1. The Effect of T-Stiffener Web and Flange Tilt on Frame Stress Evaluated using Finite Element Analysis by Dean Pasquerella MASTER OF ENGINEERING Major Subject: MECHANICAL ENGINEERING Project Adviser: Ernesto Gutierrez-Miravete Rensselaer Polytechnic Institute Hartford, Connecticut December, 2014

2. Brief Overview Goal: Use finite element analysis to determine at what angular offset a T-stiffener will exceed yield when subjected to uniform loading from submergence pressure in a submarine application. It is unavoidable during the fabrication and construction process of a plate/stiffener assembly to create geometrical imperfections. These imperfections result in an increase in stress and deflection of the stiffener due to a modified load path. However, during typical initial design, these deficiencies are not taken into account, as the assembly is analyzed as having perfect geometry. Therefore, the effect on specification requirements for stress due to tilt in the web and flange of a T-stiffener is unknown. Evaluation: The evaluation will be performed on a cylinder supported by T-stiffeners, which is externally pressurized to simulate a submarine under sea pressure. Initial engineering design will be performed on a T-stiffener in which the web and flange are perpendicular to one another and the web and cylinder are perpendicular to one another. This will serve as the baseline model. The vertical web and horizontal flange pieces of the T-stiffener will then be offset to certain angular imperfections resulting in increased stress and deflection in the T-stiffener. Varying offsets of the web and flange will be evaluated to determine what construction tolerances are required to assure that the design does not result in stresses exceeding specification tolerances, which in turn could lead to failure in the design.

3. Introduction/Background Schematic Showing the Portions of a T-Stiffener Elevation View of a Submarine Pressure Hull with Internal Stiffeners Cross Section View of Different Web and Flange Tilt Combinations

4. Theory/Methodology Assumptions: Material: HY-100 Steel Loading: 1100 psi uniformly distributed external pressure Stress Allowable: 95% of the material yield strength Geometry: stiffener size = 10.0” x 6.0” x 0.5” x 0.7”, shell thickness = 1.5”, outside diameter = 360”, frame spacing = 30” Closed Form Solution: Circular cylindrical shell reinforced by uniformly space ring fames Finite Element Analysis: Elements: 2-dimensional, four noded, quadrilateral general shell elements Model Type: Sub-model of only 4 stiffeners total

5. FEM Loading and Boundary Conditions Submarine Pressure Hull and Sub-Model Location Depiction of the Location of End Load and Displacement Boundary Conditions Depiction of the Location of End Load and Displacement Boundary Conditions in Relation to Frame Locations Section View at Cut Plane Showing Location of Displacement Boundary Conditions

6. Preliminary Evaluation Purpose: Perform a boundary condition evaluation and mesh convergence study to determine the most accurate baseline model to use in the evaluation. Convergence Analysis: Mesh Convergence Study: Section View Showing Frame Locations Results Description of Mesh Density Results

7. Closed Form Solution: Peak compressive stress on the internal face of the flange: 94.79 ksi < 95.0 ksi allowable Baseline Model: Peak compressive stress on the internal face of the flange: 94.69 ksi, 0.11% difference from closed form solution Model Iterations: Peak compressive stress on the internal face of the flange exceeds 100 ksi with a 2.0 degree web and flange tilt Peak compressive stress on the internal face of the flange with a 1.5 degree web and flange tilt: 99.38 ksi < 100 ksi maximum limit Web and Flange Tilt Model Iteration Results

8. Stress and Deflection Plots FEM Results for 2.0 Degree Web and Flange Tilt Condition

9. Conclusions Using 2-dimension quadrilateral elements, the initial design was constructed using FEA to validate the closed form solution and allow for modifications of the stiffener geometry. The baseline FEM resulted in a peak compressive stress in the frame of -94.69 ksi, which has a percent difference from the closed form solution of 0.11%. A difference of 0.11% is considered adequate for the level of accuracy required for pressure hull structure design. The baseline FEM was then modified by varying the angular offset of the web to the pressure hull and the flange to the web until a peak compressive stress exceeded the 100 ksi allowable limit. Using this approach, a web and flange tilt of 2.0 degrees resulted in a peak compressive stress of -101.42 ksi, which exceeded the allowable by 1.42 ksi, while a web and flange tilt of 1.5 degrees resulted in a peak compressive stress of -99.38 ksi, which is within the allowable limits. Therefore, for the pressure hull design evaluated herein, the specification documentation shall require a web and flange tilt of less than or equal to 1.5 degrees to assure yield of the material is not exceeded, which could result in failure of the design. The 1.5 degree requirement for web and flange tilt is within the capabilities of welding and assembly of typical pressure hull submarine structure. Knowing the allowable web and flange tilt tolerance permits engineering, design and trades personnel to make informed decisions about construction of the pressure hull. During measurement of these geometrical properties, any value below 1.5 degrees for web or flange tilt can be accepted without requiring rework of the structure. Additionally, steps can be taken in the fabrication and assembly processes to utilize this tolerance to construct the submarine while taking into account quality, time and cost.