- 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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- 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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