Abstract
An extensive survey, critical review and basic development of linear elastic analysis methods for one-, two-, and three-dimensional continua is presented. For each of the continua the basic variation principles, significant for the development and understanding of the fundamentals of the structural analysis are given, and their use in deriving the basic equations is demonstrated. In some instances the results presented are original and in some cases they are given in a novel form. The detail intermediate steps are omitted to keep the basic picture as sharp as possible. An attempt is made to select out of the tremendous number of various proposed finite elements, the ones that are adequate for engineering applications in machine design and are not too complicated to make their used cumbersome or uneconomical. No discussion of computer programs is presented, however, it is understood that many present structural analysis problems are solved by the use of a computer. References cited in the discussion of various theories contain discussion and outline of computer programs utilizing the respective theories.
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