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Abstract Static and kinematic matrix operator equations are revisited for one-, two-, and three-dimensional deformable bodies. In particular, the elastic problem is formulated in the details in the case of arches, cylinders, circular plates, thin domes, and, through an induction process, shells of revolution. It is emphasized how the static and kinematic matrix operators are one the adjoint of the other, and then demonstrated through the definition of stiffness matrix and the application of virtual work principle.

From the matrix operator formulation it clearly emerges the identity of the usual Finite Element Method definition of elastic stiffness matrix and the classical definition of Ritz-Galerkin matrix. • [1] Bathe, K.J.

And Wilson, E.L. (1976) Numerical Methods in Finite Element Analysis, Prentice-Hall, Englewood Cliffs, New Jersey. • [2] Carpinteri, A. (1992) Scienza delle Costruzioni, Vol.

1 and 2, Pitagora, Bologna. • [3] Carpinteri, A. Solow How To Read And Do Proofs Pdf To Jpg.

(1997) Structural Mechanics: A Unified Approach, Chapman & Hall, London. • [4] Carpinteri, A. (2014) Structural Mechanics Fundamentals, CRC (Taylor & Francis Group), New York.

• [5] Carpinteri, A. (2017) Advanced Structural Mechanics, CRC (Taylor & Francis Group), New York. • [6] Carpinteri, A. And Cornetti, P. (1997) Lastre a doppia curvatura, in: Carpinteri, A., Calcolo Automatico delle Strutture, Pitagora, Bologna, 159-215. • [7] Di Pasquale, S. (1975) Scienza delle Costruzioni: Introduzione alla Progettazione Strutturale, Tamburini, Milan.

• [8] Di Tommaso, A. (1981) Fondamenti di Scienza delle Costruzioni, Vol. 1, Patron, Bologna. • [9] Novozhilov, V.V. (1970) Thin Shell Theory, Noordhoff, Groningen. • [10] Zienkiewicz, O.C. (1971) The Finite Element Method in Engineering Science, McGraw-Hill, London.