Use of Hyperbolic Trigonometric Series in Rectangular Cartesian Co-ordinates for Problems with Arbitrary Rectilinear Boundaries

Abstract

The effectiveness of hyperbolic trigonometric series in rectangular Cartesian co-ordinates for analysing problems with non-rectangular but rectilinear domainsis brought out in the present work. Three typical examples simply supported triangular, rhombic and parallelograrnmic plates under uniform pressure are considered and elegant solutions presented. Fourier expansion, simple collocation and least square collocation techniques are followed for the satisfaction of the boundary conditions. Numerical results for the three examples are obtained for a range of skew angles and side ratios. The convergence of important parameters like maximum deflection and maximam moments with increasing order of approximation is studied.The results show that the method is capable of providing satisfactory results with limited effort in all the cases.