Generation of the compatibility matrix in the integrated force method

Abstract Two schemes are presented to generate the compatibility conditions for the integrated force method of discrete analysis. In the first scheme (recommended for analysis) the compatibility conditions are generated from the deformation-displacement relationship of the structure. This generation bypasses the popular concepts of redundants and basis determinate structure of the flexibility method. In the second scheme (recommended for design application), the compatibility conditions are obtained as a solution to a linear program (LP), in which the equilibrium equations are the constraints, and the linearized internal energy of the structure is the objective function. The LP is solved taking advantage of the sparsity of the coefficient matrix. The merits and limitations of the two schemes are compared to available procedures in the literature. As examples we take frame structures and plates.