Paul Slysh
PS Associates
San Diego, Calif.

Anyone designing high-performance cylindrical and conical-shell structures invariably wants to balance strength and low weight, along with several other characteristics including lowest-cost manufacturing. FEA and CAD software provide one way to shape complex forms, but these general-purpose programs work best when applied to a wider variety engineered structures and tasks.

Often hard-to-implement analysis methods may provide some assistance designing the cylindrical and conical shell structures traditionally found in aerospace products, such as rockets and launch vehicles. But these methods may not work equally well, if at all, designing structures that could be, for example, load carrying vacuum vessels or any thin-wall structure.

Software for shell structures
One particular program, Shell Structures Tools (SST), has been in development 40 years and addresses the lightweight, high-strength requirements, and more. Its start menu makes it easy to type in design requirements, and results are easy to understand and use in a format similar to Web pages. The software unifies design, manufacturing, and analysis based on classical, empirical, and FEA methods. It comprehensively and quickly produces a design along with production plans for the structure.

Shell structures designed by the software can be isogrid, waffle, monocoque, sandwich, honeycomb, or ring or stringer-rib stiffened. Several variations of those are possible. For example, sandwich structures can have fluted cores, honeycomb can have proprietary Hexcel cores, ribs can be stiffened with flanges and various skin-and-stringers can be used for shell stiffening.

When designing each structure, the software calls upon particular empirical, classical, and finite-element methods to size, analyze, and optimize about 11 characteristics the structures commonly need. This brief introduction to the software gives an idea of what designers would provide and what the software returns.

The Start Menu box outlines typical inputs needed to design and analyze a shell. The inputs for about 10 categories typically include the shell geometry such as the large and small ID for a cone, and a length. If the shell includes cutouts such as round portholes, designers supply porthole diameters and locations, and whether or not the structure will include load-bearing doors (a yes or no selection). Local loads can be applied to the shell several ways such as, normal loads and bending moments.

Users select the construction material, which can include metals, composites, and their adhesives. Depending on the material, designers may have to supply material properties at temperature. For a complete list of the input criteria see

The software lops time off design work several ways. For instance, its unformatted inputs means users need not supply a CAD model. The dimensions typed into the Start Menu, actually an Excel spreadsheet, give enough information to get things started. Users are also asked to supply edge conditions, external loads, needed safety factors, structural configurations, identify critical-failure modes, modal-response requirements, construction methods, requirements for trade-offs, and tolerances for manufacturing and structural analysis.

Using runtime files, the software generates a best design and presents results in a Web site. Results are globally modified so users might, for example, adjust the manufacturing tolerances once and the software finds all calculations that use them before recalculating. The design is complete and comprehensive for the supplied loads the first time SST produces an output.

It is not difficult to run the software but it is preferable that my firm return to clients results to the spreadsheet Start Menu submitted by clients. Hence, the first turn-around may take a day or two. But after the program generates runtime files, iterations on the original design can be a matter of minutes.

The software generates a wide range of useful information. For example, users might first evaluate a rendered CAD model of the calculated design. Then, a measure of high-cycle fatigue strength assesses how a structure will withstand exposure to high-frequency vibrations during intended use, such as afterburners on a jet engine. A damage-tolerance figure indicates how rapidly a crack might propagate in a particular structure. And a manufacturing cost indicator tells which of two or more competing designs would be less expensive to produce.

Outputs also include appropriate selections based on loading and design criteria. The software also produces factors for stability and stress, along with cross section and mass properties.

Other results include detailed geometry, body stiffness, material and flat-pattern properties, DXF file for the flat-pattern, and selected margin summaries. Sample outputs shows just one table of many. All these are generated from a single set of inputs.

