Quantum mechanics

Context (archaeology)

Biology

Linear elasticity

Nuclear physics

Classical mechanics

Statistical physics

Geology

Exponential growth

Paleontology

Type (biology)

Thermodynamics

Physics

Finite element method

Dipole

Mathematics

Elasticity (physics)

Exponential decay

Cylinder

Exponential function

Mathematical analysis

Geometry

Elastic energy

Generalization

Journal of Taibah University for Science

Our study is concerned with a generalization of the principle of Saint-Venant in the context of the theory of elastic bodies with a dipolar structure. It is an extension of the form of this principle proposed by Toupin in the case of classical linear elasticity. We consider a straight cylinder which is occupied by an dipolar elastic body that is only loaded at one end and our main finding proves that the internal energy in a portion of this cylinder, that is located at a given distance regarding the end that is loaded, is exponentially decreasing, regarding the respective distance.

On the decay of exponential type for the solutions in a dipolar elastic body