- Frontiers in Finite Element Procedures & Applications
- K.J. Bathe
- Book Title / Journal: Computational Methods for Engineering Technology, Saxe-Coburg Publications, Stirlingshire, U.K.
- Year: 2014 , Volume: , Series: Chapter 1
- Structural Analysis
- Description
- We consider in this paper some frontiers in finite element procedures, and frontiers of novel applications. We focus on theoretically well-founded procedures that advance the solution of practical problems in engineering and the sciences. For the analysis of shells, the use of interpolation covers to enhance solutions is presented and the new MITC3+ shell element is discussed. For transient dynamic solutions, insights in implicit and explicit time integration methods and the solution of large
eigenvalue problems are given. For multi-physics analyses, the full coupling between solid, fluid, electromagnetic and thermal effects is considered. Finally, we briefly also focus on the finite element modelling of Protein and DNA nano-scale structures by coarse graining, which represents a very important frontier for future research.
- Abstract
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- Towards a procedure to automatically improve finite element solutions by interpolation covers
- J. Kim ; K.J. Bathe
- Book Title / Journal: Computers and Structures
- Year: 2014 , Volume: 131 , Series:
- Structural Analysis
- Keywords: Finite elements
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- An explicit time integration scheme for the analysis of wave propagations
- G. Noh ; K.J. Bathe
- Book Title / Journal: Computers and Structures
- Year: 2013 , Volume: 129 , Series:
- Structural Analysis
- Keywords: Wave propagation ; Finite elements ; Explicit time integration
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- 3D-shell Elements for Structures in Large Strains
- T. Sussman ; K.J. Bathe
- Book Title / Journal: Computers and Structures
- Year: 2013 , Volume: 122 , Series:
- Structural Analysis
- Keywords: Shell elements ; Large strains
- Description
- We present in this paper MITC shell elements for large strain solutions of shell structures. While we focus on the 4-node element, the same formulation is also applicable to the 3-node element. Since the elements are formulated using three-dimensiona l continuum theory with the full three-dimensional constitutive behavior, they are referred to as 3D-shell elements. Specific contributions in this paper are that the elements are formulated usi ng two control vector s at each node to describe the large deformations, MITC tying and volume preserving conditions acting directly on the material fiber vectors to avoid shear locking, and a pressure interpolation to circumvent volumetric locking. Also, we present solutions to some large strain shell problems that represent valuable benchmark tests for any large strain shell analysis
capability.
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- Insights and Advances in the Analysis of Structures
- K.J. Bathe
- Book Title / Journal: Proceedings SEMC 2013 The Fifth International Conference on Structural Engineering, Mechanics and Computation,
- Year: 2013 , Volume: , Series:
- Structural Analysis
- Description
- The objective in this presentation is to survey our recent research accomplishments to advance
the state of computational simulations in engineering and the sciences. We present our novel insights and recent advances in the analysis of transient and wave propagation problems, the simulation of large strain conditions of shells, the prediction of more accurate solutions using low-order elements, and the coupling of structures to general fluid flows and electromagnetic effects. At the conference, applications are given in the analysis of traditional structures and in the modeling of nano-structures, specifically, proteins and DNA
assemblies. Also, major challenges are outlined for further advances in the field.
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- The finite element method enriched by interpolation covers
- J. Kim ; K.J. Bathe
- Book Title / Journal: Computers and Structures
- Year: 2013 , Volume: , Series: 116
- Structural Analysis
- Keywords: Enriched finite elements ; Cover functions ; Adaptive interpolation
- Description
- In this paper, we focus on an enriched finite element solution procedure for low-order elements based on the use of interpolation cover functions. We consider the 3-node triangular and 4-node tetrahedral displacement-based elements for two- and three-dimensional analyses, respectively. The standard finite element shape functions are used with interpolation cover functions over patches of elements to increase the convergence of the finite element scheme. The cover functions not only capture higher gradients of a field variable but also smooth out inter-element stress jumps. Since the order of the interpolations in the covers can vary, the method provides flexibility to use different covers for different patches and increases the solution accuracy without any local mesh refinement. As pointed out, the procedure can be derived from various general theoretical approaches and the basic theory has been presented earlier. We evaluate the effectiveness of the method, and illustrate the power of the scheme through the solution of various problems. The method also has potential for the development of error measures.
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- A stress improvement procedure
- D.J. Payen ; K.J. Bathe
- Book Title / Journal: Computers and Structures
- Year: 2012 , Volume: , Series:
- Structural Analysis
- Keywords: Finite element stress calculation ; Low-order displacement-based elements
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- Advances in the Multiphysics Analysis of Structures
- K.J. Bathe
- Book Title / Journal:
- Year: 2012 , Volume: , Series:
- Structural Analysis
- Keywords: Finite elements ; wave propagations ; shells ; Large strains ; Maxwell’s equations ; electromechanics
- Description
- In this presentation we survey the advances that we have recently accomplished for the effective analysis of solids and structures, specifically for wave propagations and transient solutions, the analysis of shells, improved stress calculations, the use of interpolation covers, and the solution of the full Maxwell’s equations. The structures may be subjected to complex fluid flows and electromagnetic effects. We briefly give the theoretical developments for the formulations, a few illustrative solutions, and conclude by mentioning some further exciting research challenges.
