The development and use of a piece-wise continuous finite element for plate and shell analysis

The implementation of general-purpose programs for the numerical analysis of plate and shell structures calls for the adoption of finite element stiffness expressions which take account of both lateral distortion and membrane action. It is important that design-oriented programs of the above kind be perfectly general. In particular the element behavior must be independent of the choice of base axes, and not prone either to singularities or to doubts over convergence with successive mesh refinement. A procedure is presented for synthesising the latter from a three node primary element which satisfies the above requirements. Lateral distortion of an element of the kind described calls for curvature changes across its surface. The basic element proposed is conceptually subdivided into congruent sub-regions having the same curvature and twist along adjoining edges, whilst changes of curvature in directions perpendicular to the latter are allowed. Comparison with a cell of grid elements shows perfect accord for homogeneous flexure, which is the laterally deflected state to which each element must tend for a sufficiently fine mesh. The element described has been incorporated into a program based on the sub-routines which UNCLE provides. Incorporation of the element described into an advanced finite element modelling system has shown that improved accuracy, convergence and versatility are thus attainable. Reference is made to the modelling of reactor primary circuit components, particularly to establish steady state and transient thermal effects, both under normal-operating and fault conditions