Discrete-Element Analysis for Discontinuous Plates

The mathematical details are applicable for plates and slabs with freely variable foundation support including holes in the subgrade. Anisotropic elasticity which governs the behavior of orthotropic plates is used to develop the necessary equations. The method is not limited by discontinuities, and uses an efficient alternating-direction iteration means of solving the resulting equations. The method allows considerable freedom in configuration, loading, flexural stiffness, and boundary conditions. Three principal features are incorporated into the method: (1) The plate is defined by a discrete-element model consisting of bars, springs, elastic blocks, and torsion bars, which are further grouped for analysis into orthogonal systems of beam-column elements and forces; (2) each individual line-element of the two dimensional system is solved rapidly and directly by recursive techniques; and (3) an alternating-direction iterative method is utilized for coordinating the solution of the individual line-elements into the slab solution. The computer program utilizes the developed equations and techniques. Several sample problems illustrate the generality of the method, and the use of the computer program. The results compare well with closed-form solutions.