Dynamically Adaptive Finite Element Mesh Generation Schemes

The finite element method(FEM) is proven to be an effective approximate method of structural analysis if proper element types and meshes are chosen, and recently, the method is often applied to solve complex dynamic and nonlinear problems. A properly chosen element type and mesh yields reliable results for dynamic finite element structural analysis. However, dynamic behavior of a structure may include unpredictably large strains in some parts of the structure, and using the initial mesh throughout the duration of a dynamic analysis may include some elements to go through strains beyond the elements' reliable limits. Thus, the finite element mesh for a dynamic analysis 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 structures 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). The shape coefficient for element mesh is used to correct overly distorted elements. The validity of the scheme is shown through a cantilever beam example under a concentrated load with varying values. The example shows reasonable accuracy and efficient computing time. Furthermore, the study shows the potential for the scheme's effective use in complex structural dynamic problems such as those under seismic or erratic wind loads.