Demosthenes Talaslidis

A simple finite element for elastic-plastic deformations of shells

Abstract The quadrilateral element of this paper is especially suited to the behavior of elastoplastic shells. It combines the simplicity needed in nonlinear analyses with a competitive accuracy. The elemental approximation shares some common features with an earlier one applied to hookean shells [1], but incorporates an important modification which leads to further simplifications and provides a mechanism for the progressive yielding within an element. The element is derived via the Hu-Washizu functional, which admits independent approximations of all basic variables. The elimination of strains and stresses results in a displacement formulation with all the desired properties, a positive-definite matrix and convergence. Some properties of the elemental matrices are outlined and special considerations are given to plasticity. Numerical tests upon plates and shells demonstrate the efficiency of the element. Finally, some distinctions are drawn between our model and certain ‘mixed’ elements.

The linear isoparametric triangular element: theory and application

Abstract The aim of the present paper is to set forth, in a simple and consistent manner, the mechanical and computational features of the linear isoparametric triangular element. Emphasis is placed upon those mechanical attributes which are important in deriving finite element formulations. The linear isoparametric triangle is treated in a very direct manner. The kinematic features of the linear fields are identified. Homogeneous and higher order deformation modes are uncoupled by appropriate approximations of the stresses and strains. Consistent relations are obtained via the Hu-Washizu theorem. The resulting model is fully consistent with the Reissner continuum theory and is well suited for thick plates and shells. By means of discrete constraints the shear-deformable element is reduced to one which aorresponds to the Kirchhoff-Love continuum theory.

Static and dynamic analysis of kirchhoff shells based on a mixed finite element formulation

Abstract Mixed curved shell elements are presented for the static and free vibration analysis of arbitrary Kirchhoff shells. Following derivation of the appropriate generalized linear element matrix and the consistent mass matrix, the properties of mixed models when applied to static and dynamic analysis of Kirchhoff shells are discussed. An outline of solution algorithms which take the special properties of generalized variational principles into consideration is given. Several numerical plate and shell examples demonstrate the applicability of the method.