## 3 Computational Analysis and Modeling
### LPG Cylinder 3D Geometry and Material  
The integration and modeling of geometry using NURBS or T-Splines functions in finite element analysis remains a major concern of researchers. In the literature, we did not find any tools to perform a complete IGA containing geometric preparation, NURBS or T-Splines mesh, boundary conditions and a solution of a matrix system of elastic linear equations. In this work, we use the T-Splines plugin [28; 29; 30] integrated in Rhinoceros 3D V5 to realize our geometry (Figure 2). This part consists of three main steps: the creation of a CAD surface in Rhino V5 using the T-Splines plugin and the conversion of T-Splines surface representations into an IGA file (Figure 3) using Bezier extraction, which contains all the necessary information used in the Matlab main code (Figure 4), such as control points, element numbers, the degree of the T-Splines function, the T-Splines function basis and the boundary conditions of our problem, including the Dirichlet and Newman conditions. Figure 2: The LPG cylinder model is designed using the T-Splines plugin for Rhino 3D V5. * IGA (*.iga) file format type surface nodN 189 elemN 108 node -0.019863644689100931 -1.0184576006959873 50.999630868823537 1 node....... node....... node....... node 0 0 0 1 node 0 0 0 1 node 0 0 0 1 node 0 0 0 1  belem 16 3  set 15 node bottom 0 18 27 36 45 54 63 81 90 99 108 117 126 135 144 set 9 node left 0 1 2 3 4 5 6 7 8 set 16 node nextbottom 119 28 37 46 55 64 73 82 91 100 109 118 127 136 145 set 9 node nextleft 18 19 20 21 22 23 24 25 26 set 6 node nextRight 154 160 163 169 172 178 set 16 node nextTop 7 25 34 43 52 61 70 79 88 97 106 115 124 133 142 151 set 7 node right 153 161 162 170 171 179 180 set 16 node top 8 26 35 44 53 62 71 80 89 98 107 116 125 134 143 152  
In the block diagram presented in Figure 4, the following contributions were made:  
Geometry design and T-Spline mesh: The geometry was created using the T-Splines plugin in Rhinoceros 3D V5. The mesh generation process was customized to ensure compatibility with the IGA approach, and additional scripts were developed to extract and organize the mesh data necessary for analysis. Boundary conditions and mechanical properties: Custom MATLAB scripts were implemented to define the boundary conditions, including Dirichlet and Newman conditions, and to assign the mechanical properties of the aluminum 6061-T6 material. Numerical resolution (Solver): The matrix system of elastic linear equations, [K][u] = [F], was formulated and solved using the MATLAB solver, specifically developed for the T-Splines IGA approach to study the mechanical performance of LPG cylinders. Post-processing: The results were visualized using MATLAB, where custom plotting routines were developed to display the deformation and stress distributions. These visualizations provided a detailed analysis of the mechanical behavior of the LPG cylinder, helping to identify areas of stress concentration and regions that may be prone to failure under loading conditions. Figure 4: The LPG cylinder analysis steps with T-Splines IGA approach. Figure 3: IGA file format of LPG cylinder. *.iga, or *. com is a consacrated notation. The materials used to manufacture LPG cylinders include carbon steel alloys [31] (Figure 5), which are the most commonly used due to their low cost, high tensile strength and good formability, making them ideal for safely withstanding high internal pressures. We also find that the aluminum alloys [32] (Figure 5) are less common and are favored for lightweight applications where portability is required, offering good corrosion resistance but lower fatigue strength than steel. Finally, we found that glass fiber-reinforced polymer composites [33; 34; 35] (Figure 5) are mainly used for lightweight and corrosion-resistant LPG cylinders and are often favored in specialized or mobile applications due to their high pressure resistance and impact tolerance (Figure 6). To investigate the LPG cylinder, the aluminum alloy 6061-T6 (Table 1) [12] was utilized.