The null space problem I. complexity
SIAM Journal on Algebraic and Discrete Methods
Computing a sparse basis for the null space
SIAM Journal on Algebraic and Discrete Methods
The null space problem II. Algorithms
SIAM Journal on Algebraic and Discrete Methods
Efficient finite element analysis by graph-theoretical force method
Finite Elements in Analysis and Design
Ant colony system: a cooperative learning approach to the traveling salesman problem
IEEE Transactions on Evolutionary Computation
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An efficient algorithm is presented for the formation of null basis of triangular plane stress and plane strain finite element models, corresponding to highly sparse flexibility matrices. This is achieved by applying a modified ant colony system (ACS). An integer linear programming formulation is also presented to evaluate the quality of the results obtained by the proposed ant colony system algorithm. The efficiency of the present algorithm is illustrated through some examples.