A Method for Solving Problems of the Isotropic Elasticity Theory with Bulk Forces in Polynomial Representation

Abstract

A method for solving problems in isotropic elasticity theory with polynomial bulk forces is substantiated. The existence of a basis for the state space generated by monomials of random orders, which are the components of a volumetric force, makes it possible to obtain a rigorous description of a corresponding stress-strain state for any polynomial force. Solutions of the basic mixed equilibrium problem are obtained: (1) for a truncated cylinder clamped at the base and exposed to the action of a nonconservative volume force and (2) for a heavy hemisphere clamped at the equatorial section and having a nonhomogeneous shear modulus typical for bodies with subsurface hardening.