Zakład Mechaniki Budowli i Zastosowań Informatyki

Comparison of some numerical integration methods for the equations of motion of systems with a finite number of degrees of freedom, Z.Kacprzyk, T.Lewiński
Engineering Transactions, 31, 2, pp. 213-240, 1983
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The subject of this paper are the numerical integration methods of the differential equations of vibration (in matrix form) of a physical system with a finite number of degress of freedom. Comparison was made between finite difference method, Newmark's method and Space-Time Finite Element method. The compared methods have been brought to a unified form, disclosing far-reaching similarities concerning the calculation methods of displacement and velocity. Analogies have been found between the recurrence formulae relating the displacement and velocity vectors in different methods. It was proved that these analogies allow for a comparative analysis of convergence of the three methods and confine it to the analysis of approximation of initial conditions and of external loads. Thirteen methods of approximation of initial conditions are discussed. New formulation is given of the Space-Time Finite Elements. The comparative analysis of convergence is limited to free oscillation of a system with a single degree od freedom.