ORIGINAL ARTICLE
Optimal Design of Rectangular Tank Walls With Ribs Using Numerical Models and Global Optimization
 
More details
Hide details
1
Department of Biosystems Engineering, Poznan University of Life Sciences, Poland
 
2
Department of Construction and Geoengineering, Poznan University of Life Sciences, Poland
 
 
Submission date: 2024-10-25
 
 
Final revision date: 2024-10-29
 
 
Acceptance date: 2024-11-05
 
 
Online publication date: 2024-11-17
 
 
Publication date: 2024-11-17
 
 
Corresponding author
Anna Szymczak-Graczyk   

Department of Construction and Geoengineering, Poznan University of Life Sciences, Poland
 
 
Civil and Environmental Engineering Reports 2024;34(4):293-306
 
KEYWORDS
TOPICS
ABSTRACT
This paper addresses the optimization of the cross-section in rectangular above-ground tank walls, incorporating vertical ribs and an optional top ring. The objective is to minimize the volume of concrete used, while maintaining key performance criteria such as keeping the maximum tensile stress below the material’s allowable limit and minimizing deflections. The analysis is performed using the finite element method (FEM), with the optimization handled through a local gradient-based algorithm (trust region method), supported by a multistart technique to navigate the complexity of the design space and avoid suboptimal solutions. The results demonstrate that this approach effectively reduces concrete consumption without exceeding the tensile stress limits or causing excessive deflection, offering more efficient and cost-effective designs for rectangular tanks used in water storage applications. This method provides valuable insights into the balance between material usage and performance constraints, contributing to sustainable engineering practices.
 
REFERENCES (36)
1.
Laks, I, Walczak, Z and Walczak, N 2023. Fuzzy analytical hierarchy process methods in changing the damming level of a small hydropower plant: Case study of Rosko SHP in Poland. Water Resources and Industry 29, 100204. doi: 10.1016/j.wri.2023.100204.
 
2.
Laks, I and Walczak, Z 2020. Efficiency of Polder Modernization for Flood Protection. Case Study of Golina Polder (Poland). Sustainability 12, 8056. doi: 10.3390/su12198056.
 
3.
Ziółko, J 1983. Zbiorniki, silosy [Tanks, silos]. In: Bogucki W (ed) Poradnik projektanta konstrukcji metalowych: Tom II [Designer’s guide to metal structures: Volume II]. Warszawa: Arkady.
 
4.
Ziółko, J 1986. Zbiorniki metalowe na ciecze i gazy [Metal tanks for liquids and gases]. Warszawa: Arkady.
 
5.
Horajski, P, Bohdal, L, Kukielka, L, Patyk, R, Kaldunski, P and Legutko, S 2021. Advanced Structural and Technological Method of Reducing Distortion in Thin-Walled Welded Structures. Materials 14, 504. doi: 10.3390/ma14030504.
 
6.
Buczkowski, W, Mikołajczak, H and Szymczak-Graczyk, A 2005. Przykładowa ocena rozwiązań materiałowo-konstrukcyjnych zbiorników cylindrycznych z żywic poliestrowo-szklanych stosowanych w przydomowych oczyszczalniach ścieków [Example evaluation of material and structural solutions for cylindrical tanks made of polyester-glass resins used in domestic sewage treatment plants]. Gaz, Woda i Technika Sanitarna 12, 25-28.
 
7.
Mang, HA and Cedolin, L 1978. Cooling tower analysis by a finite element technique based on a modified Hamilton’s principle. Meccanica 13, 208–224. doi: 10.1007/bf02128387.
 
8.
Bamu, PC and Zingoni, A 2005. Damage, deterioration and the long-term structural performance of cooling-tower shells: A survey of developments over the past 50 years. Engineering Structures 27, 1794–1800. doi: 10.1016/j.engstruct.2005.04.020.
 
9.
Wen-da, L and Hao-zhong, G 1989. Buckling of cooling tower shells with ring-stiffeners. Applied Mathematics and Mechanics 10, 583–592. doi: 10.1007/bf02115790.
 
10.
Mang, H, Gallagher, RH, Cedolin, L and Torzicky, P 1978. Deformation und Stabilität windbeanspruchter Kühlturmschalen. Ingenieur-Archiv, 47, 391–410. doi: 10.1007/bf00538360.
 
11.
Halicka, A and Franczak, D 2011. Projektowanie zbiorników żelbetowych. Tom 1. Zbiorniki na materiały sypkie [Design of reinforced concrete tanks. Volume 1. Tanks for bulk materials]. Warszawa: Wydawnictwo Naukowe PWN.
 
12.
Halicka, A and Franczak, D 2014. Projektowanie zbiorników żelbetowych. Tom 2. Zbiorniki na ciecze [Design of reinforced concrete tanks. Volume 2. Tanks for liquids]. Warszawa: Wydawnictwo Naukowe PWN.
 
13.
Sybis, M and Konował, E 2022. Influence of Modified Starch Admixtures on Selected Physicochemical Properties of Cement Composites. Materials 21, 7604. doi: 10.3390/ma15217604.
 
14.
Sybis, M, Konował, E and Prochaska, K 2022. Dextrins as green and biodegradable modifiers of physicochemical properties of cement composites. Energies 11, 4115. doi: 10.3390/en15114115.
 
