Chapter 1
Summary of Elasticity Theory: Basic
Concepts
1.1 From the History of Elasticity Theory
Elasticity theory as one of the most important parts of mathematical physics was
formed in the first half of the nineteenth century; however, many of its sections
had been developed much earlier. The works of the scientists of the seventeenth
and eighteenth centuries, Galileo, Mariotte, Hooke, Bernoulli, Euler, Coulomb, etc.,
significantly developed the bending theory for thin elastic rods.
Early in the nineteenth century, Lagrange and Sophie Jermain solved the task of
bending and oscillations of thin elastic plates. Strain features of thin elastic bodies
allowed simplifying the setting and finding the solution on their straining under the
action of external forces.
The early nineteenth century also saw a rampant development of mathematical
analysis following the occurrence of multiple important tasks in physics and
engineering. The existing situation became a basis for a new specific field of physics
called mathematical physics. New tasks assigned to this young discipline, first of
all, included the need to thoroughly study properties of elastic materials and to
build the mathematical theory based on them that would permit determining internal
forces occurring in an elastic body under the action of external forces, as well
as body strain, e. g. changes in its dimensions and/or shape. These studies were
extremely necessary to satisfy the demands of rapidly developing engineering due
to construction of railroads, bridges, steam machines, metalworking machines, etc.
Some of these issues were solved in 1825 when the French engineer A.
Navier issued the “Course of Lectures on Strength of Materials” based on existing
experimental data and including approximated theories mentioned above. A similar
course by N. F. Yastrzhembsky appeared in 1837 in Russia.
Other important engineering tasks (contact tasks, strain of massive bodies, etc.)
were still to be solved. There was a relevant need to create theoretic methods for
strength analysis of structural parts and machines of arbitrary shape.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Molotnikov, A. Molotnikova, Theory of Elasticity and Plasticity,
https://doi.org/10.1007/978-3-030-66622-4_1
3
Summary of Elasticity Theory: Basic
Concepts
1.1 From the History of Elasticity Theory
Elasticity theory as one of the most important parts of mathematical physics was
formed in the first half of the nineteenth century; however, many of its sections
had been developed much earlier. The works of the scientists of the seventeenth
and eighteenth centuries, Galileo, Mariotte, Hooke, Bernoulli, Euler, Coulomb, etc.,
significantly developed the bending theory for thin elastic rods.
Early in the nineteenth century, Lagrange and Sophie Jermain solved the task of
bending and oscillations of thin elastic plates. Strain features of thin elastic bodies
allowed simplifying the setting and finding the solution on their straining under the
action of external forces.
The early nineteenth century also saw a rampant development of mathematical
analysis following the occurrence of multiple important tasks in physics and
engineering. The existing situation became a basis for a new specific field of physics
called mathematical physics. New tasks assigned to this young discipline, first of
all, included the need to thoroughly study properties of elastic materials and to
build the mathematical theory based on them that would permit determining internal
forces occurring in an elastic body under the action of external forces, as well
as body strain, e. g. changes in its dimensions and/or shape. These studies were
extremely necessary to satisfy the demands of rapidly developing engineering due
to construction of railroads, bridges, steam machines, metalworking machines, etc.
Some of these issues were solved in 1825 when the French engineer A.
Navier issued the “Course of Lectures on Strength of Materials” based on existing
experimental data and including approximated theories mentioned above. A similar
course by N. F. Yastrzhembsky appeared in 1837 in Russia.
Other important engineering tasks (contact tasks, strain of massive bodies, etc.)
were still to be solved. There was a relevant need to create theoretic methods for
strength analysis of structural parts and machines of arbitrary shape.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Molotnikov, A. Molotnikova, Theory of Elasticity and Plasticity,
https://doi.org/10.1007/978-3-030-66622-4_1
3