- On Finite Element Methods for Nonlinear Dynamic Response
- K.J. Bathe
- Book Title / Journal: Eurodyn 2008: 7th European Conference on Structural Dynamics
- Year: 2008 , Volume: , Series:
- Structural Analysis
- Keywords: Finite element method ; structural dynamics ; Nonlinear dynamic analysis
- Description
- In this paper we briefly focus on the nonlinear analysis of solids and structures when these undergo large deformations, possibly over long time durations, and perhaps subjected to fluidstructure interactions. The analysis should be conducted with finite element methods,
including the time integration, that are reliable and effective. The requirement of reliability is particularly important in nonlinear finite element analysis because physical test data are frequently not available.
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- A New Procedure for Selection and Modification of Ground Motion for Nonlinear Dynamic Analysis Strong Ground Motion for Nonlinear Dynamic Analysis
- M. Nooraie ; F. Behnamfar
- Book Title / Journal: Proceedings of the 15th World Conference on Earthquake Engineering, Lisbon, Portugal
- Year: 2012 , Volume: , Series:
- Earthquake engineering
- Keywords: ground motion selection and modification ; Nonlinear dynamic analysis
- Description
- Nonlinear dynamic analysis is known as the most accurate method to evaluate the behavior of structures during an earthquake. In this context, the selection process of suitable records and their modification plays a vital role. An effective selection and modification of ground motion as the loads to be used in the analysis can lead to responses with low dispersion in nonlinear structural analysis. This in turn, results in much more trust in the safety of the designed structure. This fact highlights the importance of the current study. Screening process is a three-stage operation as the Coarse, Medium, and Fine-Screen sub-processes. The remaining records are modified in order to minimize the scatter in the results of nonlinear dynamic analysis of the structure under study, by calculating scale factors by different methods to be multiplied to the selected earthquake time histories. The proposed method results in least scatter in representative nonlinear dynamic response quantities.
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- On a composite implicit time integration procedure for nonlinear dynamics
- K.J. Bathe ; M.M. Irfan Baig
- Book Title / Journal: Computers and Structures
- Year: 2005 , Volume: 83 , Series:
- Structural Analysis
- Keywords: Direct time integration ; Nonlinear dynamic analysis ; Stability
- Description
- Transient analysis of nonlinear problems in structural and solid mechanics is mainly carried out using direct time integration of the equations of motion. For reliable solutions, a stable and efficient integration algorithm is desirable. Methods that are unconditionally stable in linear analyses appear to be a natural choice for use in nonlinear analyses,
but unfortunately may not remain stable for a given time step size in large deformation and long time range response solutions. A composite time integration scheme is proposed and tested in some example solutions against the trapezoidal rule and the Wilson h-method, and found to be effective where the trapezoidal rule fails to produce a stable solution. These example results are indicative of the merits of the composite scheme.
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- On direct time integration in large deformation dynamic analysis
- M.M.I. Baig ; K.J. Bathe
- Book Title / Journal: Computational Fluid and Solid Mechanics
- Year: 2005 , Volume: , Series:
- Structural Analysis
- Keywords: Direct time integration ; Nonlinear dynamic analysis ; Stability
- Description
- Direct time integration is used widely for the solution of large deformation problems in solid and structural mechanics. Direct integration schemes that are unconditionally stable for linear dynamic problems are also used for nonlinear problems. However, unconditional stability may be lost in the nonlinear regime. The Newmark method (trapezoidal rule) is used widely but may become unstable when large deformations and long time durations are considered. A composite scheme is proposed for such analysis cases, and the results obtained using the trapezoidal rule and the composite formula in a test problem are given. These results indicate the value of the composite scheme.
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