The Finite Difference Approximation Interpolating function F (x, y) The next step is to transform the differential equations into finiteĭifference equations. In the following equations, the primes are omitted: (10) then the non-dimensional dynamic plate equations are obtained.

Substituting equation (11) into equations (6), (7), (8), (9) and The plate equations can be written in non-dimensional form as Hence the integrated moment equilibrium equations are: Non-dimensional plate equations The first integrated equations ofĮquilibrium can then be written in the following form: The equations concerning the analysis of plates in bending (i.e.Įquations (6), (7), (8), (9), and (10) are derived in Turvey & Osman The Plate Equations Dimensional plate equations The iterations continue until the desiredĪccuracy is achieved. Subsequent iterationsįollow the same steps. Resultants and stress couples are computed and the appropriateīoundary conditions for stresses are applied. Satisfaction of the displacement boundary conditions, the stress In the first iteration, the velocities are obtained fromĮquation (4), and the displacements from equation (5). Velocities, displacements, and stresses equal to zero or any suitable Iterative procedure begins at time t=0 with all initial values of the The formulation is completed by computing the stress resultantsĪnd stress couples from the known displacement field. Is referred to as a displacement, are the velocityĪnd acceleration respectively, and k are the inertia and dampingĬoefficients respectively, and t is time. Where f is a function of the stress resultants and couples, u The DRM formulae begin with the dynamic equation, which can

In finite difference form and the solution is obtained by an Method, the equations of equilibrium are converted to dynamicĮquations by adding damping and inertia terms. See Rushton KR, Cassell AC & Hobbs RE, Day AS. The DRM method was first proposed and developed in 1960 Relaxation (DRM) Method, which is a numerical technique, is In the present work, finite differences coupled with dynamic

Numerical method of relaxation