Computerized Handbooks Reduce Time Required for Finite Element Input Preparation and Results Verification

The technology of finite element analysis (FEA) is used universally to calculate stress and deflection of mechanical structures. Unfortunately, finite element analysis can easily produce misleading or incorrect results if the problem is incorrectly formulated. For this reason, hand calculations are normally used in conjunction with FEA to initially understand the structure's behavior, to focus the analysis, and to ultimately validate the analysis results. For a complex problem, these hand calculations may be so time-consuming that they rival the length of time required for the analysis itself. Even worse, to save time they may be skipped, thereby overlooking possible errors.

For these reasons, many engineers have turned to the new generation of computerized engineering handbooks as a finite element analysis input preparation and verification tool. In a minute or two, these new computer tools provide basic force, stress and deflection calculations which determine whether or not the more detailed results provided by the full analysis are reasonable. These handbooks can also be used to substantially reduce modeling and analysis time and expand on the results provided by the original analysis.

This new generation of general computerized handbooks covering fundamental engineering calculations, such as stress and deflection of basic engineering structures, first became available a few years ago and its usage is already established in many engineering departments. In most cases, using closed form solutions, the program performs the appropriate equation substitutions, integration, and boundary condition analysis in exactly the way an engineer would solve the problem by hand. In some of the more complicated analyses, the computerized handbook uses finite elements to obtain a solution; however, the input and output format remains similar to the other solution modules and the user is not required to know finite element techniques. Moreover, once a problem is accurately set up and modeled, it can be quickly changed and rerun to allow the user to look at various options or modifications. An example of a computerized handbook is provided by a program called DE/CAASE (Desktop Engineering/Computer Aided Analytical Solutions for Engineers), which incorporates solutions to over 5000 structural/mechanical engineering equations found in over 100 reference books.

Judicious use of this type of tool prior to finite element analysis can significantly reduce analysis and modeling time and produce more accurate results. Going one step further, the computerized handbook can be used to quickly perform a parametric study of a component to get a better understanding of the effect of various dimensions and features on its mechanical properties. Often, this leads to pre-analysis design changes which greatly reduce the number of iterations required.

An example of the use of a computerized handbook to save time prior to analysis is provided by General Electric Nuclear Energy, San Jose, California. The task is to qualify the control panels and equipment in the control room of a nuclear power plant to ensure their structural integrity and operability. Some of the computational tools used in performing this function at GE are advanced finite element codes such as NASTRAN, ANSYS, SUPERSAP and STARDYNE. The structures involved contain a wide variety of complex sections which would not be practical to incorporate directly into a finite element model because they would significantly increase both modeling and solution time. Standard procedure in the past was to calculate section properties by searching through a reference manual or handbook to find the section property formulas, generating equations to combine properties for section components, and then solving them with a calculator.

For a typical corner post of a control panel, comprised of angles, channels, unistruts and rolled plate elements, the required calculations would include finding the neutral axis for each element, using the parallel axis theorem to find the neutral axis for the entire section, then calculating the moments of inertia, section areas and other section properties. This process typically took about an hour to calculate and verify for a typical section. With the computerized handbook, all that is essentially required is to enter the dimensions of the various sections -- the program calculates the required section properties. This typically takes less than 5 minutes. The ability to obtain results this quickly has made it possible to perform parametric studies which allow GE to evaluate far more design alternatives than were previously possible. Aside from time savings, another major advantage of the handbook is that it automatically provides complete documentation of all of the calculations that were performed.

After a finite element analysis has been completed, the closed-form solutions produced by the computerized handbook can be used to verify the accuracy of the FEA analysis. Normally verification is performed with hand calculations that take somewhere between 30 and 60 minutes. The same task can be accomplished in 5 to 10 minutes with a computerized handbook with less chance of error. In addition to verifying the overall structural analysis, the computerized handbook can be used to enhance analysis results. For example, in most cases with a global finite element analysis, it is difficult or impossible to closely examine the loading on individual members of the structure. A computerized handbook can take the internal loading generated by the analysis as well as external loads and apply them to a single beam or other member. A parametric study can be performed to determine the optimum sectional dimensions. In a similar way, the handbook can be used to examine details which may not be included in the analysis --for example stress concentration around an opening . It can also be used to quickly perform other types of analysis which may not otherwise have been performed such as calculating natural frequencies of the structure. Finally, multiple loading conditions can be examined in far less time than would be required to incorporate them in the finite element model.

Here's an example of how a computerized handbook was used for post-analysis verification. The problem was to determine the required thickness of the cylindrical walls of a storage tank in order to meet various safety requirements. A finite element model was prepared and analyzed for hydrostatic loading conditions in a few hours. The Desktop Engineer pressure vessel module verified these results in only a few minutes. How can The Desktop Engineer provide such a quick solution? The answer is due to its friendly menu system and user interface. For instance, the pressure vessel module offers a choice of top and bottom vessel configuration. A conical top and flat bottom were selected to match the design in question. The next step was entering Young's modulus and Poisson's ratio for the type of steel used. Then, dimensions were entered including the radius, height and thickness of the cylindrical shell portion, the thickness and height of the top section, and the thickness of the base. The structure was loaded by entering zero pressure at the surface of the fluid in the vessel and linear hydrostatic pressure at the base. Having specified all required inputs, the program then performed the analysis and calculated the deflections, forces and stresses. The total time required for the calculations was less than 3 minutes. The results were within 3% of the finite element results thus verifying the accuracy of the analysis.

Computerized handbooks offer tremendous versatility. For example, in the pressure vessel example the ability to quickly model flat, spherical, conical and ellipsoidal top and bottom configurations is provided. Thus, parametric studies are at the engineer's fingertips. Of course, there are some limitations to the computerized handbook approach. The stress values generated by the handbook are theoretically just as accurate as the finite element analysis because the same formulations are used. However, limitations arise from small geometric details which cannot be modeled with the handbook, such as the welding and reinforcements at the base of the shell where the base intersects the cylinder. The tank described in this example also had several openings along its circumference which were not taken into account by the handbook analysis. The effects of details such as these would, in many cases, make it impractical to use the handbook as a primary analysis tool. These effects, however, are not normally considered when verifying FEA results.

The benefits of computerized handbooks such as The Desktop Engineer far outweigh any limitations, since they allow the user to concentrate on the engineering rather than the bookkeeping aspects of structural/mechanical calculations. Furthermore, computerized handbooks: 1) eliminate the time-consuming search for analysis and design equations by providing solutions to a large collection of such equations; 2) free the user from lengthy calculations, thus reducing the risk of error and minimizing both time and cost; 3) facilitate the compilation of parametric studies with easily implemented input parameter modifications; and 4) facilitate the verification and interpretation results obtained from large scale engineering analysis codes.

Computerized handbooks are a teaching aid for the educator, an effective means of learning for the student, a time-saver for the researcher, a comprehensive guide for the engineering manager, and a practical tool for the designer and engineer.