On the influence of singular-type finite elements on the critical force in studying the buckling of a circular plate with a crack

The axisymmetric buckling (delamination) of a circular disk (plate) with a penny-shaped crack is analyzed using a continuum model, piecewise-homogeneous model, and the three-dimensional linearized theory of stability. The FEM is used. The analysis is carried out using various singular and ordinary finite elements. The numerical results obtained indicate that it is not necessary to use singular finite elements to solve the problem Published in Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 120–129, September 2007.     

Buckling delamination of a sandwich plate-strip with piezoelectric face and elastic core layers

In this study, the buckling delamination problem of a sandwich plate-strip with a piezoelectric face and elastic core layers is studied. It is assumed that the plate-strip is simply supported and grounded along its two parallel ends and is subjected to uniformly-distributed compressive forces on these ends. Moreover, we suppose that the plate-strip has two interface inner cracks between the face and the core layers and it is also supposed that before the plate-strip is loaded (i.e. in the natural state), the surfaces of these cracks have insignificant initial imperfections. Due to compressive forces acting along the cracks we investigate the evolution of the initial imperfections of the cracks’ surfaces. Hence, the values of the critical buckling delamination force of the considered plate-strip are determined from the criteria, according to which, the considered initial imperfections of the cracks’ surfaces grow indefinitely by the compressive forces. Mathematical modeling of the considered problem is formulated within the scope of the exact nonlinear equations of electro-elasticity in the framework of the piecewise homogeneous body model, the solution of which is found numerically by employing the finite elements method. Numerical results showing the influences of the geometrical and material parameters as well as the coupling of the electrical and mechanical fields on the values of the critical force are presented and analyzed.     

Bending of a Composite Material Strip with Curved Structure in the Geometrically Nonlinear Statement

To date, bending problems for strips or plates made of composite materials with curved structure have been investigated only in the linear statement. However, in many cases, the necessity arises to investigate the corresponding bending problems in the geometrically nonlinear statement. Therefore, in the present paper, some bending problems for a composite strip with a periodically curved structure is investigated in such a statement using the exact nonlinear equations of elasticity theory in Lagrangian coordinates. The numerical results are obtained by employing the FEM with the use of the Newton-Raphson and the Modified Newton-Raphson algorithms.     

Influence of Initial Stresses on Stress Intensity Factors at Crack Tips in a Composite Strip

The influence of initial tension or compression along cracks on the stress intensity factor (SIF) at crack tips under the action of additional normal forces on crack edges is studied for infinite bodies. A strip made of a composite material is considered. The strip ends are simply supported, and the strip contains a crack whose edges are parallel to its face planes. The strip is first stretched or compressed along crack edges, and then additional uniformly distributed normal forces are applied to the crack edges. The influence of the initial tension (compression) on the SIF caused by the additional normal forces is studied. The corresponding boundary-value problems are modelled with the use of the three-dimensional linearized theory of elasticity. All the investigations are carried out numerically by employing the finite-element method. The values of SIF are calculated by the energy release method.     

Forced vibration of an initially stressed thick rectangular plate made of an orthotropic material with a cylindrical hole

The forced vibration of an initially statically stressed rectangular plate made of an orthotropic material is studied. The plate is simply supported along all its edges and contains an internal across-the-width cylindrical hole of rectangular cross section with rounded corners. The initial stresses are created by uniformly distributed normal forces applied to opposite end faces of the plate. Because of the hole, these stresses are not uniform in the plate and significantly affect the stress field caused by additional time-harmonic dynamical forces acting on the upper face of the plate. Hence, for solving the boundary-value problem considered, the superposition principle is unsuitable. Therefore, our investigations are carried out within the framework of the three-dimensional linearized theory of elastic waves in initially stressed bodies. The corresponding boundary- value problems on determining the initial and additional, dynamical stress states are solved by using the three-dimensional finite-element method. Numerical results on stress concentrations around the cylindrical hole and the fundamental frequencies, and on the influence of the initial stresses on the frequencies are presented.     

On the stress distribution in a prestretched simply supported strip containing two neighboring circular holes under forced vibration

The three-dimensional linearized theory of elastic waves in initially stressed bodies under plane strain is used to study the influence of the initial stretching of a simply supported plate strip with two neighboring circular holes on the stress concentration around the holes caused by additional uniformly distributed dynamic (time-harmonic) normal forces acting on the upper face. The corresponding problem is formulated and solved by the finite-element method. Numerical results on the stress concentration around the holes and the influence of the initial stretching on this concentration are presented Published in Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 135–140, October 2007.     

Interaction between two neighboring circular holes in a prestretched simply supported orthotropic strip under bending

In this work, the influence of initial stretching of a simply supported plate-strip containing two circular holes on the stress concentration around the holes caused by bending of the strip is examined using the finite-element method. The mathematical formulation of the corresponding boundary-value problem is presented within the frame work of the three-dimensional linearized theory of elasticity (TDLTE) under a plane strain state. The material of the plate-strip is linearly elastic, homogeneous, and orthotropic. The numerical results obtained in investigating the influence of the initial stretching and the location of holes on the stress concentration are presented. In particular, it is established that the initial stretching significantly decreases the stress concentration at some characteristic points on the contour of the holes. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 827–838, November–December, 2008.