Analysis of Elastic-Plastic Buckling of a Thin Rectangular Plate, Considering Nonlinear Strain Terms Roy N Mushonga Faculty of Engineering, Isfahan University of Technology, Iran Faculty of Engineering, University of Zimbabwe, Harare, Zimbabwe [email protected] Mehdi Salmani-Tehrani Faculty of Engineering, Isfahan University of Technology, Iran Luxmore Madiye Faculty of Engineering, University of Zimbabwe, Harare, Zimbabwe [email protected] Loice Gudukeya Faculty of Engineering, University of Zimbabwe, Harare, Zimbabwe Faculty of Engineering and the Built Environment, University of Johannesburg, Johannesburg, South Africa [email protected] Abstract The present study is concerned with the elastic/plastic buckling of a thin rectangular plate when nonlinear strain terms are put into consideration in the equation of uniqueness. Buckling analyses of the plate was placed under different loading conditions i.e. uniaxial compression, biaxial compression and pure shear loading. The equilibrium and stability equations are derived and analysed based on the elastic theory presented by Hooke’s law and two theories of plasticity i.e. deformation theory (DT) and incremental theory (IT). Rayleigh-Ritz method was used as a discretization technique to solve the buckling of plate equation. A comparison of results between nonlinear strains versus linear strains was carried out and a 6.7% difference was observed when the plate was subjected to pure shear loading. The variation between the two cases was seen to increase as boundary equations became complicated when pure shear stress was considered. Furthermore, different parameters have been discussed i.e., effects of aspect ratio, thickness to width ratio and loading ratios, effect of different boundary condition and the type of plasticity theory considered. Keywords Elastic-Plastic Buckling, Rectangular Thin Plate, Nonlinear Strain Terms, Incremental Theory, Deformation Theory 1. Introduction Plates and plated structures have a variety of purposes in engineering applications and are frequently subjected to different boundary conditions and loadings. The vast majority of applications of plates is seen in aerospace, marine engineering and civil structures such as bridges. Due to their relatively small thickness to length ratio, the design strength of these structures is commonly governed by their buckling capacities. Buckling is as a phenomenon in which a structure undergoes visibly large transverse deflection in one of the possible instability modes. Buckling of a structural component may affect the strength or stiffness of the whole structure and may even result in an unexpected global failure of the structure. Therefore, it is of paramount importance to know buckling capacities of such structures in order to avoid premature failure. Bryan (1891) was one of the pioneers who first carried out a theoretical examination of buckling of plates. In his research, he analysed the buckling of rectangular plate under uniform uniaxial loading using the energy criterion of stability. Many researchers have seen that the application of the energy criterion proved to be a very useful analytical tool for the buckling problems which could not be solved by conventional analytical methods. Many of them have studied the buckling of a plate with various shapes, loading and boundary conditions using a variety of methods for analysis. In elastic buckling research, it has been assumed that buckling occurs when the critical load remains below the elastic limit of the plate material. In real life situation the plate may be stressed beyond the elastic limit before buckling Proceedings of the 2nd African International Conference on Industrial Engineering and Operations Management Harare, Zimbabwe, December 7-10, 2020 © IEOM Society International 1654
Analysis of Elastic-Plastic Buckling of a Thin Rectangular Plate, Considering Nonlinear Strain Terms
Jun 20, 2023
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