Higher Order Responses of Three-Dimensional Elastic Plate-Like Structures and their Visualization

Abstract. The displacement of three-dimensional linearly elastic plate-like domains can be expanded as a compound power series asymptotics, when the thickness parameter tends to zero. The leading term in this expansion is the well-known Kirchhoff-Love displacement eld, which is the solution to the limit case when. Herein we focus our discussion on plate-like domains with either clamped or free lateral boundary conditions, and characterize the loading conditions for which the leading term vanishes. In these situations the rst non-zero term in the expansion appears for, or and is denoted as higher-order response of order, or respectively. The mathematical analysis for higher-order responses is backed-up by numerical simulation using the-version nite element method.