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Newmark method

Standard Newmark method can be employed to perform time integration of basic differential equations of motion. Two basic parameters β and γ describing the evolution of displacements and velocities, respectively, must be introduced.

Setting γ = 0.5 a β = 0.25 gives the average acceleration method (trapezoidal rule). This setting recommended and complies with the following stability condition:

which ensures that the integration scheme is unconditionally stable (stability does not depend on the magnitude of the selected time step).

For γ = 0.5 the method is second order accurate (the rate of convergence with the time step reduction is 2). Also, the material damping has in such a case no effect on stability.

Setting of Newmark method

Further details are available in the theoretical manual on our website.

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