Elastic-plastic analysis of complex structures using finite element method with Lagrange multipliers

The method of analysis developed in this paper is designed to overcome the difficulty by reducing the number of unknowns in the simultaneous equation regarding the finite element method. In other words, superior elements typified by three-dimensional isoparametric ones are employed only at the important regions of stress and strain concentration in the whole structure, while the other part of the structure is discretized with the use of one- or two-dimensional lower class of elements, e.g. beam, plate and shell elements. In order to combine the different types of elements together, the fictitious elements without occupied volume, the characteristics of which are determined by employing the Lagrange multiplier concept, are introduced between the real elements. Unknown parameters of the resulting simultaneous equation consist of usual nodal displacements of the whole structure and the generalized coordinate concerning the Lagrange multipliers for the fictitious elements. Several numerical examples are solved using the above theory. Comparisons of the present method with the conventional one where three-dimensional elements are used throughout the structure indicate significant reductions in the computer storage and computational time without loss of accuracy at the important region of stress and strain concentration. It is also found that the present solution is compared favourably with experimental value for local elastic-plastic behavior at the corner point of thick pipe subjected to shearing force at the end