- 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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- Approximation of incompressible large deformation elastic problems: some unresolved issues
- F. Auricchio ; L. Beirão da Veiga ; C. Lovadina ; A. Reali ; R. Taylor ; P. Wriggers
- Book Title / Journal: Computational Mechanics
- Year: 2013 , Volume: 52 , Series:
- Structural Analysis
- Keywords: Incompressible nonlinear elasticity ; Stability ; Mixed finite elements
- Description
- Several finite element methods for large deformation elastic problems in the nearly incompressible and purely incompressible regimes are considered. In particular, the method ability to accurately capture critical loads for the possible occurrence of bifurcation and limit points, is investigated. By means of a couple of 2D model problems involving a very simple neo-Hookean constitutive law, it is shown that within the framework of displacement/pressure mixed elements, even schemes that are inf-sup stable for linear elasticity may exhibit problems when used in the finite deformation regime.The roots of such troubles are identified but a general strategy to cure them is still missing. Furthermore,
a comparison with displacement-based elements,
especially of high order, is presented.
- Abstract
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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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