Rapid re-meshing and re-solution of three-dimensional boundary element problems for interactive stress analysis

Abstract

(2012) 'Rapid re-meshing and re-solution of three-dimensional boundary element problems for interactive stress analysis.', Engineering analysis with boundary elements., 36 (9). pp. 1331-1343. Further information on publisher's website:http://dx.doi.org/10.1016/j.enganabound.2012.02.020Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Engineering Analysis with Boundary Elements. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version was subsequently published in Engineering Analysis with Boundary Elements, 39, 9, September 2012, 10.1016/j.enganabound.2012.02.020. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractStructural design of mechanical components is an iterative process that involves multiple stress analysis runs; this can be time consuming and expensive. It is becoming increasingly possible to make significant improvements in the efficiency of this process by increasing the level of interactivity. One approach is through real-time re-analysis of models with continuously updating geometry. A key part of such a strategy is the ability to accommodate changes in geometry with minimal perturbation to an existing mesh. This work introduces a new re-meshing algorithm that can generate and update a boundary element mesh in real-time as a series of small changes are sequentially applied to the associated model. The algorithm is designed to make minimal updates to the mesh between each step whilst preserving a suitable mesh quality that retains accuracy in the stress results. This significantly reduces the number of terms that need to be updated in the system matrix, thereby reducing the time required to carry out a re-analysis of the model. A range of solvers are assessed to find the most efficient and robust method of re-solving the system. The GMRES algorithm, using complete approximate LU preconditioning, is found to provide the fastest convergence rate.

Interactive three-dimensional boundary element stress analysis of components in aircraft structures

“…This scheme will be applied according to Table 2. A full description of the quality measures used in this work can be found in [8]. It should be noted that the outer pair of loops in Figure 2 are interchangeable.…”

“…In such cases a full re-mesh may be performed from time to time as suggested by an error indicator. Such a scheme, and fuller details of the re-meshing algorithm used by the authors, are available in [8].…”

“…Integration can then be carried out and the [H] and [G] sub-matrices corresponding to the current element-node pairing constructed. With the application of boundary conditions these are assembled to form the [A] matrix and {b} vector given in (8). The strongly singular terms on the diagonal of [A] taken from [H] are calculated by applying rigid body motion, the weakly singular terms from [G] are already computed to sufficient accuracy using the singular integration scheme.…”

“…To realise the goals of the current work in three dimensions, new boundary element techniques which incorporate a new re-meshing scheme and a modified re-integration algorithm, have been developed [8].…”

“…The reconstruction of these equations is the subject of this paper as, for the small problems assessed in this work, the system construction time takes a significantly higher proportion of the total re-analysis time than re-solving the system; this can be seen in Figures 22 and 23. The solution is carried out using a generalised minimal residual (GMRES) solver with full approximate LU preconditioning as developed by Foster et al [8].…”