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Non-linear Structural Dynamics (non-linear + structural_dynamics)
Selected AbstractsNon-parametric,parametric model for random uncertainties in non-linear structural dynamics: application to earthquake engineeringEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 3 2004Christophe Desceliers Abstract This paper deals with the transient response of a non-linear dynamical system with random uncertainties. The non-parametric probabilistic model of random uncertainties recently published and extended to non-linear dynamical system analysis is used in order to model random uncertainties related to the linear part of the finite element model. The non-linearities are due to restoring forces whose parameters are uncertain and are modeled by the parametric approach. Jayne's maximum entropy principle with the constraints defined by the available information allows the probabilistic model of such random variables to be constructed. Therefore, a non-parametric,parametric formulation is developed in order to model all the sources of uncertainties in such a non-linear dynamical system. Finally, a numerical application for earthquake engineering analysis is proposed concerning a reactor cooling system under seismic loads. Copyright © 2003 John Wiley & Sons, Ltd. [source] Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2010Christian Soize Abstract A new generalized probabilistic approach of uncertainties is proposed for computational model in structural linear dynamics and can be extended without difficulty to computational linear vibroacoustics and to computational non-linear structural dynamics. This method allows the prior probability model of each type of uncertainties (model-parameter uncertainties and modeling errors) to be separately constructed and identified. The modeling errors are not taken into account with the usual output-prediction-error method, but with the nonparametric probabilistic approach of modeling errors recently introduced and based on the use of the random matrix theory. The theory, an identification procedure and a numerical validation are presented. Then a chaos decomposition with random coefficients is proposed to represent the prior probabilistic model of random responses. The random germ is related to the prior probability model of model-parameter uncertainties. The random coefficients are related to the prior probability model of modeling errors and then depends on the random matrices introduced by the nonparametric probabilistic approach of modeling errors. A validation is presented. Finally, a future perspective is introduced when experimental data are available. The prior probability model of the random coefficients can be improved in constructing a posterior probability model using the Bayesian approach. Copyright © 2009 John Wiley & Sons, Ltd. [source] A-scalability and an integrated computational technology and framework for non-linear structural dynamics.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003Part 1: Theoretical developments, parallel formulations Abstract For large-scale problems and large processor counts, the accuracy and efficiency with reduced solution times and attaining optimal parallel scalability of the entire transient duration of the simulation for general non-linear structural dynamics problems poses many computational challenges. For transient analysis, explicit time operators readily inherit algorithmic scalability and consequently enable parallel scalability. However, the key issues concerning parallel simulations via implicit time operators within the framework and encompassing the class of linear multistep methods include the totality of the following considerations to foster the proposed notion of A-scalability: (a) selection of robust scalable optimal time discretized operators that foster stabilized non-linear dynamic implicit computations both in terms of convergence and the number of non-linear iterations for completion of large-scale analysis of the highly non-linear dynamic responses, (b) selecting an appropriate scalable spatial domain decomposition method for solving the resulting linearized system of equations during the implicit phase of the non-linear computations, (c) scalable implementation models and solver technology for the interface and coarse problems for attaining parallel scalability of the computations, and (d) scalable parallel graph partitioning techniques. These latter issues related to parallel implicit formulations are of interest and focus in this paper. The former involving parallel explicit formulations are also a natural subset of the present framework and have been addressed previously in Reference 1 (Advances in Engineering Software 2000; 31: 639,647). In the present context, of the key issues, although a particular aspect or a solver as related to the spatial domain decomposition may be designed to be numerically scalable, the totality of the aforementioned issues simultaneously play an important and integral role to attain A-scalability of the parallel formulations for the entire transient duration of the simulation and is desirable for transient problems. As such, the theoretical developments of the parallel formulations are first detailed in Part 1 of this paper, and the subsequent practical applications and performance results of general non-linear structural dynamics problems are described in Part 2 of this paper to foster the proposed notion of A-scalability. Copyright © 2003 John Wiley & Sons, Ltd. [source] A-scalability and an integrated computational technology and framework for non-linear structural dynamics.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003Part 2: Implementation aspects, parallel performance results Abstract An integrated framework and computational technology is described that addresses the issues to foster absolute scalability (A-scalability) of the entire transient duration of the simulations of implicit non-linear structural dynamics of large scale practical applications on a large number of parallel processors. Whereas the theoretical developments and parallel formulations were presented in Part 1, the implementation, validation and parallel performance assessments and results are presented here in Part 2 of the paper. Relatively simple numerical examples involving large deformation and elastic and elastoplastic non-linear dynamic behaviour are first presented via the proposed framework for demonstrating the comparative accuracy of methods in comparison to available experimental results and/or results available in the literature. For practical geometrically complex meshes, the A-scalability of non-linear implicit dynamic computations is then illustrated by employing scalable optimal dissipative zero-order displacement and velocity overshoot behaviour time operators which are a subset of the generalized framework in conjunction with numerically scalable spatial domain decomposition methods and scalable graph partitioning techniques. The constant run times of the entire simulation of ,fixed-memory-use-per-processor' scaling of complex finite element mesh geometries is demonstrated for large scale problems and large processor counts on at least 1024 processors. Copyright © 2003 John Wiley & Sons, Ltd. [source] | ||||||||||