A semi-analytical analysis of the elastic buckling of cracked thin plates under axial compression using actual non-uniform stress distribution |
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Affiliation: | 1. Department of Aerospace Engineering, Semnan University, Semnan, Iran;2. Physics Department, Qom Branch, Islamic Azad University, Qom, Iran;3. 16 South Maple Street, Hartford, MI 49057-1225, USA;4. Islamic Azad University, Shahrekord Branch, Shahrekord, Iran;1. Key Laboratory of High Performance Ship Technology of Ministry of Education, Wuhan University of Technology, Wuhan, 430063, Hubei, PR China;2. Departments of Naval Architecture, Ocean and Structural Engineering, School of Transportation, Wuhan University of Technology, Wuhan, 430063, Hubei, PR China |
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Abstract: | 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. |
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Keywords: | Cracked thin plates Non-uniform stress distribution Elastic buckling Complex variable method Domain decomposition method Raleigh–Ritz energy method |
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