For a closer look at the outputs, consider the margins and trades summaries. They tell more about a proposed design. The Table of margins organizes the actual and critical stresses for several engineering characteristics. For example, a stress margin is a function of the ratio of allowable stress to actual stress divided by a user selected safety factor:

M = [(Sa/Sc)/ fs] -1

where M = margin value, Sa = allowable stress, a fixed material property; Sc = calculated stress, from SST; and fs = factor of safety, a value greater than 1. Super Traces show the methods implemented that defend results and are provided for all margin calculations. The Start Menu lets users supply allowable ultimate and limit stresses as well as safety factors for various failure modes. Twelve different margins can be selected as sizing criteria.

Fine-tuning a design usually calls for many engineering decisions. The trades or trade-off graphs can guide those. Critical tolerances can also be selected, or based on software defaults for computing the indicated margins and associated stresses. The other outputs also update with each input-menu change.

Digging deeper in the results shows design definitions, flat patterns, dimensioned rib cross sections, and mass properties at tolerance. Additional tables include SP8007 analysis, (a NASA-developed evaluation for aerospace structures), modal response, and internal line loads on structure elements for each external load case.

For manufacturing, the software generates NC toolpaths for constant chip-load machining. The software also shows how to make bolted flanges, bosses, and mounting devices that are part of these structures. And some users have said the software lets them master the art of producing metallic isogrid, waffle, and skin stringer structures.

Additional manufacturing output predicts the minimum cold-forming radii of isogrid and waffle structures. The predictions are for isogrid or waffle pockets filled, or not, with a hard elastomer that prevents skin buckling during forming. These predictions are based on manufacturing tolerances and minimum allowable gauges. The predictions for postmachine forming enter the design, sizing, and optimization calculations where their effects on structural performance and weight are taken into account.

Guidelines for trade-offs
The trade or trade-off table is one of many SST outputs. For the selected fixed parameters in the heading, the software generates a trade graph for plate thickness in the abscissa and number of longitudinal ribs in the field. In this case the parameters selected for trading are minimum-margin value (in the right ordinate) with unit-area weight (in the left ordinate). The dark line (top right) shows a locus of optimum results. Software results might indicate a plate thickness greater than what might be available at reasonable cost. The designer could want to know what increase in weight, or decrease in effective margin, or both would result from the use of a thinner plate that might be more readily available. The designer may or may not find the off-optimum results acceptable. Sometimes, minimum-allowable gauges, flange widths, material types, and tolerances can enter design decisions the same way, and may require revised design approaches.


Cone sweet cone
An unusual application for a shell structure came from a NASA request for ideas on how to protect space travelers from small meteors and radiation. SST let PS Associates propose a series of conic isogrid structures that could provide lightweight housing and protection needed by the agency’s SBIR (Small business innovative research) X6.01 (

The habitat concept uses inner and outer conical structures with isogrids for light weight and strength. The cones would be nested for transport into space and there bolted together into a tunnellike volume. The outer structure (larger cones) and a thermal layer (not shown) protect against meteorites and space debris. The inner structure would use O-rings at flanged joints for airtight seals.


Thinking outside the shell
SST software can be applied to more than curved-shell structures. For example, bolting or welding plates together allows building structures for other functions, such as howitzer mounts and hospital beds.


SST software can be applied to aerospace equipment such as launch vehicle primary structures, aircraft engine ducts and firewalls, along with more down-to- Earth applications such as vacuum vessels and solar panels.

SST can generate these and other shell structures. Designs can include bolted flanges, kick rings, and bosses, and features designed into structures. Isogrid and waffle structures can be machined or chemically milled to control dimensions on the ribs and skin.

The table shows dimensions for ribs, frames, and plate thicknesses used in a design.

This abbreviated table presents margins and critical stress along with safety factors and other values that guide engineering decisions. In the Tolerance column, T refers to skin thickness, W to plate thickness, and B is rib width.

Outputs from SST are used to create rendered versions of the design inputs, in this case, as a Pro/E model.

Nested inner structures are stowed within the nested outer structures. Dimensions are in inches.

The rectangular cradle made for the Navy’s Phalanx machine gun consists of several panels reinforced and lightened with isogrids. Design goals were to make the cradle stiff enough to withstand vibrations when the gun fired.