Higher-order responses of three-dimensional elastic plate structures and their numerical illustration by p-FEM

The displacements of three-dimensional linearly elastic plate domains can be expanded as a compound power-series asymptotics, when the thickness parameter tends to zero. The leading term u0 in this expansion is the well-known Kirchho?–Love displacement Aeld, which is the solution to the limit case when →0. Herein, we focus our discussion on plate domains with either clamped or free lateral boundary conditions, and characterize the loading conditions for which the leading termvanishes. In these situations the Arst non-zero term uk in the expansion appears for k =2; 3 or 4 and is denoted as higher-order response of order 2; 3 or 4, respectively. We provide herein explicit loading conditions under which higher order responses in three-dimensional plate structures are visible, and demonstrate the mathematical analysis by numerical simulation using the p-version Anite element method. Owing to the need for highly accurate results and ‘needle elements’ (having extremely large aspect ratio up to 10 000), a p-version Anite element analysis is mandatory for obtaining reliable and highly accurate results