Effectiveness of the Trefftz method in different engineering optimization procedures

Abstract

In a large class of linear, mathematically modelled engineering problems the Trefftz algorithms give accurate solutions in a relatively short computational time. Moreover, the Trefftz functions, fulfilling the governing differential equations, can be used as shape functions of finite elements (T-elements), also with openings and notches. This suggested the authors to investigate the advantages and limitations of the method in optimization of structures with the stress concentrators, e.g. perforated plates. Certain auxiliary object functions, which included simultaneously the objective of the optimization and the constraints, were introduced and investigated. Different optimization strategies were also taken into consideration. To improve the optimization task in case of a large number of variables the authors suggested an algorithm, which used the engineering sensitivity analysis to eliminate less important variables in the particular stages of the procedure.