Journal of Engineering Mathematics

, Volume 78, Issue 1, pp 181–197

# Elastoplastic deformation of nonhomogeneous plates

• Eteri Hart
• Sergey Ryabokon’
Article

## Abstract

Efficient projective-iterative schemes for the numerical implementation of the finite-element method are developed to calculate the stress and strain fields in elements of plate-and-shell systems, in particular in nonhomogeneous plates, under elastic and elastoplastic deformation. Rectangular plates with variously shaped (rectangular, circular, elliptic) holes in a plane stress state are considered. The effect of the elastoplastic deformation of the material on the stress and strain fields due to a slowly increasing load is studied. Schemes of successive approximations to account for plastic deformations in combination with projective-iterative schemes of numerical implementation of the finite-element method are constructed. The interaction of variously shaped holes is studied. The efficiency of projective-iterative variants of the finite-element method offering a several-fold reduction in running time is demonstrated. The proposed schemes are particularly attractive for the use of the finite-element method in numerical simulation of the nonlinear deformation of nonhomogeneous plate-and-shell systems. The numerical models considered can be used to good advantage in the study of the effect of other nonhomogeneities (geometrical shape irregularities, various inclusions, reinforcements). They can be used in fracture mechanics: failure starts with the development of discontinuities in variously shaped holes. The hole shape and dimensions can change during loading.

## Keywords

Elastoplastic deformation Finite-element method Holes Projective-iterative schemes

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