Virtual tools and methods are becoming increasingly important in order to predict the geometric outcome in early phases of the product realization process. Method of influence coefficients (MIC) in combination with Monte Carlo simulation (MCS) is a well-known technique that can be used in nonrigid variation simulation. In these simulations, contact modeling is important to ensure a correct result. Contact modeling simulates how mating surfaces are hindered from penetrating each other, giving rise to contact forces that contribute to the deformation of the parts when assembled and the final shape of the subassembly after springback. These contact forces have to be taken into consideration in each MCS-iteration. To secure reasonable response times, the calculation of the contact forces needs to be fast. In this paper, we formulate a quadratic programming (QP) problem to solve the contact problem. The case studies presented show that node-based contact modeling can be efficiently solved through QP.

During multidisciplinary design of welded aircraft components, designs are principally optimized upon component performance, employing well-established modelling and simulation techniques. On the contrary, because of the complexity of modelling welding process phenomena, much of the welding experimentation relies on physical testing, which means welding producibility aspects are considered after the design has already been established. In addition, welding optimization research mainly focuses on welding process parameters, overlooking the potential impact of product design. As a consequence, redesign loops and welding rework increases product cost. To solve these problems, in this article, a novel method that combines the benefits of design of experiments (DOE) techniques with welding simulation is presented. The aim of the virtual design of experiments method is to model and optimize the effect of design and welding parameters interactions early in the design process. The method is explained through a case study, in which weld bead penetration and distortion are quality responses to optimize. First, a small number of physical welds are conducted to develop and tune the welding simulation. From this activity, a new combined heat source model is presented. Thereafter, the DOE technique optimal design is employed to design an experimental matrix that enables the conjointly incorporation of design and welding parameters. Welding simulations are then run and a response function is obtained. With virtual experiments, a large number of design and welding parameter combinations can be tested in a short time. In conclusion, the creation of a meta-model allows for performing welding producibility optimization and robustness analyses during early design phases of aircraft components.

Geometrical variation is closely related to fulfillment of both functional and esthetical requirements on the final product. To investigate the fulfillment of those requirements, Monte Carlo (MC)-based variation simulations can be executed in order to predict the levels of geometrical variation on subassembly and/or product level. If the variation simulations are accurate enough, physical tests and try-outs can be replaced, which reduce cost and lead-time. To ensure high accuracy, the joining process is important to include in the variation simulation. In this chapter, an overview of nonrigid variation simulation is given and aspects such as the type and number of joining points, the joining sequence and joining forces are discussed.

During product development one important aspect is the geometric robustness of the design. This is due to the fact that all manufacturing processes lead to products with variation. Failing to properly account for the variability of the process in the design phase may lead to expensive redesign. One important tool during the design phase in many industries is variation simulation, which makes it possible to predict and optimize the geometric quality of the design. However, despite the increase in computer power, calculation time is still an obstacle for the wider use of variation simulation. In this article, we propose a new method for efficient compliant variation simulation of spot-welded sheet metal assemblies. The method is exact, and we show that the method leads to time savings in simulation of approximately 40–50% compared to current state-of-the-art variation simulation.