- Advances in finite element provedures for non-linear dynamic response
- K.J. Bathe
- Book Title / Journal: 2nd South-East European Conference on Computational Mechanics
- Year: 2009 , Volume: , Series:
- Structural Analysis
- Description
- The objective in this presentation is to briefly survey some recent developments in finite element procedures that we have pursued to solve dynamic problems more accurately and more efficiently, and to solve new classes of problems. We present some developments regarding the finite element analysis of shells, the solution of wave propagation problems
with mode conversions, the time integration in long-time large deformation analyses, the solution of normal modes of proteins with the subspace iteration method in nonlinear conformations, and fluid flow-structure interactions.
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- A triangular six-node shell element
- D-N Kim ; K.J. Bathe
- Book Title / Journal: Computers and Structure
- Year: 2009 , Volume: 87 , Series:
- Structural Analysis
- Keywords: shells ; Finite element ; Triangular element ; Spatial isotropy ; MITC method ; Six-node element
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- A Holistic Method to Design an Optimized Energy Scenario and Quantitatively Evaluate Promising Technologies for Implementation
- C. Deilmann ; K.J. Bathe
- Book Title / Journal: International Journal of Green Energy
- Year: 2009 , Volume: 6 , Series:
- Structural Analysis
- Keywords: Energy system analysis ; Normative scenario technique ; Bottom-up analysis
- Description
- In this article we focus on today’s worldwide energy system, a fundamentally illogical and unsustainable system. Today, 85% of the world wide energy system depends on carbon-based fossil fuels. We develop a holistic method to analyze mankind’s use of energy in a broad way and to design optimized, normative energy scenarios that conform to important scientific principles. The procedure is based on an abstraction process and helps to overcome thinking barriers and prejudice. The proposed method is applied to a general analysis of energy and to a simplified normative energy scenario for the United States in 2060. Important technologies for the implementation are evaluated in a bottom-up analysis. Since research endeavors and
policies affect free-market decisions within the energy system, the developed method aims at
guiding researchers and politicians to embark on strategies toward sustainable and scientifically optimized energy concepts for the future.
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- Advances in Finite Element Procedures for Nonlinear Dynamic Response
- K.J. Bathe
- Book Title / Journal: 2nd South-East European Conference on Computational Mechanics
- Year: 2009 , Volume: , Series:
- Structural Analysis
- Keywords: dynamic ; nonlinear
- Description
- The objective in this presentation is to briefly survey some recent developments in finite element procedures that we have pursued to solve dynamic problems more accurately and more efficiently, and to solve new classes of problems. We present some developments regarding the finite element analysis of shells, the solution of wave propagation problems
with mode conversions, the time integration in long-time large deformation analyses, the solution of normal modes of proteins with the subspace iteration method in nonlinear conformations, and fluid flow-structure interactions.
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- 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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- The Finite Element Method
- K.J. Bathe
- Book Title / Journal: Wiley Encyclopedia of Computer Science and Engineering
- Year: 2008 , Volume: , Series:
- Structural Analysis
- Keywords: Finite element method
- Description
- The objective in this article is to give an overview of finite element methods that currently are used extensively in academia and industry. The method is described in general terms, the basic formulation is presented, and some issues regarding effective finite element procedures are summarized. Various applications are given briefly to illustrate the current use of the method. Finally, the article concludes with key challenges for the additional development of the method.
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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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- 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 a Theoretical and Computational Framework for Large Strain Anisotropic Plasticity
- F.J. Montáns ; K.J. Bathe
- Book Title / Journal: Proceedings 8th International Conference on Computational Plasticity
- Year: 2005 , Volume: , Series:
- Structural Analysis
- Keywords: Large strains ; Plasticity ; Anisotropic Behavior
- Description
- The modelling of large strain anisotropic plasticity based on hyperelasticity, the multiplicative decomposition into the elastic and plastic deformation gradients, and the use of the logarithmic strain measure and its work-conjugate stress measure are considered. The integration of the plastic deformation gradient is performed using an exponential mapping. First, the continuum mechanics formulation of the proposed theory is given, and then some results considering anisotropic elastic behavior, anisotropic yield
functions and mixed hardening are summarized.
