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Item type:Publication, Access status: without files , Nonlinear structural dynamic analysis by a stabilized central difference method(2018-10-15); In this work, a simple stabilized central difference technique is discussed, to analyse nonlinear models. The proposed technique is unconditionally stable for linear systems and it provides enhanced stability features for nonlinear applications. The proposed method stands as a direct single step procedure, avoiding any iterative computations when solving nonlinear models; thus, it is very efficient. In addition, it is extremely accurate, providing much reduced period elongation and amplitude decay errors, compared to standard methods. The present work also introduces a criterion for updating the nonlinear system matrices, significantly reducing the computational complexity of the simulation and enhancing the efficiency of the technique. Numerical results are presented along the manuscript, illustrating the performance and accuracy of the proposed methodology.Publicationtype: Journal Article144 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , An efficient staggered time-marching procedure for porodynamicsThe present work proposes a novel time-marching procedure, which is designed for the dynamic simulation of the coupled two phase Biot equations, considering the displacement-pressure (u - p) formulation. The new approach provides unconditional stability and excellent efficiency. Due to the staggered character of the temporal discretization, where equilibrium is established at time t for the u group of governing equations and at time t + δ t for the p group of governing equations, the resulting systems of equations have an improved format and can be factorized/solved at significantly less computational effort when compared to standard approaches, such as the generalized Newmark scheme. In addition, the resulting new systems of equations are characterized by considerably lower condition numbers, reducing correlated numerical issues. Unconditional stability is achieved by a consistent manipulation of the mass and compressibility matrix of the model, which causes virtually no computational overhead. As a byproduct of the altered compressibility matrix, the method is capable of simulating incompressible and impermeable phenomena without the need for any further feats. The newly developed time-marching technique is implemented and tested considering different benchmark problems. For comparison, the commonly used Newmark scheme is also applied and both direct (LU decomposition) and iterative (GMRES) linear solvers are employed, in order to assess the efficiency of the new technique.Publicationtype: Journal Article25 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A stabilized central difference scheme for dynamic analysisIn this work, a new, unconditionally stable, time marching procedure for dynamic analyses is presented. The scheme is derived from the standard central difference approximation, with stabilization being provided by a consistent perturbation of the original problem. Because the method only involves constitutive variables that are already available from computations at previous time steps, iterative procedures are not required to establish equilibrium when nonlinear models are focused, allowing more efficient analyses to be obtained. The theoretical properties of the proposed scheme are discussed taking into account standard stability and accuracy analyses, indicating the excellent performance of the new technique. At the end of the contribution, representative nonlinear numerical examples are studied, further illustrating the effectiveness of the new technique. Numerical results obtained by the standard central difference procedure and the implicit constant average acceleration method are also presented along the text for comparison.Publicationtype: Journal Article40