A NEW TYPE OF BODY FORCE IN THE MECHANICS OF ELASTICALLY DEFORMABLE SOLIDS

Abstract

Based on the analysis and comparison of atomic physical and engineering models of solid matter, the existing classification of volumetric forces used in the resistance of materials and the theory of elasticity is expanded (magnetic, electromagnetic, inertial, gravitational). This fundamentally new addition is justified by replacing the force of interatomic interaction with a statistically averaged analogous equivalent in the form of a quasi-elastic volumetric load acting between infinitesimal material particles of a solid body which are displaced during its deformation. For continuous homogeneous isotropic materials obeying Hooke's law, using the fundamental law of conservation of mechanical energy, a general theory has been developed for determining the quasi-elastic body force function, the three projections of which  on the coordinate axes x, y, z linearly depend on the corresponding displacements u, v, w in x, y, z direction. The proposed calculation method is illustrated by the simplest example from the classical course of resistance of materials to uniaxial tension by external static forces P of a linearly elastic weightless beam of constant cross-section. In the course of a mathematically accurate solution to this innovative problem: 1) it was proven that the new quasi-elastic mass force depends on the location (coordinates) of an arbitrary point of the body, the external load acting on the structure, its volume and Poisson’s ratio μ, and at μ = 0,5 this volumetric load becomes zero; 2) the relevance and great importance of taking into account the quasi-elastic volumetric force in the equilibrium equations in the process of mathematical modeling of the stress-strain state and design of load-bearing structures has been confirmed.