propagation problem is investigated a cantilever plate under a uniform dynamic traction on its upper side. The triangular function of loading increases from zero at time t = 0 to P0 at t = 3, and then decreases to zero at t = 6.

The plate is fixed on its left side, with traction-free bottom and right boundary. Initial displacements and velocities are null. The initial and boundary conditions are given in solid_ic_bc.hpp file.

This problem has material properties: Young modulus E = 1, density rho = 1, and Poissons ratio 0.3, as assigned in file props.txt file.

The mesh is subdivided into 5e-3 m elements size, as defined in mesh.geo file.

The generalized alpha method is employed with rho inf 0.75 and zero acceleration, with a time step of 0.01 s (setup.txt file).

Gales results compare well with the reference solution.

Reference

Khodakarami et al. “Modeling transient elastodynamic problems using a novel semi-analytical method yielding decoupled partial differential equations” (2012) CMAME