The von-K arm an non-linear, dynamic, partial differential system over rectangular domains is solved by the Chebyshev-collocation method in space and the implicit Newmark-b time marching scheme in time. In the Newmark-b scheme, a non-linear fixed point iteration algorithm is employed. We monitor both temporal and spatial discretization errors based on derived analytical solutions, demonstrating...

The Newmark method is an effective method for numerical time integration in dynamic problems. The results of Newmark method are function of its parameters (β, γ and ∆t). In this paper, a stationary mode I dynamic crack problem is coded in extended finite element method )XFEM( framework in Matlab software and results are verified with analytical solution. This paper focuses on effects of main pa...

Abstract In this contribution, we present a space-time formulation of the Newmark integration scheme for linear damped structures under both harmonic and transient excitations. The incremental set equations motion approximations are transformed into their corresponding equivalents. dynamic system is then represented by one algebraic equation only. This projected coupled pair equations, which so...

Three direct integration schemes for the matrix equations of motion of structural dynamics-the Newmark generalized acceleration operator, the Wilson averaging variant of the linear acceleration operator and an averaging method based on a variational principle derived by Gurtin-are investigated for stability and approximation viscosity. Using established techniques developed by J. von Neumann an...

development of a numerical model which describes launching of offshore jackets from barge is presented in this paper. in this model, in addition to capabilities of commercial softwares, water entry forces on jacket members and an implicit newmark solution technique are included. the results are in general agreement with other numerical software’s available (sacs). fluid forces acting on jacket ...

A one-dimensional Klein-Gordon problem, which is a physical model for a quantum particle submitted to a potential barrier, is studied numerically : using a variational formulation and a Newmark numerical method, we compute the mean position and standard deviation of the particle as well as their time evolution.