Asymptotical optimal modeling of plate bending on an elastic basis under longitudinal and transverse loading

Abstract

In this paper, we use a mixed boundary-value problem to describe the deflection of a plate under longitudinal and transverse loading located on an elastic basis, with the mandatory presence of a Dirichlet boundary condition. We fictitiously continue the boundary-value problem across the boundary with a Dirichlet condition and then approximate the continued problem using the finite element method. The numerical solution to the continued problem is iteratively approximated through numerical solutions to extended problems. The iterative extension method is asymptotically optimal for numerically solving the original problem, meaning it has unimproved asymptotic performance in terms of computation time.