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.     

Solution of problems involving the stress state of composite materials with curved layers in the geometrically nonlinear statement

Mechanics Institute, Academy of Sciences of the Ukraine, Kiev. Institute of Mathematics and Mechanics, Academy of Sciences of the Azerbaijan Republic, Baku. Translated from Prikladnaya Mekhanika, Vol. 28, No. 6, pp. 3–8, June, 1992.     

Support vector regression for warranty claim forecasting

Forecasting the number of warranty claims is vitally important for manufacturers/warranty providers in preparing fiscal plans. In existing literature, a number of techniques such as log-linear Poisson models, Kalman filter, time series models, and artificial neural network models have been developed. Nevertheless, one might find two weaknesses existing in these approaches: (1) they do not consider the fact that warranty claims reported in the recent months might be more important in forecasting future warranty claims than those reported in the earlier months, and (2) they are developed based on repair rates (i.e., the total number of claims divided by the total number of products in service), which can cause information loss through such an arithmetic-mean operation.To overcome the above two weaknesses, this paper introduces two different approaches to forecasting warranty claims: the first is a weighted support vector regression (SVR) model and the second is a weighted SVR-based time series model. These two approaches can be applied to two scenarios: when only claim rate data are available and when original claim data are available. Two case studies are conducted to validate the two modelling approaches. On the basis of model evaluation over six months ahead forecasting, the results show that the proposed models exhibit superior performance compared to that of multilayer perceptrons, radial basis function networks and ordinary support vector regression models.     

Wave propagation in a pre-strained compressible elastic sandwich plate

The extensional and flexural Lamb waves in a sandwich plate with finite initial strains made from compressible highly elastic materials is investigated. It is assumed that the initial strains are caused by the uniformly distributed normal compression forces acting on the face planes of the plate. The cases where the compression forces are “dead” (Case 1) and “follower” (Case 2) are considered. The investigations are carried out within the scope of the piecewise homogeneous body model with the use of the 3D linearized theory of elastic waves in initially stressed bodies. Numerical results for the dispersion of the extensional and flexural Lamb waves on the influence of the initial strains and on the influence of the character of the external compression forces are presented and discussed.     

On loss of stability of a strip with two parallel macro-cracks under finite precritical deformation

Loss of stability of a simply supported strip with two parallel cracks is analyzed within the framework of the three-dimensional linearized theory of stability of deformable bodies with finite precritical strains. The corresponding eigenvalue problem is solved by the finite-element method. It is supposed that the strip material is isotropic, homogeneous, compressible, and hyperelastic, and its elasticity relations are expressed in terms of a harmonic potential. Numerical critical values of the elongation of the strip obtained for different values of problem parameters are presented     

Stress distribution caused by two neighboring out-of-plane locally cophasally curved fibers in a composite material

In the present paper, within the framework of a piecewise homogenous body model, with the use of the exact three-dimensional equations of elasticity theory, a method proposed earlier is developed for investigating the stress distribution caused by two neighboring out-of-plane locally cophasally curved fibers located along two parallel planes in an infinite elastic body. The body is loaded at infinity by uniformly distributed normal forces in the direction of fiber location. The self-equilibrated normal and shear stresses caused by the curved fibers are analyzed, and the influences of interaction between the fibers and of the geometric nonlinearity on the distribution of these stresses are studied. Numerical results for this interaction are obtained.