Solving basic problems of compliant tolerance analysis by static analogy

Predicting the geometric variation of sheet metal assemblies is a complex task, because deformation during joining operations influences the propagation of initial part deviations. To consider this effect, the paper proposes a method that formulates tolerance analysis as an equivalent problem of static analysis. Previously proposed for rigid parts, the static analogy is extended to compliant parts and applied to two-dimensional problems modeled with straight beams under the assumptions of small displacements and normal distributions of errors. For such simple cases, the method solves the problem by linearization, avoiding the use of Monte Carlo simulation and the related computational burden. Compared to existing linearization methods, the static analogy is less efficient in the integration with a finite element solver. However, it features an especially simple procedure that does not require the calculation of deflections, thus allowing a streamlined solution and even manual calculations. The comparison with alternative methods provides a first verification of the feasibility of the method, in view of further developments with the aim of dealing with cases of realistic complexity.