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- A shell problem ‘highly sensitive’ to thickness changes
- K.J. Bathe ; D. Chapelle ; P.S. Lee
- Book Title / Journal: International Journal for Numerical Methods in Engineering
- Year: 2003 , Volume: 57 , Series:
- Structural Analysis
- Keywords: shells ; asymptotic analysis ; finite element solution
- Description
- In general, shell structural problems can be identied to fall into one of the categories of membrane-dominated, bending-dominated and mixed shell problems. The asymptotic behaviour with a well-defined load-scaling factor shows distinctly into which category a given shell problem falls. The objective of this paper is to present a shell problem and its solution for which there is no convergence to a well-dened load-scaling factor as the thickness of the shell decreases. Such shells are unduly sensitive in their behaviour because the ratio of membrane to bending energy stored changes signicantly and indeed can uctuate with changes in shell thickness. We briefly review the dierent asymptotic behaviours that shell problems can display, and then present the specic problem considered and its numerical solution using nite element analysis.
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- Measuring convergence of mixed finite element discretizations: an application to shell structures
- J.F. Hiller ; K.J. Bathe
- Book Title / Journal: Computers and Structures
- Year: 2003 , Volume: 81 , Series:
- Structural Analysis
- Keywords: Finite elements ; shell structures
- Description
- We consider the problem of assessing the convergence of mixed-formulated finite elements. When displacementbased formulations are considered, convergence measures of finite element solutions to the exact solution of the mathematical problem are well known. However when mixed formulations are considered, there is no well-established method to measure the convergence of the finite element solution. We first review a number of approaches that have been employed and discuss their limitations. After having stated the properties that an ideal error measure would possess, we introduce a new physics-based procedure. The new proposed error measure can be used for many different types of mixed formulations and physical problems. We illustrate its use in an assessment of the performance of the MITC family of shell elements.
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- Towards improving the MITC9 shell element
- K.J. Bathe ; P.S. Lee ; J.F. Hiller
- Book Title / Journal: Computers and Structures
- Year: 2003 , Volume: 81 , Series:
- Structural Analysis
- Keywords: Shell elements ; MITC9
- Description
- The objective in this paper is to present some results regarding the predictive capabilities of the MITC9 shell element when the tying points in the element are changed. The MITC9 element is a general nine-node shell element based on the formulation approach of using mixed-interpolated tensorial components. Different tying points are very simple to implement and are not decreasing the computational efficiency of the element. Hence, the use of the ‘‘best’’ tying points is clearly of value.
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- An evaluation of the Lyapunov characteristic exponent of chaotic continuous systems
- S. Rugonyi ; K.J. Bathe
- Book Title / Journal: International Journal for Numerical Methods in Engineering
- Year: 2003 , Volume: 56 , Series:
- Structural Analysis
- Keywords: stability analysis ; Lyapunov characteristic exponent ; non-linear dynamics ; dynamic stability
- Description
- A procedure to calculate the Lyapunov characteristic exponent of the response of structural continuous systems, discretized using nite element methods, is proposed. The Lyapunov characteristic exponent can be used to characterize the asymptotic stability of the system dynamic response, and it is frequently employed to identify a chaotic behaviour. The proposed procedure can also be used in the stability characterization of uid–structure interaction systems in which the focus of the analysis is on the behaviour of the structural part.
- Abstract
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- On the asymptotic behavior of shell structures and the evaluation in finite element solutions
- P.S. Lee ; K.J. Bathe
- Book Title / Journal: Computers and Structures
- Year: 2002 , Volume: 80 , Series:
- Structural Analysis
- Keywords: shells ; Asymptotic behaviors ; Finite element solutions
- Description
- The objective of this paper is to demonstrate how the asymptotic behavior of a shell structure, as the thickness (t) approaches zero, can be evaluated numerically. We consider three representative shell structural problems; the original Scordelis–Lo roof shell problem, a herein proposed modified Scordelis–Lo roof shell problem and the partly clamped hyperbolic paraboloid shell problem. The asymptotic behavior gives important insight into the shell load bearing capacity. The behavior should also be known when a shell problem is used to test a shell finite element procedure. We briefly review the fundamental theory of the asymptotic behavior of shells, develop our numerical schemes and perform
the numerical experiments with the MITC4 shell finite element.
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- The Method of Finite Spheres with Improved Numerical Integration
- S. De ; K.J. Bathe
- Book Title / Journal: Computers and Structures
- Year: 2001 , Volume: 79 , Series:
- Structural Analysis
- Keywords: finite spheres ; Meshless methods
- Description
- The method of finite spheres was introduced as a truly meshless technique with the goal of achieving computational efficiency in a mesh-free procedure. In this paper several new numerical integration rules are reported that result in a significant reduction in computational cost.
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