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- A finite element method enriched for wave propagation problems
- S. Ham ; K.J. Bathe
- Book Title / Journal: Computers and Structures
- Year: 2012 , Volume: , Series: 94-95
- Structural Analysis
- Keywords: Wave propagation ; Spectral methods ; Enriched finite elements
- Description
- An enriched finite element method is presented to solve various wave propagation problems. The
proposed method is an extension of the procedure introduced by Kohno, Bathe, and Wright for onedimensional problems [1]. Specifically, the novelties are: two-dimensional problems are solved (and three-dimensional problems would be tackled similarly), a scheme is given to overcome ill-conditioning, the method is presented for time-dependent problems, and focus is on the solution of problems in solids and structures using real arithmetic only. The method combines advantages of finite element and spectral techniques, but an important point is that it preserves the fundamental properties of the finite element method. The general formulation of the procedure is given and various examples are solved to illustrate the capabilities of the proposed scheme.
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- Crushing and crashing of tubes with implicit time integration
- Z. Kazancı ; K.J. Bathe
- Book Title / Journal: International Journal of Impact Engineering
- Year: 2012 , Volume: , Series: 42
- Structural Analysis
- Keywords: Dynamic axial crushing ; Implicit time integration ; Bathe method ; 3D-shell element
- Description
- The axial crushing and crashing of thin-walled high-strength steel tubes is performed using 3D-shell finite elements and an implicit time integration scheme. The calculated results are compared with published experimental data and results obtained using explicit time integration. The objective is to show that, while for such analyses generally explicit time integration is used, with the current state of the art also an implicit time integration solution should be considered, and such solution approach can provide an effective alternative for a simulation.
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- Insight into an implicit time integration scheme for structural dynamics
- K.J. Bathe ; G. Noh
- Book Title / Journal: Computers and Structure
- Year: 2012 , Volume: , Series: 98-99
- Structural Analysis
- Keywords: structural dynamics ; Finite elements ; Implicit time integration ; Newmark method
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- The MITC9 shell element in plate bending: mathematical analysis of a simplified case
- K.J. Bathe ; F. Brezzi ; L.D. Marini
- Book Title / Journal: Computational Mechanics
- Year: 2011 , Volume: 47 , Series:
- Structural Analysis
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- Improved stresses for the 4-node tetrahedral element
- D.J. Payen ; K.J. Bathe
- Book Title / Journal: Computers and Structures
- Year: 2011 , Volume: 89 , Series:
- Structural Analysis
- Description
- The objective in this paper is to present the method for the calculation of improved stresses published by Payen and Bathe in [1] for the 4-node three-dimensional tetrahedral element. This element is widely used in engineering practice to obtain, in general only "guiding" results in the analysis of solids because the element is known to be poor in stress predictions. We show in this paper the potential of this novel approach to significanlty enhance the stress predictions with the 4-node tetrahedral element at a relatively low computational cost.
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- The quadratic MITC plate and MITC shell elements in plate bending
- P.S. Lee ; K.J. Bathe
- Book Title / Journal:
- Year: 2010 , Volume: , Series:
- Structural Analysis
- Keywords: Plate ; shell ; mixed formulation ; Finite elements
- Description
- The analysis of plates can be achieved using the quadratic MITC plate or MITC shell elements. The plate elements have a strong mathematical basis and have been shown to be optimal in their convergence behavior, theoretically and numerically. The shell elements have not (yet) been analyzed mathematically in depth for their rates of convergence, with the plate/shell thickness varying, but have been shown numerically to perform well. Since the shell elements are general and can be used for linear and nonlinear analyses of plates and shells, it is important to identify the differences in the performance of these elements when compared to the plate elements. We briefly review the quadratic quadrilateral and triangular
MITC plate and shell elements and study their performances in linear plate analyses.
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- Insight into a model for large strain anisotropic elasto-plasticity
- D.N. Kim ; F.J. Montáns ; K.J. Bathe
- Book Title / Journal: Computational Mechanics
- Year: 2009 , Volume: , Series:
- Structural Analysis
- Keywords: Plasticity ; Anisotropic plasticity ; Orthotropy ; Plastic spin
- Description
- Efficient and accurate simulation of the deformations in anisotropic metallic sheets requires a constitutive model and an accompanying algorithm at large strains which take into account the anisotropy of both the elastic and plastic material behaviors, as well as their evolution with plastic
strains. Recently we proposed such a constitutive model based on continuum energy considerations, the Lee decomposition and an anisotropic stored energy function of the logarithmic strains in which the rotation of the orthotropic axes is also considered. We obtained a framework similar to the one used in isotropic elasto-plasticity. In the presentwork we give some physical insight into the parameters of the model and their effects on the predictions, both in proportional and in non-proportional loading problems.We also present a procedure to obtain the spin parameter of the model from Lankford R-values.
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