ELASTO - PLASTIC DYNAMIC ANALYSIS OF SHELLS

Abstract

It is well known from theory of shells that classical solution of shells subjected to different type of loads involves tedious calculations and it is extremely difficult or impossible especially for shells of arbitrary shape, anisotropic material properties and elasto-plastic material behaviour. The finite element method of analysis is very much suited for the analysis of shells in general because of its flexibility in accounting for arbitrary geometry, loading, boundary conditions and variation in material behaviour and properties. In this work, the three dimensional theory of continuum mechanics has been briefly reviewed. Finite element fOrinulations based on Mindlin-Reissner hypothesis using degenerated shell element including dynamic analysis is discussed. The elasto-plastic material behaviour is included in the analysis. Elasto-plastic constitutive relationship is briefly discussed and the evaluation of elasto-plastic tangent modulus matrix based on Huber-Mises yield criterion is included. For laminated plates and shells of composite material, to consider the stiffness contribution from each layer and to represent the gradual through thickness plastification, thickness is divided into layers and numerical integration is employed through thicknes§. Dynamic behaviour of certain points of continuum structures under dynamic pulse or step loads is obtained using implicit or explicit or combined time integration schemes and are examined critically.