Analysis of thick perforated slabs using an energy method

The work presents an analysis of thick perforated slabs as a basis for analysis of thick plates with a square array of circular holes. The problem is solved approximately by the Rayleigh-Ritz method, modified in order to facilitate the handling of kinematic boundary conditions by adding a fictitious boundary domain with linear coordinate functions to the slab domain.

The technique is developed for a square slab with a central, circular hole, and numerical results for a number of slab configurations involving both static and kinematic boundary conditions are shown. Comparison with existing solutions to problems of uniaxial tension is made and the agreement is found to be good. Effective elastic moduli are computed for one cell of an infinite sheet, and the results agree well with known results. Stress concentrations around the hole in a thick square slab to those of results for a hole in an infinite thick plate. The results deviate less than 15% from the results of a finite thin plate and the deviations are largest near the slab surfaces.

The merits of the present technique are discussed and compared with those of the finite element method. The main advantages of the present method are its hierarchal properties and continuous stress results while the main disadvantage is, that it is restricted to domains of regular shapes. Although the boundary domain technique has performed satisfactorily the modified Rayleigh-Ritz technique should still be considered a special purpose method.