FAST CONVERGENT SERIES SOLUTIONS FOR THERMAL BENDING OF THIN RECTANGULAR PLATES

Thermally induced bending of thin rectangular plates with one clamped and three simply supported edges is studied in detail for the case of a spacewise constant thermal moment. Using this sample problem, it is demonstrated that classical series representations for thermally induced bending moments and shear forces may exhibit numerical instabilities, slow convergence, and divergence. Fast convergent solutions are developed by replacing hyperbolic functions in the classical series representations by means of exponential functions with a negative argument and by utilizing Kummer's transformation. Divergence is overcome using Cesaro's generalized C₁-summation method. The presented series solutions are checked numerically via finite element computations. Symbolic computation is used to derive and to evaluate the series solutions and to derive limiting values at the plate corners. For practical use, tables and graphical representations of results are presented in the form ofCzerny's Tables for force-loaded rectangular plates.