Submarine design typically follows American Bureau of Shipping (ABS) code, which establishes properties such as hull thickness, frame stiffness, and porthole and hatch design. During certification, ABS evaluates whether a design follows the relevant codes and then certifies it or not on that basis. The design of a deep-diving submarine was so unique that some ABS rules could not be adhered to.

The submarine design company had specific requirements for its vessel. First, it had to be capable of diving to a depth of 1,200 feet. Second, the company wanted extra-large viewing ports and a sophisticated video imaging system with sufficient lighting to intimately observe the marine environment. Comfortable seating for 10 passengers (including crew) was another requirement. In terms of performance, the submarine was to have a submerged endurance time of 8 to 10 hours, and emergency life-support sufficient to sustain 10 adults for at least 72 hours. Finally, the weight of the submarine could not exceed the limitations of the existing surface support unit, which was a very large yacht.

The design firm enlisted Predictive Engineering when the design was nearly finished. Knowing they had deviated from ABS code, they wanted a virtual evaluation of the performance of the submarine prior to construction and actual sea trials, including prediction of global buckling behavior and local stress concentrations using finite element analysis (FEA) software.

Creating the finite element model of the submarine was the first and most important task. CAD geometry representing the vessel was in two formats: Pro/Engineer (the sub's superstructure) and Autodesk Inventor (the hull skin, the hatches, view ports, and their forgings). The Inventor data was a combination of surfaces and solids. The preprocessor used — Femap from UGS — imported the different formats and enabled the engineers to set up the data exactly as needed for an accurate analysis.

The model for predicting hull buckling and stress concentrations was particularly difficult, and size had to be such that multiple analysis iterations could be run. Engineers also had to deal with the disparity between the thin shell of the hull and the thicker, non-uniform forged structures such as the hatches and viewing ports. The model was constructed as a blend of 4- node plate elements (representing the hull's skin and outer reinforcement rings) and 8-node brick elements (representing the forgings).

The model had approximately 67,000 nodes and 58,000 elements — extremely small by typical FEA standards — and required a run time of about five minutes for the linear runs, and 30 minutes for the geometrically non-linear buckling analyses using the Nastran solver.

Applying the pressure loads was difficult, because as a sub dives, it is under hydrostatic pressure, which means that the pressure field is completely balanced. If one sums the forces over the entire sub, the sum should be zero. Femap applied the loads and verified that when the loads were summed, they actually come out to zero.

Numerous analysis runs were made, always refining the model. In the analyses, the submarine was taken to well below the target depth of 1,200 feet. The results ultimately were verified against strain measurements made during a carefully validated dive test. (The strain measurements were taken using a fiber Bragg grating strain system.) In almost all cases, the strain measurements correlated well with the FEA predictions.

The finite element model, extensive FEA results, and the experimental (strain gauge) data were sent to the ABS for certification. The organization accepted this data and certified the submarine based on the numerical methods instead of ABS code.

This work was performed by George Laird, Ph.D., P.E., and Chief Technologist at Predictive Engineering, using software from UGS. For more information, visit .