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Gallagher led the development of finite-element analysis methods that took advantage of the capabilities of digital computers to enable the unprecedented design of complex structures. His book, Finite Element Analysis Fundamentals, was translated into seven languages. His success in securing grants and funding enabled him to compete successfully with much larger organizations for top talent, and his groups at Bell included top engineers and researchers in matrix analysis, rocket analysis, dynamics, inelastic analysis, optimization, fracture, and composite materials. Under his guidance, Bell researchers pioneered the development of FEM, including inelastic analysis, design optimization, composite materials analysis, linear fracture applications, thermal analysis methods, solid- and shell-element formulations, and the super-element substructuring technique.

While working in industry, Gallagher also published seminal publications, including papers in refereed journals and his first book, A Correlation Study of Matrix Methods of Structural Analysis (Pergamon Press, 1964). In his early work, he expanded the practice of finite-element analysis from two-dimensional to three-dimensional analysis, from structural analysis to heat-transfer analysis, from linear analysis to nonlinear analysis, and from aerospace applications to civil engineering applications. During this time, he also made his first presentation at an international conference, in Germany, the first of his invited visits to 78 countries on six continents.

Still working at Bell, Gallagher taught engineering courses and pursued doctoral studies at the State University of New York (SUNY)-Buffalo, where he earned the school’s first Ph.D. in engineering in 1966. Shortly thereafter, he became a full professor of civil engineering at Cornell University, where he was soon appointed chairman of the Department of Structural Engineering. Under his leadership, the reputation of the department improved markedly, particularly in the Master of Engineering Program, a fifth-year professional degree that prepared students to become practicing engineers. The department also offered traditional research-oriented graduate degrees. With first-rate faculty, Cornell was soon

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