The Effect of T-Stiffener Web and Flange Tilt on Frame Stress Evaluated using Finite Element Analysis

byDean Pasquerella

MASTER OF ENGINEERINGMajor Subject: MECHANICAL ENGINEERING

Project Adviser: Ernesto Gutierrez-Miravete

Rensselaer Polytechnic InstituteHartford, Connecticut

December, 2014

Brief OverviewGoal: 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.

Introduction/BackgroundSchematic 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

Theory/MethodologyAssumptions: Material: HY-100 SteelLoading: 1100 psi uniformly distributed external pressureStress 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 elementsModel Type: Sub-model of only 4 stiffeners total

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

Preliminary EvaluationPurpose: 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:

Frame # Frame Stress (ksi) % Change1 -92.56 -2 -94.21 1.783 -94.35 0.154 -94.32 0.035 -94.32 0.006 -94.32 0.00

Section View Showing Frame LocationsResults

Circumferentially Longitudinally Per BayConverge1.cdb 120 = 3 degrees 4 9.4 x 7.5 2 5.2 2 3.5Converge2.cdb 180 - 2 degrees 4 6.3 x 7.5 3 3.5 2 3.5Converge3.cdb 270 - 1.5 degrees 8 4.2 x 3.8 3 3.5 4 1.8Converge4.cdb 360 = 1 degrees 8 3.1 x 3.8 4 2.6 4 1.8

Model Name# of Elements # of Elements

Shell# of Elements

Size (in.)

Web Height

Length (in.)

Flange Width

Length (in.)

Description of Mesh Density Results

ResultsClosed 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 tiltPeak 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 (Degrees)

Peak Compressive Stress in Frame (ksi)

0.0 -94.690.5 -96.361.0 -97.871.5 -99.382.0 -101.42

Web and Flange Tilt Model Iteration Results

Stress and Deflection Plots

FEM Results for 2.0 Degree Web and Flange Tilt Condition

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.