Application of an orthotropic macro-strip plate element with stiffness discontinuities

Abstract

Several plate-type civil structures exhibit stiffness and/or cross-sectional discontinuities in one direction. Examples for concrete slabs include ribbed plates, slabs with drop panels, and slabs with varying cross-section or reinforcement. Similarly, longitudinal stress-laminated timber bridge decks stiffened with thin steel plates present suddent stiffness discontinuities along the deck width. When modeling such complex structures with conventional finite elements, the drastic stiffness discontinuities can lead to ill-conditioning of the stiffness matrix, inaccurate results, and even singularity. To overcome this problem, we present in this paper the formulation and application of an orthotropic macro-strip element suitable to model rectangular plates with discontinuities along one principal axis. The stiffness jumps are described by unit step functions, which are used to derive stiffness distributions for any number of segments within the element. The number of segments selected does not increase the element degrees of freedom, and in contrast to the requirements of a finite element mesh with conventional plate or solid elements, the present model requires only a few macro-elements to model a structure. The system model is assembled and solved with the mathematics software MAPLE. The present model is validated with finite element solutions using solid and plate elements. As a practical application, the present model is used to predict displacements for three stress-laminated timber bridges currently in service, and the results compare closely with field-measured values.