PSI - Issue 54

Wojciech Skarka et al. / Procedia Structural Integrity 54 (2024) 498–505 Bartosz Rodak/ Structural Integrity Procedia 00 (2019) 000 – 000

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An unremarkable field when it comes to adapting surface shape is parametric geometry. Parametric geometry is a branch of mathematics that deals with describing and modeling shapes using mathematical functions. Unlike traditional geometry, in which figures are described by fixed coordinates, in parametric geometry figures are described by variable parameters. Parametric geometry is particularly useful in fields such as design, engineering and computer graphics, where accurate and precise modeling of shapes is necessary. In parametric geometry, figures are described by functions, which makes it easy to change their shape by changing parameter values. And consequently, thanks to parametrization, optimization algorithms can be easily combined with geometry editing. 2 This paper will present the theoretical basis of the optimization methodology and its application in practice, taking into account the various problems that can occur during the optimization process. 2. Parameterization and geometry Parametric geometry allows shapes to be described and modeled using mathematical functions. In optimization problems, these functions are used to describe many variables that can affect the final result. In this way, it is easy to change the value of the variables and determine the best solution for a given problem. Given this, generating a fully parameterized geometric model is crucial in an optimization problem. One of the main tools of parametric geometry is the equation of a curve. A curve is described by a parametric equation, which defines the position of a point on the curve depending on the value of a parameter. It is also possible to create solids using curve equations to model more complex shapes. A linear spline [1] will be used in solving the optimization problem using the design of experiments (DOE) method [2], which will be described in detail later in the paper. 3

2.1. CAD models

A CAD model of the connection between the wing and the nacelle was created. Separately - the model of the connecting element itself and the model of the whole with the wing and nacelle in order to simplify simulation and later verification of the whole structure. The connecting element is shown in Figure 1a, while the coordinates of the nodes of its sketch and the radius of the rounded leading

Fig. 1. (a) the connecting element; (b) coordinates of the nodes of its sketch and the radius of the rounded leading edge. edge are shown in Figure 1b.

The coordinates of the sketch nodes are input parameters in parametric geometry. The linear spline is based on these nodes. By parameterizing the sketch nodes, it is possible to modify the shape of the spline element at will. In a separate simulation for the optimal height of the connecting element, the input parameter will be the height of the connecting element. In this simulation, an analysis will be carried out on the entire structure to determine the optimal length of the connecting element between the wing and the nacelle.

Fig. 2. - CAD model of the entire wing structure, nacelle and connecting element Such a procedure will save time and computing power resources. Figure 2 shows a CAD model of the entire structure. It is assumed that the shape and size of the wing and nacelle are fixed. The nacelle is symmetrical in each axis.