A new family of generalized‐α time integration algorithms without overshoot for structural dynamics

Abstract

SUMMARYA new family of generalized-(G-) algorithm without overshoot is presented by introducing seven free parameters into the single-step three-stage formulation for solution of structural dynamic problems. It is proved through finite difference analysis that these algorithms are unconditionally stable, secondorder accurate and numerical dissipation controllable. The comparison of the new G-algorithms with the commonly used G-algorithms shows that the newly developed algorithms have the advantage of eliminating the overshooting characteristics exhibited by the commonly used algorithms while their excellent property of dissipation is preserved. The numerical simulation results obtained using a singledegree-of-freedom system and a two-degree-of-freedom system to represent the character of typical large systems coincide well with the results of theoretical analyses.

On the advantages of using the first-order generalised-alpha scheme for structural dynamic problems

“…A considerable amount of research has gone into developing implicit schemes which possess the above-listed attributes. Newmark-β scheme [9], Wilson-θ scheme [10], HHT-α scheme [11], Collocation scheme [8], WBZ-α scheme [12], HP-θ 1 scheme [13], CH-α scheme [14] and G-α scheme [15] are few such schemes which satisfy some or all of the above listed criteria. Though all these schemes are unconditionally stable, implicit, single-step and second-order in nature, their differences are in the amount of numerical dissipation and whether or not they suffer from overshoot.…”

“…Though all these schemes are unconditionally stable, implicit, single-step and second-order in nature, their differences are in the amount of numerical dissipation and whether or not they suffer from overshoot. HHT-α, CH-α and WBZ-α schemes have been proven to suffer from overshooting, see [15] and references therein. Erlicher et al [16] have proven the overshoot behaviour of CH-α scheme in the context of nonlinear dynamic problems.…”

“…Erlicher et al [16] have proven the overshoot behaviour of CH-α scheme in the context of nonlinear dynamic problems. KaiPing [15] has improved upon CH-α scheme and devised a new family of generalised-α schemes without overshoot. Though NOHHT-α and NOWBZ-α schemes, proposed by [15], are without overshoot and have better dissipation properties when compared with their counterparts with overshoot, the amount of numerical dissipation of NOCH-α remained exactly same as that of the CH-α scheme.…”

“…KaiPing [15] has improved upon CH-α scheme and devised a new family of generalised-α schemes without overshoot. Though NOHHT-α and NOWBZ-α schemes, proposed by [15], are without overshoot and have better dissipation properties when compared with their counterparts with overshoot, the amount of numerical dissipation of NOCH-α remained exactly same as that of the CH-α scheme. On the similar lines, Kuhl and Crisfield [17] developed energy conserving generalised energy-momentum methods based on CH-α scheme.…”

Parabolic and cubic acceleration time integration schemes for nonlinear structural dynamics problems using the method of weighted residuals

“…An ideal integration scheme is suggested to have the following criteria: at least second order accuracy, unconditional stability in linear problem applications, controllable algorithmic damping, no overshoot, self-starting, single-step, and asymptotic annihilation [1,19,33]. From a practical point of view, computational cost, accuracy, stability, parametric damping, design of propagation of information, and type of inertia matrices are the important features that a time integration method should ideally contain.…”