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2 2024

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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.

Influence of Geometric Parameters on Internal Forces in the Walls of Rectangular Tanks

Szymczak-Graczyk Anna, Grabowski Tomasz, Ksit Barbara

Inżynieria Mineralna

2024

Vol. 1, no. 2

art. no. 27

Rectangular tanks are commonly used in various industries for storing materials and products. The design of reinforced concrete liquid tanks, which must be preceded by a static analysis, is a complex issue requiring specialized knowledge and engineering experience. All types of actions, design situations, and resulting load combinations must be considered, including deformations caused by temperature gradients and the interaction of the bottom plate with the ground. Most tanks are designed and constructed with constant wall thickness, regardless of their rectangular or circular cross-section. However, tanks with variable wall thickness (e.g., trapezoidal cross-section) are rarely designed, despite their optimal fit to stress distribution. For hydrostatically loaded tanks, the load on walls increases with depth, causing the highest bending moments at the wall-bottom connection, while the value at the top, free edge is zero. Thus, structural and economic considerations favour walls with thickness increasing with depth. This article presents the results of a verification of static calculations of a monolithic rectangular tank with trapezoidal cross-section walls, comparing it with three other commonly designed tanks with different thickness and wall designs. Static calculations were performed using the finite difference method in terms of energy, employing the condition for the minimum energy of elastic strain stored in a bent plate resting on the elastic base. Traditional calculation methods were used by discretizing the object and creating systems of equations. Analysis of the results shows that constructing walls of linearly variable thickness results in a redistribution of bending moments compared to tanks with uniform wall thickness. This significantly impacts the required reinforcement area. Tanks with linearly variable wall thickness are more economical in terms of material use, aligning with the principles of sustainable construction.