**4.5 Sustainability analysis of GP**

SW Sustainability allows getting immediate feedback on the carbon footprint and other environmental impacts of the GP throughout its entire lifecycle, including material selection, production, transportation, use and end of life (Fig. 17).

Fig. 17. Environmental impact of the frame component of GP calculated by SW Sustainability.

#### **4.6 Shape optimization of GP**

258 Advanced Topics in Measurements

SW Sustainability allows getting immediate feedback on the carbon footprint and other environmental impacts of the GP throughout its entire lifecycle, including material selection,

Fig. 17. Environmental impact of the frame component of GP calculated by SW Sustainability.

Fig. 16. The mode shapes of the four lower natural frequencies of GP.

production, transportation, use and end of life (Fig. 17).

**4.5 Sustainability analysis of GP** 

In this specific situation one of the solutions could be increasing the GP bracket cross-section thickness and changing the shape at the most stressed place. The cross-section shape for bracket's strengthening is defined by the 3 knot points (Fig. 18 a) of NURBS. Design parameters are coordinates of the knot points varied in the following ranges: 3 ≤ *X*1 ≤ 6; 2 ≤ *X*2 ≤ 5; 0 ≤ *X*3 ≤ 3. As a cross-section profile is defined, the 3D-shape is created using the path curve (Fig. 18 b). The same shape for strengthening is created on the second bracket of the GP frame component. A maximal von Mises stress in the bracket was minimized with constraint on the GP volume (*v* <770500 cm3).

Fig. 18. Shape definition of bracket: (a) cross-section shape; (b) 3D- shape creation through path curve; (c) shape optimization result.

Von Mises stresses are compared in the design of the obtained shape and the initial shape (Fig. 19). There are 6 check points that show von Mises stresses distribution in the most stressed bracket cross-section. Volume of the obtained design is *v* = 770430 cm3. Change of

Fig. 19. Von Mises stress distribution in considered cross-section of: (a) initial design of GP and (b) optimized design of GP.

Shape Optimization of Mechanical Components for Measurement Systems 261

Of course, there are possibilities of further optimization of the path curve shape (Fig. 18b) and taking into account simultaneously the additional particular objectives such as maximal von Mises stress in material of the GP from dynamic loading in case of harmonic vibration excitations; styling of the GP using α-cut method (Zimmermann, 2001), the carbon footprint and other environmental impacts of the GP throughout its entire lifecycle calculated by SW

For the obtained optimal solution the dynamic behavior of the GP must be verified in case of

The results of shape optimization of the mechanical components for two different measurement systems are presented. The described approach allows obtaining smooth shapes that are easy to implement technologically. The jagged forms are excluded from the optimization process and there's no need for excessive computational resources. The most time-consuming step of the current approach is the FEM analysis of the full model for variants defined by design of experiments, the results of which are used for building metamodels of appropriate responses. Then the solution of various single objective problems and the implementation of different aggregation strategies for multiobjective

It will be interesting to compare the effectiveness of the current approach by using the metamodels obtained by kriging and radial basis functions instead of locally weighted

The research work reported here was made possible by partial financial support of Latvian

Audze, P. & Eglajs, V. (1977). New Approach for Design of Experiments. *Problems of* 

Auzins, J. Direct Optimization of Experimental Designs. (2004). 10th AIAA/ISSMO

Auzins, J. & Janushevskis, A. (2002). New Experimental Designs for Metamodelling and

Auzins, J.; Janushevskis, J.; Janushevskis, A. & Kalnins, K. (2006). Optimisation of designs

*Multidisciplinary Analysis and Optimization Conference*, Albany, NY, 28 Aug.-2 Sep.

Optimization, *Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V)*, July 7-12, 2002, Vienna, Austria, Editors: Mang, H.A.; Rammerstorfer, F.G.; Eberhardsteiner, J., Publisher: Vienna University of Technology, Austria,

for natural and numerical experiments*, Extended Abstracts of the 6th Int ASMO-UK/ISSMO conference on Engineering Design Optimization*. Oxford, UK, pp. 118 – 121.

the uniform base random excitations (see Fig. 21) by analysis of the full FEM model.

optimization are relatively easy in order to obtain an acceptable final solution.

Science Council grant No. 09.1267 and EU Project Filose (ID 231495).

Arora, J. S. (2004). *Introduction to Optimum Design.* – 2nd ed. – Elsevier

ISBN 3-9501554-0-6, pp. 1-10

*Dynamics and Strength*, Vol. 35, Riga: Zinatne, RU, pp. 104-107

2004., AIAA Paper 2004-4578, CD-ROM Number 17, pp. 1-17 Auzins, J. & Janushevskis, A. (2007). *Design of Experiments and Analysis.* Riga, LV

Sustainability, as well as natural frequencies of the GP.

**5. Conclusion** 

polynomial approximations.

**6. Acknowledgment** 

**7. References** 

the assembly volume is insignificant, but maximal von Mises stress level is reduced on ~82.4 %. Von Mises stress level changes in the cross-section of the GP bracket for initial and optimized variants are presented in Fig. 20.

Fig. 20. Von Mises stress distribution in the bracket check points.

Fig. 21. PSD of vertical displacement in characteristic points of the GP.

Of course, there are possibilities of further optimization of the path curve shape (Fig. 18b) and taking into account simultaneously the additional particular objectives such as maximal von Mises stress in material of the GP from dynamic loading in case of harmonic vibration excitations; styling of the GP using α-cut method (Zimmermann, 2001), the carbon footprint and other environmental impacts of the GP throughout its entire lifecycle calculated by SW Sustainability, as well as natural frequencies of the GP.

For the obtained optimal solution the dynamic behavior of the GP must be verified in case of the uniform base random excitations (see Fig. 21) by analysis of the full FEM model.
