Exact deflection expressions for a thin solid circular plate loaded by periphery couples

A mechanical analysis is carried out for a thin, solid, circular plate, def lected by a series of periphery-concentrated couples with a radial or circu mferential axis. Although such couples need not be of equal intensity or an gularly equispaced, they must constitute a self-equilibrated system of coup les. This problem is decomposed into a combination of two basic models, the first of which considers a single periphery couple with a radial axis, and the second addresses an edge couple with a circumferential axis. In both m odels the concentrated border couple is equilibrated by a sinusoidal bounda ry line load of proper intensity, whose wavelength equals the plate edge. W hen such basic configurations are combined, respecting the condition that t he system of concentrated couples be self-equilibrated, the effects of the sinusoidal loads cancel out, and the title problem is recovered. A classica l series solution in terms of purely flexural plate deflections is achieved for the two basic models, where the series coefficients are computed with the aid of an algebraic manipulator. For both models, the series is summed in analytical form over the whole plate region. Closed-form deflection form ulae can thus be easily derived from the two basic models for any combinati on of self-equilibrated edge couples, where some selected relevant situatio ns are developed in detail.