Abstract
A method for analyzing densely perforated plates loaded in pure bending is described. The problem is solved based on the plate theory using a structurally orthotropic model. The parameters of the orthotropic material in the form of stiffness reduction coefficients were determined from the solution of the problem of deformation of a cyclically reiterating structural element with different perforation densities (porosity) loaded in tension and shear. The structural element was analyzed using the methods of continuum mechanics and the theory of Timoshenko-type shells and plates. As a result, stiffness reduction coefficients were obtained for different porosity values, and the scope of applicability of the theory of plates for such problems was assessed. The numerical results obtained were compared with the analytical evaluations of E.I. Grigolyuk and L.A. Filshtinskiy. The numerically obtained orthotropy parameters were verified by solving the problem of bending of a plate with a single row of perforations. It is shown that the use of finite elements of a structurally orthotropic shell with the parameters determined from the solution of a 3D problem of tension and shear of the structural element is justified in bending problems with long waves. Stress distribution in the perforation area of densely perforated plates was studied for different thicknesses and porosities in the geometrically linear and nonlinear formulations. Stress concentration coefficient values were obtained as a function of porosity and thickness of the pate for tension and bending. Keywords: densely perforated plate, orthotropic material, finite element method, pure bending, stress concentration coefficient.
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