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Optimization of Rectangular Tank Cross-Section Using Trust Region Gradient Method

Grabowski Tomasz, Szymczak-Graczyk Anna, Rutkowski Janusz

Inżynieria Mineralna

2024

Vol. 1, no. 2

art. no. 99

In various industries, rectangular tanks are commonly used for storing liquids and other materials. The design and optimization of these tanks are crucial for ensuring structural integrity and material efficiency. Traditional designs often utilize constant wall thickness, which does not align optimally with the stress distribution, leading to potential overuse of materials and increased costs. Recent studies have shown that tanks with variable wall thickness, such as trapezoidal cross-sections, can better match stress distributions, particularly under hydrostatic loads, resulting in more efficient use of materials. This research aims to build upon previous studies by introducing an advanced optimization algorithm based on the Trust Region Gradient Method to further refine the cross-sectional design of rectangular tanks. The primary objective is to minimize the material usage while maintaining structural safety and performance under various load conditions, including hydrostatic pressure and thermal effects. The proposed algorithm iteratively adjusts the tank's wall thickness, seeking an optimal configuration that reduces bending moments and material costs. Initial static calculations is verified using the finite difference method, emphasizing energy minimization conditions for elastic strain in bent plates on elastic foundations. This approach is compared with traditional discretization methods to validate accuracy. The trust region method is then applied to optimize the design, with a focus on achieving a balance between structural integrity and economic feasibility. Preliminary results indicate that the trust region gradient method can significantly enhance the design process, leading to substantial material savings and improved structural performance. The algorithm's effectiveness is demonstrated through case studies comparing tanks with constant and variable wall thickness. This research contributes to sustainable construction practices by promoting designs that use materials more efficiently and meet safety standards.

Gradient structure of ductile cast iron

Tomaszewska A., Woźnica H.

Inżynieria Materiałowa

2007

Vol. 28, nr 3-4

481-485

W artykule przedstawiono wyniki badań struktury żeliwa w gatunku EN-GJS-400-15 o strukturze ferrytyczno-perlitycznej w próbce o zmiennej grubości ścianki. Dokonano oceny podstawowych cech wydzieleń grafitu oraz osnowy żeliwa. Ustalono zależność pomiędzy liczbą wydzieleń grafitu oraz stosunek udziału ferrytu i perlitu w strukturze odlewu płytki "schodkowej" o grubości ścianki 5, 10, 15 i 20 mm. Stwierdzono, że w miarę zwiększania grubości ścianki odlewu zmniejsza się liczba wydzieleń grafitu, natomiast wzrasta ich wielkość oraz udział powierzchniowy, zwiększa się też udział powierzchniowy ferrytu. Zaobserwowano również, iż przy powierzchni badanej próbki udział ferrytu jest większy niż w środku.

In the article results of a research of the structure of EN-GJS-400-15 grade with a ferritic-pearlitic cast iron in a sample with a changeable thickness of its wall have been presented. An assessment of basic qualities of a graphite precipitations and the matrix of cast iron has been made. Relations in the amount of a graphite precipitations and the ratio of ferrite to pearlite in the structure of the cast of a 'step' plate with a wall of 5, 10, 15 and 20 mm in tfiickness have been determined. It has been found that the thicker the wall of the cast is, the more a number of graphite precipitations decreases; yet their size and surface grow, as well as the surface of ferrite. It has also been observed that at the surface of the tested sample the share of ferrite is much bigger than the one inside.