On the elastoplastic stability of a plate under shear forces, taking into account its real bending form

Using the theory of elastoplastic processes and the modified elastic solution method we investigate the stability outside elastic limit problem of a plate under shear forces, taking into account its real bending form after the loss of stability. An expression for determining the critical force is obtained and numerical calculations with various ratio of thickness have been fulfilled, from the results one can see the convergence of the modified elastic solution method

Non-linear analysis of laminated composite doubly curved shallow shells

This paper deals with governing equations and approximate analytical solutions based on some wellknown assumptions to the non-linear buckling and vibration problems of laminated composite doubly curved shallow shells. Obtained results will be presented by analytical expressions of the lower critical load, the postbuckling load-deflection curve and the fundamental frequency of non-linear free vibration of the shell

On the elasto-plastic stability problem of shells of revolution

This paper deals with the elasto-plastic stability problems of shells of revolution subjected to complex loading process. The governing equations were derived and were solved by using the Bubnov-Galerkin method and the loading parameter method. Some examples were considered

Elasto-plastic stability of thin plates subjected to complex loading process

Analyzing an elastic-plastic stability problem, the complex loading process acted on the body has an essential influence on the values of critical loads. For clearing up this effect, in the present paper the general elasto-plastic process theory, theory of process with average curvature and the simple loading process theory are applied into the consideration of the mentioned problem. A numerical comparison is given

Non-linear buckling analysis of functionally graded shallow spherical shells

In the present paper the non-linear buckling analysis of functionally graded spherical shells subjected to external pressure is investigated. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. In the formulation of governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. Using Bubnov-Galerkin's method to solve the problem an approximated analytical expression of non-linear buckling loads of functionally graded spherical shells is obtained, that allows easily to investigate stability behaviors of the shell

The local theory of elastoplastic deformation processes and the stability beyond elastic limits of thin-walled structures subjected to complex loading

The paper is concerned with the complete constitutive relations of elasto-plastic deformation process theory. Using this theory the stability beyond elastic limits of thin-walled structures subjected to complex loading is analyzed. The proposed method of loading parameter is a combination of numerical and analytical solutions. Calculations have been carried out for rectangular plates and cylindrical shells in order to compare this method and its results with other theoretical and experimental works

Parametric conditions and exact solution for the Duffing-Van der Pol class of equations

This paper presents a methodology to find the exact solution and respective parametric conditions to the Duffing-Van der Pol class of equations. The supposed method in this paper is different from the Prelle and Singer method and the Lie symmetry method. The main idea of the supposed method is implemented in finding the first integrals of the original equation and leading this equation to a solved equation of lower order to which the exact solution can be obtained. As results the parametric conditions and the exact solutions in parametric forms are indicated. The algorithm for determining integral constants and the investigation of solution characteristics are considered

Non-linear dynamical analysis of laminated reinforced composite doubly curved shallow shells

The present paper deals with a non-linear dynamical analysis of laminated reinforced composite doubly curved shallow shells. The motion equations of shell based upon the thin shell theory considering the geometrical non-linearity and the Lekhnitsky's smeared stiffeners technique. Simultaneous ordinary differential equations are obtained by means of Bubnov-Galerkin's procedure. Non-linear responses are calculated by using an iterative procedure in conjunction with Newmark constant acceleration scheme. Obtained results allow to discover the influence of stiffeners, the shell geometry on the non-linear response of eccentrically stiffened laminated composite shells

A new approach for investigating corrugated laminated composite plates of wave form

Corrugated plates of wave form made of isotropic elastic material were considered as flat orthotropic plates with corresponding orthotropic constants determined empirically by the Seydel’s technique. In some recent researches the extension of this technique was given for corrugated laminated composite plates. In the present paper a new approach for investigating corrugated composite plate of wave form is proposed, regarding this plates as a combination of parts of shallow cylindrical shells with alternative curvatures. It reduces to no use of Seydel’s empirical formulas and sufficiently apply to composite plates. Based on this approach governing equations of corrugated laminated composite plate of wave form are developed and application to the non-linear stability problem of this plate is considered. Obtained results are compared with those of Seydel’s technique

On the solutions of the Mathieu’s equation

As shown in [1] solutions of the Mathieu’s equation were classified on three fundamental kinds depending mainly on its parameters. These solutions were constructed in the form of infinite series. This paper presents a new approach in which approximated analytical solutions of the Mathieu’s equation are constructed in the finite form. Depending on parameters of Mathieu’s equations general solutions may obtain following behaviors: either bounded almost periodic, or infinitely increased combining with infinitely decreased and or infinitely increased combining with periodic