Selected Topics of Elastostatics

Abstract

Only linearized problems are considered in this section, ie linearized geometric relations and Hooke’s law are taken into account [see Eqs. (1.21) and (4.15)]. The consequences of these assumptions are illustrated by considering a linear elastic body loaded on its surface by a self-equilibrating system of single forces F ₁ , F ₂ , ..., F _n , (reaction forces in the point supports are included). The loading is applied to the body by means of a common load factor λ , which is slowly increased from 0 ≤ λ ≤ 1 to reach the terminal configuration by passing successively through states of equilibrium. The displacement u _i of a material point to the deformed state, the reference configuration is assumed free of stresses, is determined by the generalization of the linear law of a Hookean spring [see Eqs. (4.3) and (3.46)], and the common load factor λ cancels

$$ {{\text{u}}_{\text{j}}}\text{=}\sum\limits_{\text{j=1}}^{\text{n}}{{{\text{a}}_{\text{ij}}}{{\text{F}}_{\text{j}}}} $$

(6.1)

where the influence coefficients a _ij are independent of the load intensity. They depend on the location and direction of the displacement and they are functions of the points of application of the forces F _j , as well as of their directions.