The late architect Eero Saarinen built more than a glamorous façade for postwar corporate America glamorize postwar corporate America as his new exhibit “Eero Saarinen: Shaping the Future” at the Museum of the City of New York reveals. Through his buildings, Saarinen showed America’s confidence and progress, but this exhibit, which opened Thursday, breaks through the smooth outer shell to reveal some of the struggles beneath Saarinen’s designs. The show follows the Finnish-born designer, who was originally trained as a sculptor in Paris, from his early partnership in suburban Detroit with his father, a Modernist who emigrated to America. Saarinen made a name for himself, however, as the United States did the same in becoming a universal superpower. Over his brief but fruitful career, Saarinen designed the General Motors Technical Center, the TWA Flight Center at John F. Kennedy Airport, at St. Louis’ signature Gateway Arch. Organized by Donald Albrecht, the Museum of the City of New York’s curator of architecture and design, the exhibit of these works and many more will be on display through January 31.