Elastoplastic Bending of the Console with Transverse Force

In the article an elastoplastic boundary for the console being bent with transverse force when the point of force is not situated in the centroid of transverse section was built with the use of the conservation laws. In this case bending moments and torques appear of the console. The case when the point of force is situated in the centroid of transverse section is considered in the previous works of the authors. In the work an infinite system of conservation laws has been built that allows us to reduce the problem of calculating elastoplastic boundary to a few quadratures, at the outer contour of transverse section. At that the contour can be random piecewise smooth. It is assumed that the lateral surface of the console is free from strains and is in its plastic condition

Residual Stresses in Elastoplastic Bending of Round Bar

Elastoplastic deformation on the presses and high-temperature heating of the steel sheet cause the large residual stresses in the sheet’s and bar’s wall. The technological operations of the obtaining of metal products, their shape and linear dimensions strongly affect on the distribution within the metal and the maximum values of residual stresses. The uneven cooling of various parts of the sheet and bar, obtained by bending, stamping and forging, also leads to the large residual stresses inside the metal. The greatest residual stresses occur in the weld area, where there is a strong heterogeneity of mechanical and physical properties of the metal due to uneven heating and cooling. Below the new analytical method for calculating of the residual stresses of a round steel bar in the elastoplastic bending is obtained. This method takes into account the diameter of the bar, as well as the modulus of elasticity, the yield strength and the hardening modulus of steel’s bar.

Analytical Solution for Elastic and Elastoplastic Bending of a Curved Beam Composed of Inhomogeneous Materials

We present an analytical solution for elastic and elastoplastic bending problem of a curved beam composed of inhomogeneous materials. Suppose the material is isotropic, ideally elastoplastic and it obeys Tresca’s yield criterion and the corresponding associated flow rule. And the elastic modulus and yield limit of the material vary radially according to general power functions. The expressions of stresses and displacements of a curved beam in both purely elastic stress state and partially plastic stress state are derived. The influence of material inhomogeneity on the elastoplastic behavior of a curved beam is demonstrated in numerical examples. Analytical solutions presented here can serve as benchmark results for evaluating numerical solutions.