Abstract
A special class of quadratic programming (QP) problems is considered in this paper. This class emerges in simulation of assembly of large-scale compliant parts, which involves the formulation and solution of contact problems. The considered QP problems can have up to 20,000 unknowns, the Hessian matrix is fully populated and ill-conditioned, while the matrix of constraints is sparse. Variation analysis and optimization of assembly process usually require massive computations of QP problems with slightly different input data. The following optimization methods are adapted to account for the particular features of the assembly problem: an interior point method, an active-set method, a Newton projection method, and a pivotal algorithm for the linear complementarity problems. Equivalent formulations of the QP problem are proposed with the intent of them being more amenable to the considered methods. The methods are tested and results are compared for a number of aircraft assembly simulation problems.
Highlights
In the last decade a new modeling approach has been developed and applied to variation simulation and assembly optimization in aerospace and automotive industry
By using the variational formulation (Galin 1961; Tu and Gazis 1964; Lions and Stampacchia 1967; Kinderlehrer and Stampacchia 1980) and the substructuring (Turner et al 1956; Guyan 1965; Wriggers 2006; Petukhova et al 2014), contact detection is reduced to a quadratic programming problem that allows for large-scale computations of contact problems during variation simulation and assembly optimization
The choice of starting point for solving contact problem is discussed in Stefanova et al (2018), where the starting point for feasible interior-point method (IPM) is determined based on the physical interpretation of the quadratic programming (QP) problem (1), and is compared to the infeasible one with the starting point from D’Apuzzo et al (2010)
Summary
In the last decade a new modeling approach has been developed and applied to variation simulation and assembly optimization in aerospace and automotive industry (see Lupuleac et al 2010, 2011, 2019b; Dahlström and Lindkvist 2007; Lindau et al 2016; Yang et al 2016). The permanent fastening elements (e.g., rivets or bolts) are modelled by constraining the relative displacements of parts in the corresponding computational nodes In some cases, these two ways are combined by applying the normal fastening load while constraining the relative tangential displacement of the assembled parts. In industrial applications (e.g., see Lupuleac et al 2019b) the variation simulation is realized by generation of the large number of initial gap vectors g (cloud of gaps) and subsequent massive solving of contact problem (1). Such an approach can be considered as generalization of the Method of Influence Coefficients proposed in Liu and Hu 1997
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