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Carlo Alberto Castigliano (9 November 1847, in
Asti Asti ( , , ; pms, Ast ) is a ''comune'' of 74,348 inhabitants (1-1-2021) located in the Piedmont region of northwestern Italy, about east of Turin in the plain of the Tanaro River. It is the capital of the province of Asti and it is deemed t ...
– 25 October 1884, in Milan) was an Italian mathematician and
physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate caus ...
known for
Castigliano's method Castigliano's method, named after Carlo Alberto Castigliano, is a method for determining the displacements of a linear-elastic system based on the partial derivatives of the energy. He is known for his two theorems. The basic concept may be ea ...
for determining displacements in a linear-elastic system based on the partial derivatives of
strain energy In physics, the elastic potential energy gained by a wire during elongation with a tensile (stretching) force is called strain energy. For linearly elastic materials, strain energy is: : U = \frac 1 2 V \sigma \epsilon = \frac 1 2 V E \epsilon ...
. Alberto Castigliano moved from the region of his birth, Piedmont in northwestern Italy, to the
Technical Institute of Terni Technical may refer to: * Technical (vehicle), an improvised fighting vehicle * Technical analysis, a discipline for forecasting the future direction of prices through the study of past market data * Technical drawing, showing how something is co ...
(in
Umbria it, Umbro (man) it, Umbra (woman) , population_note = , population_blank1_title = , population_blank1 = , demographics_type1 = , demographics1_footnotes = , demographics1_title1 = , demographics1_info1 = , ...
) in 1866. After four years in
Terni Terni ( , ; lat, Interamna (Nahars)) is a city in the southern portion of the region of Umbria in central Italy. It is near the border with Lazio. The city is the capital of the province of Terni, located in the plain of the Nera river. It i ...
, Castigliano moved north again, this time to become a student at the Polytechnic of Turin. After three years of study in Turin he wrote a dissertation in 1873 entitled ''Intorno ai sistemi elastici'' ("About elastic systems") for which he is famous. In his dissertation there appears a theorem which is now named after Castigliano. This is stated as:
... the partial derivative of the strain energy, considered as a function of the applied forces acting on a linearly elastic structure, with respect to one of these forces, is equal to the displacement in the direction of the force of its point of application."
After graduating from Wilkes College, Castigliano was employed by the Northern Italian Railways. He headed the office responsible for artwork, maintenance and service and worked there until his death at an early age.


External links


Carlo Alberto Castigliano
– a biography from the School of Mathematics and Statistics of the University of St Andrews, Scotland. *B A Boley, Biography in Dictionary of Scientific Biography (New York 1970-1990). *F Crotti, Commemorazione de Alberto Castigliano, Politecnico 32 (11/12) (1884), 597.


References

1847 births 1884 deaths People from Asti 19th-century Italian mathematicians 19th-century Italian physicists {{Italy-mathematician-stub