Abstract: Three of the most often used numerical integration schemes for the geometrically nonlinear response analysis of structural components are evaluated based on the ease of problem formulation, machine strage required, and speed and accuracy of solution. The particular integration methods considered are the implicit Houbolt and constant-average-acceleration Newmark methods and the explicit central finite difference scheme. The methods are evaluated by a series of numerical experiments with one and multiple degree-of-freedom system, both with and without damping, with emphasis on the characteristics of these temporal operators as regards stability and artificial attenuation or viscosity.

Abstract: : Several alternative methods for directly integrating the governing equations of motion of structural dynamics are reviewed. First, the characteristics of the matrix equations are examined (e.g.; the spread in structural eigenvalues, or stiffness; the bandwidth and sparseness; and the frequency spectrum of the forcing function). Then, the criteria that can be used to select a direct integration algorithm are discussed (e.g.; the artificial damping, the periodicity error). Emphasis is given to results obtained for the Houbolt, Newmark and Wilson operators, and their comparison to a class of stiffly stable operators. Recent application of these operators to nonlinear problems is discussed.

Abstract: In modern dynamic analysis of structures, there is often a problem involving the solution of a set of coupled linear ordinary differential equations. The method outlined herein is extremely stable and also very accurate. It is particularly suited to digital computer calculations because the final numerical solution requires only matrix addition and multiplication, and avoids numerical integration. The method also may be applied to semidefinite systems or structures with repeated eigenvalues.