Eigen-Matrix Method for Beams and Plates

by Benhosuke Tanimoto,

Serial Information: Journal of the Structural Division, 1963, Vol. 89, Issue 5, Pg. 173-216

Document Type: Journal Paper


A new, powerful approach to the problem of the bending of beams and plates is presented. Beginning with a certain form of expression for the deflection, the entire analysis procedure is derived from matrix algebra. This expression has as its basis a 4 × 4 square matrix, which is characteristic of the system considered, and which can be referred to the eigen-matrix. It can be stated, therefore, that the eigen-matrix is the solution for the system. Because of the fourth degree of governing differential equations for beams and plates, the eigen-matrix is in substance a 4 × 4 square matrix, and is frequently subdivided into 2 × 2 or 2 × 4 submatrices. This degree, which is higher than that in the theory of electricity, will derive an increased efficiency in computations. The last step of the individual examples leads to the treatment of the inverse of a 2 × 2 square matrix. Simultaneous equations of many unknowns can then be dispensed with, so that the analytical computation necessary is simplified.

Subject Headings: Matrix (mathematics) | Beams | Plates | Computing in civil engineering | Bending (structural) | Displacement (mechanics) | Differential equations | Electric power

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