Using finite-element analysis to predict springback saves time and expense in assembly operations.

CAD model of Boeing's next generation 737 defines the entire outer contour of the aircraft to be covered with sheetmetal skin sections individually designed and fabricated on different stretch-forming blocks.

Hydraulic grippers clamp both ends of a sheetmetal section and force it down over a stretch-form block. When the part is released, its shape springs back so that the final contour deviates from the block, often several hundredths of an inch.

Shell elements allowing for both membrane and bending are used to construct the FEA models, with a typical mesh density of approximately 4,000 elements. In this model, a curved node routine generates a point path for elements representing the countered end sections of the panel.

Analysts and press operators examine workpiece stress patterns such as on this 737 cab skin to find and correct potential production problems that could produce warpage and breakage. Once there is concurrence between the shop floor and engineering, the optimized model design is released for final surface preparation.


Sheetmetal often springs back after being stretch-formed to make aircraft outer body panels. When this happens, the skin may become wavy, necessitating the need for shims to fit the panels into place. Not only does this add weight, but it also increases the assembly time. Nonlinear finite-element analysis (FEA) accurately predicts this deflection so manufacturing processes can be compensated to produce panels with the proper contour.

Aircraft outer body panels are produced by bending aluminum sheet-metal over stretch-form blocks made to an exact surface contour. During the process, concentrated membrane and bending stresses force the workpiece to undergo complex wrinkling and buckling as it is formed. When the fixtures clamping the part are released, the elastoplasticity of the metal makes the piece spring back, which means the final shape of the panel deviates from the proper contour by several hundredths of an inch.

Standard calculations or empirical methods are not accurate or reliable in predicting springback because of complex material behavior, compound-surface geometry, and numerous process-boundary conditions. In the past, engineers would measure this deviation and then undercut the stretch-forming blocks until the die shape would satisfactorily compensate for springback.

Such trial-and-error methods are not practical in today's aircraft industry because of the significant time and expense needed to develop blocks for the large number of panels on a modern jetliner. Therefore, each block is NC machined to tight tolerances, which takes several days or even months.

Until recently, assemblers had to contend with panels that did not fit together properly, especially large compound-contoured skin sections.

Predicting springback
At Boeing's Wichita plant, nonlinear FEA predicts spring-back before stretch-form blocks are built. Compensation is then fed back into the CAD program before the stretch-form block is machined.

This approach has saved time and expense in assembly operations and reduced the extra weight formerly added by the many shims needed to fit skin panels in place. In a recent case, 100 lb of shims were eliminated from the cab section and installation time for the skins was shortened several days.

In addition to springback analysis, FEA plays an important role in optimizing the overall manufacturing process by letting press operators and analysts examine workpiece stress patterns during forming. By working together, potential production problems can be identified and corrected so that sheet-metal warpage and breakage can be reduced or eliminated. When agreement is reached between the shop floor and engineering, the optimized design is released for final surface preparation.

The FEA solution
Boeing needed to model contact forces between the sheet-metal and stretch-form blocks. It also wanted functions to handle non-linear material properties and large-displacement elastoplastic deformation. For this reason, it selected Marc and Mentat software from MARC Analysis Research Corp., Palo Alto, Calif.

To represent the materials typically used for aircraft skin sections, material characteristic data for the analysis is obtained by physically testing 2024-T3 and C188- T3 aluminum sheet-metal samples, with thickness ranging from 0.04 to 0.18-in. At least three samples are taken from each sheet in the longitudinal and transverse directions. The resulting stress versus strain curve is then fed into the Mentat data deck.

The geometry of the stretch-form block is imported from the Catia design package via IGES translator into Mentat for creation of the FEA model. For simplicity, multiple surfaces treated separately in Catia are linked into one contour, and patches are reduced before being imported.

Physical size of the sheetmetal sections being modeled are 90-in. wide, with lengths ranging from 250 to 460 in. Shell elements allowing for both membrane and bending are used to construct the FEA models, with a typical mesh density of approximately 4,000 elements.

Custom meshing is generally needed for complex skin geometry around areas such as the cockpit, while standard rectangular meshing is sufficient for other smoother sections. Severely compound-contoured areas require a friction coefficient to simulate loads between the block and workpiece and for monitoring separation forces at nodes to avoid sticking. To represent the jaws holding the ends of the sheetmetal in place on the stretch-forming block, a user-written subroutine, which established the proper boundary conditions, was developed.

The analysis performed by Marc software is cycled through four major steps representing the manufacturing process. In the initial wrap phase, jaws bend the sheet-metal over the block. Next, a stretch phase simulates large deformation of the sheet-metal as it conforms to the shape of the block. Then in an unloading phase, pressure reduction on the workpiece begins. Finally, the workpiece is brought entirely off the block in a release step.

Springback results are taken in the release portion of the analysis. The mesh is converted to a surface, points swept, and unused nodes and points removed to clean up the model. The final result is a group of points representing nodal locations of the sheet after it has sprung back off the block surface. The points are sent via IGES to Catia, where a routine subtracts the springback data from the original surface to create a new compensated contour.

In addition to springback analysis, Marc and Mentat are also used for thermal studies, creep-forming evaluation, and analysis of composite-forming processes where epoxy and graphite are used in making sections like engine nacelles.