# Combined Analysis by Substructures and Recursion

*by*Moshe F. Rubinstein,

**Serial Information**:

*Journal of the Structural Division*, 1967, Vol. 93, Issue 2, Pg. 231-236

**Document Type:**Journal Paper

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**Abstract:**Structures which can be partitioned into a continuous series of sections in which each section is coupled to two adjacent sections have a tridiagonal band matrix as the stiffness matrix. The displacements and internal stresses of such a structure can be obtained by a recursion procedure. The largest matrix that must be inverted is equal to the largest number of coordinates at the region connecting two sections. The recursion procedure is useful when the analysis is conducted for a few loading conditions and when the number of coordinates at the regions connecting adjacent sections is small. When a structure has the form of a closed ring, it is not possible to number the coordinates so as to yield a tridiagonal band matrix in which all the connections between sections of the structure will contain a small number of coordinates. In such a case it is advantageous to combine the analysis by substructures and by recursion. Substructures are selected so that they are most readily analyzed by recursion.

**Subject Headings:**Matrix (mathematics) | Substructures | Continuous structures | Coupling | Stiffening | Displacement (mechanics) | Load factors

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