A semi-analytical analysis of the elastic buckling of cracked thin plates under axial compression using actual non-uniform stress distribution

• Published in: Thin-walled structures Vol. 73; pp. 229 - 241
• Main Authors: Pan, Zuxing, Cheng, Yuansheng, Liu, Jun
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.12.2013
• Subjects: Boundary conditions; Complex variable method; Cracked thin plates; Cracks; Deflection; Domain decomposition method; Elastic buckling; Mathematical analysis; Mathematical models; Non-uniform stress distribution; Raleigh–Ritz energy method; Shape functions; Stress concentration; Stress distribution; Thin plates; Cracked thin plates; Non-uniform stress distribution; Raleigh–Ritz energy method; Elastic buckling; Domain decomposition method; Complex variable method
• ISSN: 0263-8231; 1879-3223
• DOI: 10.1016/j.tws.2013.08.007

An improved hybrid semi-analytical method for calculating elastic buckling load of a thin plate with a central straight through-thickness crack subject to axial compression is proposed. In the study, the actual non-uniform in-plane stress distribution is firstly conducted by using Muskhelishvili's complex variable formulation in conjunction with boundary collocation method. A deflection shape function, satisfying not only the outer boundary conditions but also the inner boundary conditions of the crack edges, is obtained by using domain decomposition method. Finally the buckling load of a cracked plate using Raleigh–Ritz energy method is calculated based on the actual in-plane stress distribution and the reasonable deflection shape function obtained. The effects of crack length, plate's aspect ratio are studied for thin plates with different boundary conditions. Results obtained from the proposed method are in good agreement with the existing numerical results and experimental ones. It is finally shown that the proposed method, based on a correct non-uniform in-plane stress distribution, is more accurate than the few existing analytical methods based on a uniform in-plane stress distribution. •An improved hybrid method for compressive buckling of cracked plates is proposed.•The actual non-uniform in-plane stress distribution is considered.•The importance of the actual stresses on buckling of cracked plates is shown.•Reason for the conflict of some existing analytical and numerical results is given.