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 induc ed bending moments and shear forces may exhibit numerical instabilitie s, slow convergence, and divergence. Fast convergent solutions are dev eloped by replacing hyperbolic functions in the classical series repre sentations by means of exponential functions with a negative argument and by utilizing Kummer's transformation. Divergence is overcome using Cesaro's generalized C-1-summation method. The presented series solut ions are checked numerically via finite element computations. Symbolic computation ir used to derive and to evaluate the series solutions an d to derive limiting values at the plate corners. For practical use, t ables and graphical representations of results are presented in the fo rm of Czerny's Tables for force-loaded rectangular plates.