Dynamic response of structural plates undergoing moving loads and thermal strains using Finite Elements–Part 2

A wide array of basics and concepts emanate from and can be easily understood from application of simple beams, straight and/or curved under the influence of moving mechanical loads as presented in Part 1 of this article. Although the basics are essentially the same, another level of complexity arises due to the added dimension for plates in contrast to beams which is of focus in this article in Part 2. Involving thermal effects in addition to moving mechanical loads, is yet another added degree of complexity but is not unbearable. The necessary mathematical models subjected to appropriate boundary conditions involved is presented. The numerical procedure is also presented for plates influenced by moving loads with particular attention to the Mindlin-Reisner plate theory. Thermal effects are then introduced. The class of applications include bridges, railway and subway tracks, aircraft carrier decks, etc. A variety of speeds of the moving-load problems are briefly studied along with a few cases with different temperature gradients. The finite element method in conjunction with a general-purpose time integration computational framework is employed with focus upon the MPR-EPA/MPA algorithms which seems to serve well as a tool for this class of problems. These developments provide a baseline for future research in the areas of combined transient thermo-mechanical problems using the GSSSS family of algorithms.