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Essential boundary conditions and multi-point constraints in finite element analysis

Ainsworth, M. (2001) Essential boundary conditions and multi-point constraints in finite element analysis. Computer Methods in Applied Mechanics and Engineering, 190 (48). pp. 6323-6339.

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Abstract

The application of boundary conditions and other constraints to the stiffness matrix and load vector is an integral part of any finite element code. This process is usually trivial but can present difficulties to the point where some codes disallow certain combinations of commonly occurring boundary conditions. A general approach to this problem is presented and applied to representative examples. Necessary and sufficient conditions are obtained under which constraints can be applied sequentially. Bounds are obtained for the condition number of the reduced system showing it is essentially the same as for the original problem.