Fast Meshless Reanalysis Using Combined Approximations, Preconditioned Conjugate Gradient, and Taylor Series

Multiple design iterations often require repeated stress analyses to be performed as the design is modified slightly. A method is presented that combines the meshless stress analysis method with a reanalysis technique to avoid repeating the time-consuming steps of remeshing and solving for small design changes. An iterative reanalysis method based on the preconditioned conjugate gradient method is introduced and compared to the linear Taylor series, simple iteration, and combined approximations reanalysis methods. The asymptotic running time is presented for each reanalysis method, and accuracy is compared for two example problems: a cantilever beam and a hole-in-plate. Results show the Taylor series to have the fastest run time, followed in order by simple iteration, preconditioned conjugate gradient, and combined approximations. For the two example problems, accuracy of the simple iteration method is poor for design changes greater than 5%. Taylor series accuracy depends greatly on the choice of the design variable, the example problem, and the method for computing the sensitivity. The combined approximations and preconditioned conjugate gradient methods both demonstrate less than 10% error up to a 100% change in height for the cantilever beam and 30% change in radius for the hole-in-plate example. [PUBLICATION ABSTRACT]