Error evaluation in approximate reanalysis of structures
It was found in previous studies that the combined approximations (CA) approach developed recently provides accurate results in approximate reanalysis of structures. In this study it is first shown that nonlinear reanalysis and eigenproblem reanalysis can be formulated as a linear reanalysis problem. Then, the convergence behaviour of approximate linear and eigenproblem reanalysis is investigated, and expressions for error evaluation are developed. Some numerical examples show that small errors in the response are obtained for very large changes in the design variables by low-order approximations. The errors evaluated by the expressions developed are similar to the true errors. It was found that lower and upper bounds introduced by the CA method provide good estimation of the exact eigenvalues.
error evaluation approximate reanalysis reanalysis of structures