Numerical Methods in Structural Dynamics

Abstract

The dynamic analysis of a structure subjected to a random forcing function from a source such as earthquake, blast, or wind requires the use of a numerical integration technique. The efficiency and accuracy of the technique employed is of great importance for both research and practical design. The more effective methods of numerical integration belong to the category designated as ‘predictor-corrector’ methods. A systematic method is presented for the derivation of single-point and multiple-point predictor-corrector formulae. It is shown that most of the methods of numerical integration presently employed in structural dynamics are single-point predictor-corrector methods. A scheme of iteration is usually employed for the solution of the difference equations obtained by the application of these methods. It is shown that for problems in structural dynamics, it is not necessary to use an iterative scheme; a process of elimination is feasible and also gives considerable economy in computation time. It is further shown that the choice of an appropriate multi-point method for the numerical integration of the equations of motion of an elastic system can lead to a considerable saving in computation time and cost. One such multi-point method is presented, and its truncation error and stability are examined.