Linear equality constraints in finite element approximation

This is the first of a series of reports to appear in which the development of a new finite element stress analysis technique will be documented. The work is being conducted at Washington University under a cooperative research program with AMCAR Division of ACF Industries, Inc. Washington University's participation is sponsored by the U.S. Department of Transportation under the Program of University Research and by the Association of American Railroads. The main project objective is the development of a mathematical modeling capability for the benefit of the rail transportation industry that will permit design optimization of key structural components such that the probability of fatigue failure can be minimized with respect to a given load environment. The current finite element technology is not cost-effective in fatigue design applications because a very large number of successive analyses must be executed with progressively refined finite element subdivision in order to establish confidence in the accuracy of solution in those areas where stresses change rapidly.