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K2 Engineering, Inc.         Contact us

Specializing in Engineering & Manufacturing Automation since 1996

High-End Analysis (including FEA)

Many engineering problems lend themselves quite readily to simplifying assumptions and approximations which allow the problem to be re-cast into a formulation for which a direct solution is available.  In the Structural, Civil, and Mechanical design realms, Roark and Young's classic handbook "Formulas for Stress and Strain" is a good example of this.  Hundreds of common (and some not so common) geometries and loading and fixity configurations have been tabulated, allowing the design engineer to enter some known values and determine an unknown result - be it stress, deflection, rotation, etc.   The so-called "plug and chug" method.  Likewise, similar handbooks are available for other areas of engineering and scientific endeavor.

Serious difficulty arises, however, when the engineering problem to be solved is of a more complex or unusual nature for which simplifying assumptions and approximations are not apparent, not applicable, or simply not prudent based upon sound engineering judgment.

Two avenues for dealing with these more difficult problems are: numerical modeling-based methods (numerical analysis) and experiment-based methods.  Numerical modeling methods essentially break down intractable large problems into a collection of inter-related smaller and simpler (and thereby, solvable) problems, which when taken together closely approximate the original problem.  Experiment-based solutions are more of a "build it, try it, see what happens" approach.  This can be done with: sub-components of the item to be designed; with scaled-down models of the item; or occasionally, with the actual item to be designed.

Each methodology type, of course, has its pros and cons.  Experiment-based methods are often more straight-forward and yield more satisfying results, especially for full-test tests.  However, they are more suited to testing an established configuration rather than developing a new design, which is a much more iterative and repetitive process.  How affordable this can be depends upon whether you are designing a simple hand tool or a new type of superstructure for a high-rise office building.  Also, depending upon the type of problem, testing can often lead to revealing what happened but not necessarily why it happened.  Proper design of the experiment is critical to gleaning as much understanding of the nature of the problem as possible.

Numerical solutions provide a fairly quick and economical way to tackle problems which are not well-defined and/or are imprudent or impractical to experimentally test.  Since numerical solutions exist in a virtual world, they can be readily revised and refined to iterate to a solution or to explore a variety of alternatives.  However, numerical methods, it must be remembered, are composed of numerous simplifications and approximations.  The tradeoff that makes the problem solvable also often reduces the model's fidelity to the actual behavior of the item being modeled.  Proper choice of, and configuration of, the employed numerical method is critical to gaining as complete an understanding of the nature of the problem as is possible.

K2 Engineering's engineers have an extensive background in, and experience with, both methodology classes.  As regards experimental methods, this experience is centered mostly on: strain gauge and pitot tube testing; and two forms of modal testing - forced excitation (shaker) and impact excitation (bump).  We can assist in devising a testing program particular to your needs and can coordinate with several local labs to set up and run the required testing, either in their facilities or on-site.  We'll be happy to meet with you to discuss your needs.  We're accustomed to working with your in-house personnel, or other third parties, on projects of this nature and will be glad to discuss that with you as well.

K2 Engineering's engineers also have extensive experience in applying numerical methods to solve a wide variety of thorny problems, such as: un-steady heat transfer though process equipment; static and dynamic analyses of rotating equipment; design of steel chimneys, mono-poles, and other tubular structures and components; and optimization of trusses and other lattice-type structures.

Two major types of numerical methods which K2 Engineering has focused on are: Explicit Solver methods; and Finite Element methods.  Both types work by breaking down the large, intractable problem into a collection of smaller, inter-related problems, which, taken together, provide a good approximation of the large problem.  The idea is to formulate directly-solvable (i.e., closed form solution) equations to represent the behavior of the smaller units.  Essentially, a "divide and conquer" approach.

The differences between them are substantial, however.  These differences cause each method to perform best in the solution of a distinct sub-set of problems with little overlap between the two.  The Finite Difference method, as implied with its name, as based upon formulations involving difference between values, typically in a field.  Accordingly, it works quite well with field problems like fluid flow or heat transfer.  Often, the solution is of an interative form, processing one element at a time.  A pleasant side effect is that Finite Difference solutions are usually easy to program.

Finite Element methods, in contrast with Finite Difference methods, are developed based upon infintesimal differences which are then integrated across the individual element.  Each element is dependant upon all its adjoining elements and shares one or more property or state values, called degrees of freedom, at each point (called nodes) where it is connected to adjoining elements.  This inter-dependence between elements casts the solution in a matrix form requiring simultaneous solution of the equations, a much more difficult programming problem.  This method is generally more suited to solution of non-field-based problems, like static and dynamic analysis of mechanisms or structures.

K2 Engineering's experience with numerical methods fall into three categories: use of third party numerical methods software; development of numerical methods software; and development of tools and utilities to assist in the application of various numerical methods.  Specifcs are noted below:

Third party numerical methods software




        SAPS (in various flavors, both stand-alone and embedded)


        SuperSAP (Algor)




Development of numerical methods software

        Explicit solvers for high-energy, short duration (i.e., blast) loadings.

        Finite Difference-based, 3D, un-steady, transient heat transfer analysis package.

        Embeddable Finite Element solver featuring: 3D beam elements; 3D truss elements; 3D linear and Torsional
        spring elements; and 3D Lumped Mass elements.  Both Linear Static and Eigenvalue capabilities.

Development of tools and utilities

        Various graphics-based modeling and mesh generation tools.

        Several graphics-based converters/translators (between DWG, DXF, OPENGL, OpenSceneGraph and proprietary formats).

        Several post-processing and visualization tools, including OPENGL and OpenSceneGraph shaded renderings.

Screen shot of a test harness used to develop and test an embedded FEA solver.

A screen shot of a test harness used to develop and test a software class which permits an FEA (Finite Element Analysis) solver to be embedded in an analysis program.   Rather than make some sort of kludge to use a stand-alone FEA package, an FEA solver, and optional pre- and post-procesor, can be embedded in and tightly integrated with a design package.   For a non-trivial structure or part, this means that the actual material and physical properties can be directly modeled instead of relying on "cookbook" simplifications and/or approximations.

Screen shot of a rendering of a shaft being analyzed for potentially dangerous critical speeds.

A screen shot of a rendering of a shaft being analyzed for potentially dangerous critical speeds.   Similar to a car tire which has lost it's balance weight, there are certain speeds at which a rotating shaft can experience excessive vibration.   This software package performs an dynamic analysis to determine those dangerous speeds.   The dynamic analysis is in the form of an embedded Finite Element-based EigenValue solver, embedded in the program source code.

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