Elasto-plastic Analysis of Plate With and Without Cut-outs

Abstract

Plates and shells are important parts of several engineering applications. Therefore analysis and design of these elements are always of interest to the engineering community. Accurate and conservative assessments of the maximum load the structure can carry, along with the equilibrium path followed in elastic and inelastic range are of utmost importance to understand accurate behavior of structures. The elasto-plastic behavior of structural elements can be modelled following mathematical theory of plasticity involving various failure criteria like von Mises , Tresca criteria. The present study is made to investigate the effect of material nonlinearity on static behavior of plate with and without cutout. A finite element formulation for plate bending problem involving isotropic hardening material following von Mises criteria has been presented. The formulations have incorporated the shear deformation of the plate. The numerical approach has been formulated in incremental form and based on the tangent stiffness concept. The analysis has been carried out following modified Newton Raphson solution technique. The coding based on the formulation has been written in MATLAB environment. A non-layered and layered plate models have been adapted to understand the real elasto-plastic behavior of the plate. The complex nonlinear behavior was graphically traced through load deflection diagrams, plastic flow diagrams at different load factors and first yield and collapse loads. The same plate problems were analyzed by using commercial software ABAQUS and results were compared and found to be in good agreement. In ABAQUS analysis were performed by taking quadrilateral shell element S8R5 with through the thickness stress integration (with three integration points) and von Mises yield criterion. The effect of shape and size of cutout on the yield, collapse loads and plastic flow patterns have been included in the research.