This paper presents a step-by-step time integration algorithm for efficiently solving second-order nonlinear dynamic problems. The method employs the rewriting of motion as two sets of first-order differential equations. The interpolation of the relevant quantities is achieved by a particular quadratic polinomial expression for the velocities and forces and is defined by values at the boundaries of the time step. Then the time definite integrals of both first-order ordinary differential equations define the numerical relations in the step. An accurate extrapolation predictor and an adaptive time stepping procedure are used as the time predictor–corrector method.

A predictor–corrector time integration algorithm for dynamic analysis of nonlinear systems

Lopez S.
2020-01-01

Abstract

This paper presents a step-by-step time integration algorithm for efficiently solving second-order nonlinear dynamic problems. The method employs the rewriting of motion as two sets of first-order differential equations. The interpolation of the relevant quantities is achieved by a particular quadratic polinomial expression for the velocities and forces and is defined by values at the boundaries of the time step. Then the time definite integrals of both first-order ordinary differential equations define the numerical relations in the step. An accurate extrapolation predictor and an adaptive time stepping procedure are used as the time predictor–corrector method.
2020
Adaptive time stepping
Direct time integrations
Predictor–corrector schemes
Stability and accuracy
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/310519
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