Adaptive Finite Element Mesh Generation for Dynamic Planar Problems

Abstract

In structural design and analysis used for hazard mitigation systems, automation is becoming an essential feature. For analysis, the finite element method has proven to be an effective approximate method if proper element types and meshes are chosen. Recently, the method has been successfully applied to solve complex dynamic and nonlinear problems; and with a properly chosen element type and mesh, reliable results have been obtained. However, in automation and in complex analyses of a structures, using the initial mesh throughout the analysis may involve some elements to go through strains beyond the elements' reliable limits. Thus, the finite element mesh for these types of analyses must be dynamically adaptive, and considering the rapid process of analysis in real time, the dynamically adaptive finite element mesh generating schemes must be computationally efficient. In this paper, a computationally efficient dynamically adaptive finite element mesh generation scheme for dynamic analyses of planar problems is described. The concept of representative strain value is used for error estimates and the refinements of meshes use combinations of the h-method (node movement) and the r-method (element division). A coefficient that depends on shape of elements is used to correct overly distorted elements. The validity of the scheme is shown by a deep cantilever beam example under a dynamic concentrated load. The example shows reasonable accuracy and efficient computing time. Furthermore, the study shows the potential for the scheme's effective use in complex structural problems such as those under severe environmental hazards such as seismic or erratic wind loads.

An Adaptive Mesh Generation Scheme for the Finite Element Method

“…A parametric study recommends a value between 12.0 and 15.0 for optimal value of α for general dynamics problems. Significant deviations of α from this range result in computational inefficiency for no apparent increase in accuracy (Yoon, 2012).…”

“…Various means of combining have been studied (de Las Casas, 1988;Jang and Lee 2011;Yoon, 2012). To obtain an optimal combination of the r-method and the h-method, first the representative strain values are normalized at each step so that the minimum and maximum values are from 0 to 100.…”

“…(8), the representative error of element i is weighted by the element's area with respect to the total area and thus the relative order of errors for all elements are computed to identify elements to be adaptively changed. Previous studies have shown that this is computationally very efficient for achieving this (Yoon, 2012;Yoon, 2013).…”

Automated Finite Element Analyses for Structural Integrated Systems

“…The finite element method is an approximate structural analysis method most widely used in the world. The popularity of the method is partly due to ease of use; however, the user must provide finite element mesh and the number of elements in this mesh dictates the required computation time and the quality of the mesh influences error in the results (Bathe and Wilson, 1976;Belytschko et al, 1996;Yoon, 2014;Zienkiewcz et al, 2005).…”

Efficient Adaptive Finite Element Mesh Generation for Dynamics

“…Through diverse studies on many practical problems, the scheme is an improved and refined algorithm of the basic procedure presented in reference Yoon and Park(2010) and Yoon(2012). A general adaptive mesh generation process involves two basic steps : estimation of error given a mesh and generation of a new improved mesh based on the error (Choi and Jung, 1998;de Las Casa, 1988;Zienkiewcz and Zhu, 1987).…”