Computation of fundamental solutions for laminated anisotropic shallow shells (Q1905531)

The shell equations considered here form an elliptic system of five partial differential equations with constant coefficients. The effect of (in-plane) anisotropy is incorporated in the constants of the constitutive relations. Applying Hörmander's method and plane wave decomposition leads to an ordinary differential equation for \(\varphi(x)\) -- the generating function for the fundamental solution. The aim is to give approximations of \(\varphi (x)\) and its derivatives with a high degree of accuracy. To this end, the \(x\)-interval is splitted, and on each subinterval the function \(\varphi (x)\) is approximated by rational functions or continued fractions.