SUMMARYThis paper discusses the Bossak-Newmark algorithm, which is an extension of the well-known Newmark algorithm' for the numerical integration of the equations of discretized structural dynamics problems. The extra parameter introduced here enables the method (when used on the test equation i = -0 2 x ) to be simultaneously second order, unconditionally stable and with positive artificial damping.Com arisons are made with another modification of Newmark introduced by Hilber, Hughes andTaylor. PIn many structural dynamics applications the equations of motion for the discretized system have the formwhere M, C, K are the mass, damping and stiffness matrices, respectively; x, x, f are the displacement, velocity and acceleration vectors, respectively; and F is the external force vector.The well-known Newmark algorithm' for the numerical integration of equation ( where the Newmark parameters are distinguished by the subscript 'N' to avoid confusion with other parameters in this paper. The idea of introducing an additional parameter for controlling the damping properties of Newmark's algorithm was proposed in 1977 by Hilber, Hughes and Taylor.' Hilber, Hughes and Taylor introduce a parameter, called here aH to avoid confusion, which they apply to the equation without natural damping and with which equation (4) is replaced by A particular version of this algorithm has also been used by A b~u d i .~
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