A Chebyshev collocation multidomain method to solve the Reissner-Mindlin equations for the transient response of an anisotropic plate subjected to impact

The transient response of an anisotropic rectangular plate subjected to impact is described through a Chebyshev collocation multidomain discretization of the ReissnerÐMindlin plate equations. The trapezoidal rule is used for time-integration. The spatial collocation derivative operators are represented by matrices, and the subdomains are patched by natural and essential conditions. At each time level the resulting governing matrix equation is reduced by two consecutive block Gaussian eliminations, so that an equation for the variables at the subdomain corners has to be solved. Back-substitution gives the variables at all other collocation points. The time history as represented by computed contour plots has been compared with analytical results and with photos produced by holographic interferometry. The agreements are satisfactory