15.
Buczkowski, W, Szymczak-Graczyk, A and Walczak, Z 2017. Experimental validation of numerical static calculations for a monolithic rectangular tank with walls of trapezoidal cross-section. Bulletin of the Polish Academy of Sciences: Technical Sciences 65, 799–804. doi: 10.1515/bpasts-2017-0088.
 
16.
Szymczak-Graczyk, A 2020. Numerical Analysis of the Bottom Thickness of Closed Rectangular Tanks Used as Pontoons. Applied Sciences 10(22), 8082. doi: 10.3390/app10228082.
 
17.
Szymczak-Graczyk, A 2018. Floating platforms made of monolithic closed rectangular tanks. Bulletin of the Polish Academy of Sciences: Technical Sciences 66, 209–219. doi: 10.24425/122101.
 
18.
Buczkowski, W and Szymczak-Graczyk, A 2020. Monolityczne zbiorniki prostopadłościenne obciążone temperaturą [Monolithic rectangular tanks subjected to temperature loads]. Przegląd Budowlany 9, 24-29.
 
19.
Buczkowski, W 2008. On reinforcement of temperature loaded rectangular slabs. Archives of Civil Engineering 54(2), 315-331.
 
20.
Buczkowski, W, Czajka, S and Pawlak, T 2006. Analiza pracy statycznej zbiornika prostopadłościennego poddanego działaniu temperatury [Static analysis of a rectangular tank subjected to temperature loads]. Acta Scientiarum Polonorum, Architectura 5(2), 17-29.
 
21.
Szymczak-Graczyk, A 2019. Rectangular plates of a trapezoidal cross-section subjected to thermal load. IOP Conference Series: Materials Science and Engineering 603, 032095. doi: 10.1088/1757-899X/603/3/032095.
 
22.
Staszak, N, Garbowski, T and Szymczak-Graczyk, A 2021. Solid Truss to Shell Numerical Homogenization of Prefabricated Composite Slabs. Materials 14, 4120. doi: 10.3390/ma14154120.
 
23.
Staszak, N, Szymczak-Graczyk, A and Garbowski, T 2022. Elastic Analysis of Three-Layer Concrete Slab Based on Numerical Homogenization with an Analytical Shear Correction Factor. Applied Sciences 12, 9918. doi: 10.3390/app12199918.
 
24.
Staszak, N, Garbowski, T and Ksit, B 2023. Optimal Design of Bubble Deck Concrete Slabs: Sensitivity Analysis and Numerical Homogenization. Materials 16, 2320. doi: 10.3390/ma16062320.
 
25.
Staszak, N, Garbowski, T and Ksit, B 2022. Application of the Generalized Nonlinear Constitutive Law in Numerical Analysis of Hollow-Core Slabs. Archives of Civil Engineering 68(2), 125-145. doi: 10.24425/ace.2022.140633.
 
26.
Gajewski, T, Staszak, N and Garbowski, T 2023. Optimal Design of Bubble Deck Concrete Slabs: Serviceability Limit State. Materials 16, 4897. doi: 10.3390/ma16144897.
 
27.
Azmakan, A, Ahmadi, J, Shahani, A, Badarloo, B and Garbowski, T 2024. Optimal Quantity Investigation of Metakaolin and Silica Fume in Production of Durable Acid Resistance Alkali Activated Slag Concrete. Buildings 14(1), 21. doi: 10.3390/buildings14010021.
 
28.
Szymczak-Graczyk, A, Garbowski, T and Ksit, B 2024. Influence of geometric parameters on internal forces in the walls of rectangular tanks. Proceedings of the 9th World Multidisciplinary Congress on Civil Engineering, Architecture and Urban Planning, Ostrava, Czech Republic, September 2-6, [in print].
 
29.
Garbowski, T, Szymczak-Graczyk, A and Rutkowski, J 2024. Optimization of Rectangular Tank Cross-Section Using Trust Region Gradient Method. Proceedings of the 9th World Multidisciplinary Congress on Civil Engineering, Architecture and Urban Planning, Ostrava, Czech Republic, September 2-6, [in print].
 
30.
MATLAB 2023b. MATLAB version 9.14.0 (R2023b). Natick, Massachusetts: The MathWorks Inc.
 
31.
Lee, J and Fenves, GL 1998. Plastic-Damage Model for Cyclic Loading of Concrete Structures. Journal of Engineering Mechanics 124(8), 892–900.
 
32.
Hillerborg, A, Modeer, M and Petersson, PE 1976. Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements. Cement and Concrete Research 6, 773–782.
 
33.
Lubliner, J, Oliver, J, Oller, S and Oñate, E 1989. A Plastic-Damage Model for Concrete. International Journal of Solids and Structures 25, 299–329.
 
34.
Ugray, Z, Lasdon, L, Plummer, J, Glover, F, Kelly, J and Martí, R 2007. Scatter Search and Local NLP Solvers: A Multistart Framework for Global Optimization. INFORMS Journal on Computing 19(3), 328–340. doi: 10.1287/ijoc.1060.0175.
 
35.
Neumaier, A 2004. Complete Search in Continuous Global Optimization and Constraint Satisfaction. Acta Numerica 13, 271–369. doi: 10.1017/S0962492904000194.
 
36.
Horst, R and Pardalos, PM 1995. Handbook of Global Optimization. Boston, MA: Springer. doi: 10.1007/978-1-4615-2025-2_20.
 
eISSN:2450-8594
ISSN:2080-5187
Journals System - logo
Scroll to top