Adaptive superposition of finite element meshes in elastodynamic problems

• Published in: International journal for numerical methods in engineering Vol. 63; no. 11; pp. 1604 - 1635
• Main Authors: Yue, Z., Robbins Jr, D. H.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 21-07-2005; Wiley
• Subjects: adaptive solution; Computational techniques; error estimation; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; mesh superposition; Physics; Solid mechanics; Structural and continuum mechanics; transient analysis; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Transient response; Vibration; Error estimation; Newmark method; Refinement method; Elastic wave; Modeling; Direct method; Finite element method; Time varying system; mesh superposition; transient analysis; Non linear effect; Elastodynamics; Superposition method; adaptive solution; Mesh generation; Structural analysis
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.1331

An adaptive finite element procedure is developed for modelling transient phenomena in elastic solids, including both wave propagation and structural dynamics. Although both temporal and spatial adaptivity are addressed, the novel feature of the formulation is the use of mesh superposition to produce spatial refinement (referred to as s‐adaptivity) in transient problems. Spatial error estimation is based on superconvergent patch recovery of higher‐order accurate stresses and is used to guide mesh adaptivity, while the temporal error estimation is based on the assumption of linearly varying third‐order time derivatives of the displacement field and is used to adjust the time step size for the HHT‐α variant of the Newmark direct numerical integration method. Spatial adaptivity of the mesh is performed using a hierarchical h‐refinement scheme that is efficiently implemented using a structured version of finite element mesh superposition. This particular spatial adaptivity scheme is extremely fast and consequently makes it feasible to repeatedly update both the mesh and the time increment as required in an adaptive transient analysis. This work represents the initial effort in applying this type of spatial adaptivity to transient problems. Three example problems are given to demonstrate the performance characteristics of the s‐adaptive procedure. Copyright © 2005 John Wiley & Sons, Ltd.