Adaptive superposition of finite element meshes in linear and nonlinear dynamic analysis

2005 2005

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Abstract (summary)

The numerical analysis of transient phenomena in solids, for instance, wave propagation and structural dynamics, is a very important and active area of study in engineering. Despite the current evolutionary state of modern computer hardware, practical analysis of large scale, nonlinear transient problems requires the use of adaptive methods where computational resources are locally allocated according to the interpolation requirements of the solution form. Adaptive analysis of transient problems involves obtaining solutions at many different time steps, each of which requires a sequence of adaptive meshes. Therefore, the execution speed of the adaptive algorithm is of paramount importance. In addition, transient problems require that the solution must be passed from one adaptive mesh to the next adaptive mesh with a bare minimum of solution-transfer error since this form of error compromises the initial conditions used for the next time step.

A new adaptive finite element procedure (s-adaptive) is developed in this study for modeling transient phenomena in both linear elastic solids and nonlinear elastic solids caused by progressive damage. The adaptive procedure automatically updates the time step size and the spatial mesh discretization in transient analysis, achieving the accuracy and the efficiency requirements simultaneously. The novel feature of the s-adaptive procedure is the original use of finite element mesh superposition to produce spatial refinement in transient problems. The use of mesh superposition enables the s-adaptive procedure to completely avoid the need for cumbersome multipoint constraint algorithms and mesh generators, which makes the s-adaptive procedure extremely fast. Moreover, the use of mesh superposition enables the s-adaptive procedure to minimize the solution-transfer error.

In a series of different solid mechanics problem types including 2-D and 3-D linear elastic quasi-static problems, 2-D material nonlinear quasi-static problems, and 2-D transient problems for linear elastic and material nonlinear materials, the s-adaptive solution is compared to a solution obtained using a non-adaptive, uniform refined mesh. These comparisons clearly demonstrate that the s-adaptive method is capable of generating a solution with the same accuracy level as a non-adaptive, uniform refined mesh; however, the s-adaptive solution uses far fewer DOF and consequently executes much faster.

Indexing (details)

Mechanical engineering;
Aerospace materials
0548: Mechanical engineering
0538: Aerospace materials
Identifier / keyword
Applied sciences; Adaptive meshes; Meshes; Superposition
Adaptive superposition of finite element meshes in linear and nonlinear dynamic analysis
Yue, Zhihua
Number of pages
Publication year
Degree date
School code
DAI-B 66/12, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
9780542472008, 0542472007
Robbins, Donald, Jr.
University of Maryland, College Park
University location
United States -- Maryland
Source type
Dissertations & Theses
Document type
Dissertation/thesis number
ProQuest document ID
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
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