Many legal professionals are exposed to Finite Element Analysis (FEA) in the courtroom. Having a fundamental understanding of how the method works can help an attorney (i) recognize when FEA can strengthen a case, (ii) choose a capable expert and (iii) develop meaningful challenges to the opposition's expert. As discussed in the last issue of Courtroom FEA, if a loss, injury or death is due to something bending or breaking, FEA can help identify the cause of failure and hence the responsible party. But how does it work?
Laptop Battery Divide and conquer.
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Thinkpad But first, let's back up and discuss what is being conquered. FEA is applied to many types of problems, such as temperatures in consumer electronics, airflow around aircraft, and magnetic fields in electric motors. By far the most common application is structural FEA -- determining how a solid body responds to various forces. The structural problem amounts to writing down some "governing equations" that describe the material and how it behaves, and then solving those equations for the physical part being analyzed subject to how it is held and loaded. This can be done on paper for some simple part shapes. The resulting "closed form solution" is another equation that provides the answer in terms of the basic variables, such as the part's dimensions.
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Microsoft But reality intervenes, and most parts are too complicated to solve in closed form. FEA comes to the rescue by providing a "numerical solution" for each individual problem. This is a large gathering of numbers approximating the desired answers, such as displacements and stresses, across the part. But each solution is unique to a specific case; there is no simple answer in equation form.
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Laptop Computers Now then, how does FEA divide and conquer the problem to provide the numerical solution? The answer lies in the name, "Finite Element Analysis".
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Laptop Computer "Analysis" is obvious: the part is being analyzed under certain conditions.
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Desktop Computer "Element" describes a small section of the part. In fact, the governing equations mentioned above can generally be derived by considering a small section, writing the equations for what's happening in that section, and then mathematically allowing the size of the section to become infinitesimal, or infinitely small. In FEA, each section is called an "element", and the elements are not made infinitely small.
Notebooks "Finite", then, refers to the countable number of elements used to represent the structure. The elements are of finite, measurable size. A computer can handle the computations on this finite number of elements.
Lenovo Each element acts on its neighboring elements. FEA assembles the equations from all the elements into one large matrix equation, and the computer is used to determine the numerical solution. A key concept of FEA is this: if the elements are made small enough and are spread advantageously across the part, the numerical solution can closely approximate reality.
Hard Drive An experienced analyst can prepare the finite element model such that it accurately predicts the part's behavior, and can ensure that the solution algorithms do not interject significant errors. Results from the less-experienced are often suspect, and identifying them as so can be a tremendous advantage in the courtroom.
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Gateway Steve Roensch is a mechanical engineering consultant with more than 20 years of professional experience. He has analyzed hundreds of product designs and has served as an expert witness across many industries, including giving depositions and court testimony. Learn more about mechanical engineer expert witness services at www.FiniteElement.com.
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Steve Roensch is a mechanical engineer with 23 years of professional experience in failure analysis and litigation consulting. He has analyzed hundreds of product designs and has provided expert witness services across many industries, including giving depositions and court testimony.
Mr. Roensch has provided litigation consulting in the energy, construction, industrial, transportation, commercial, utility and residential industries. He has supplied legal team technical support, and has given depositions and testified in court and arbitration hearings.
Mr. Roensch specializes in analyzing the physical stresses that arise in a product under various loading conditions, and in determining if the design is sufficient to survive such loads. He investigates product failures and accidents from a fundamental engineering perspective, often applying finite element analysis. He documents his efforts thoroughly from the start, for concise presentation to the legal team, other experts and the jury. Complex engineering principles are explained using everyday concepts that everyone can understand. Color stress plots and animations are used whenever possible to convey complicated engineering results in an easy to understand visual format.
Learn more about mechanical engineer expert witness services at www.FiniteElement.com.
