Reinforced openings in plastically deforming plates: A finite-difference analysis

This investigation deals with the stress and strain distribution in a large plate containing a reinforced circular hole when loaded monotonically in uniaxial tension beyond the elastic range. The hole is reinforced with a cylindrical member which is symmetrical with respect to the plate to which it is continuously joined. Consideration is given to various degrees of plastic deformation of plate and reinforcement corresponding to various uniaxial tension loads. Whole-field analyses of the reinforcement in cylindrical co-ordinates and of the plate in plane polar co-ordinates are obtained by the finite-difference method in which the governing equilibrium equations are expressed in terms of displacements and plastic strains. Deformation theory of plasticity is employed. Limitations of the ‘compact’ reinforcement assumption result from the subsequent whole-field investigation. Results are obtained for material of a specific stress-strain curve so that strain-gauge results could be compared with the strains predicted by the finite-difference analysis. It is demonstrated that the compact reinforcement is adequate for analysis of the plate, but for a very significant range of reinforcement geometry it neglects a more serious stress concentration in the reinforcement. For the whole-field analysis, prediction of first yield is made for four critical points: tensile-stress concentration in the plate; tensile-stress concentration in the reinforcement; and shear-stress concentrations in both plate and reinforcement at their joint.