A David Smith stainless steel sculpture brought $572,000 here tonight at auction, establishing a record price for the artist and exceeding by 2 1/2 times the previous auction record for a Smith work. Record prices also were set for contemporary artists Robert Rauschenberg, Richard Lindner and Richard Diebenkorn.

Smith's "2 Doors" (1964), a towering geometric construction which is similar to other examples now on view in the large Smith exhibitions at the Hirshhorn and the National Gallery in Washington, was the top lot of a special evening sale of the noted collection of Dr. and Mrs. Joseph Gosman held at Christie's main salesroom here.

A total of $3,603,960, including the 10 percent buyer's premium, was paid for 47 works of art from the past 50 years. The sale included two Washington School paintings. The auction was the first single-owner sale of contemporary art since the famous sale of taxi-magnate Robert Scull's collection in October 1973, making it the main event of the fall art auctions held here this week, and everyone seemed particularly pleased by the results.

David Bathurst, tonight's auctioneer and president of Christie's in America, was ecstatic: "Wheeeeeee! . . . It brought more than we expected it to, which is highly unusual for a contemporary art sale."

Unlike the Scull sale, however, which possessed as much decorum as post-game festivities in Shea Stadium, this sale was relatively low-key. While the Gosmans, of Toledo, Ohio, looked on quietly from a back row from the audience of 1,000 people, private collectors outbid dealers for many of the key lots. Nonetheless, there was much enthusiasm, excitement and relatively few disappointments.

Rauschenberg's "Studio Painting" (1960-1961) was sold for $385,000 to a private New York collector. Rauschenberg was awarded $3,200 for the painting at the 1964 Venice Biennale where the picture was first exhibited.

Lindner's "The Walk" (1961) was sold for $220,000 to the Donald Morris Gallery in Detroit for a private collector. The underbidder was Denise Lindner, the artist's widow, and a friend who accompanied her.

Diebenkorn's "Seated Nude -- Black Background" (1961) was sold for $198,000 to Mr. and Mrs. Jay Schidler, private collectors from Honolulu.

The Washington School paintings brought mixed results. A large and exceptionally vibrant Morris Louis veil, "Beth Lamed" (1959), failed to sell although bidding reached $140,000. Kenneth Noland's "Plus 10" (1964) was sold for $62,000. Before the sale, Mrs. Gosman said that the Noland, a rust, green and yellow painting from his Chevron series, was one of her favorites. She said she hung it in her bedroom so she could "understand it."

The Louis was the second large Louis this week to fail to sell at auction. Tuesday night bidding for "Delta Kappa" reached $190,000 at Sotheby's, also failing to match the reserve (minimum) price set by the consigner.

Andre Emmerich, the New York art dealer who represents the Louis estate, offered an explanation after the sale: "It is hard to sell pictures that large at auction because few people have walls that large and most of those people like to take them home and try them out, which you can't do if you buy at auction."

For small walls, however, there was much to choose from. Georgia O'Keeffe's "Red Barn -- Wisconsin," an atypical picture for the artist, was sold for $308,000 to a New York dealer. Vincent Vallarino, an agent on the behalf of Calvin Klein, was also bidding on the picture. Another O'Keeffe, "White Lotus" (1939), an early flower painting, was sold for $132,000 to Mrs. C. M. Stanley, a private collector from Muscatine, Iowa. Ruth Syrett, who acted as Stanley's agent, reported that her client has always wanted an O'Keeffe flower study because she was in the same sorority the artist had been in earlier.

Even the Gosmans, who said they were selling their collection to "pursue other adventures" now that Gosman has retired from his medical practice, were pleased.

"I just hope we can get visitation rights," said Mrs. Gosman after the sale.