The Finite Element Method

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Aircraft have always presented the structural engineer with some of the most challenging of problems.footnote 1 The constraints of minimum weight and maximum performance and safety led engineers by the 1940s to develop strong, super-light-weight alloys, and to refine methods of structural analysis. But with the advent of jet aircraft, new technologies were needed. The much higher velocities of the jet meant that new wing designs and better materials had to be developed. And the old methods of calculating structural stresses no longer were adequate.

During the early 1950s, the Boeing Company approached UW engineering professor Harold C. Martin about a solution to the structural analysis problem. In response to that request, work by Martin and colleagues at the University contributed significantly to the development of an analysis technique now known as the finite element method. Employed almost universally today in industry and academia, the finite element method has become one of the main computing tools of scientists and engineers and a standard element of any engineering curriculum. It is used to analyze complex structures, and to solve problems in fluid mechanics and heat transfer.

Martin's blend of academic and industrial experience made him ideally suited to tackle the problem. He had worked for both the Republic Aviation Corporation and the Boeing Company; he had completed a doctoral degree at California Institute of Technology and had teaching experience at Princeton. Martin served on the faculty of the UW Department of Astronautics and Aeronautics from 1948 to 1970.

The basic scheme of the finite element method is to substitute a simplified problem for a complex one. An odd-shaped wing panel of a high-speed aircraft can be represented as an assemblage of tiny panels of triangular shape. Taking advantage of the computational power of modern computers and some advanced techniques of matrix mathematics, the large number of small triangular elements can be used to solve complex problems that otherwise would be intractable for the complete structure.

After the publication of his seminal paper in 1956 about the finite element method,footnote 3 Martin continued work in the field, publishing two books on the subject.footnote 1comma footnote 2 Although Martin and his colleagues were not the sole developers of finite element analysis, they are widely recognized as pioneers in the field.footnote 4comma Footnote 5

  1. Introduction to Finite Element Analysis, H. C. Martin and G. F. Carey, McGraw-Hill, 1973.
  2. Introduction to Matrix Methods of Structural Analysis, H. C. Martin, McGraw-Hill, 1966.
  3. M. J. Turner, R. W. Clough, H. C. Martin and L. J. Topp, "Stiffness and Deflection Analysis of Complex Structures," J. of Aero. Sci., 23 (9), Sept. 1956.
  4. Early FEM Pioneers, J. Robinson, Pitman Press, 1985.
  5. Finite Element Analysis, D. S. Burnett, Addison-Wesley, 1987.

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