Yield-line elements: for elastic bending of plates and slabs

Abstract

A new four-node rectangular element is proposed for the elastic analysis of plates in bending. This element has been formulated in view of the complex nature of existing nonlinear theory. The elastic theory developed in this paper has been derived in a form that allows a natural progression to plastic theory. The proposed method is mixed in the sense that moments and out of plane deflections are chosen as the unknowns. The solution matrix is developed from flexibility and equilibrium equations. Flexibility equations (expressing the relationship between the rotations and nodal moments) assume a partial quadratic moment field and are equated to obtain interelement compatibility. Equilibrium equations are formulated from virtual work expressions used in yield-line theory that are modified to include the twisting moment. For one-way plate action (single curvature), the solution is exact irrespective of the aspect ratio or the number of elements. For two-way action (double curvature), acceptable accuracy is achieved. Comparisons with exact solutions and the displacement method are included to indicate the accuracy of the proposed element.