Stability of the critical equilibrium of a compressed column on a Winkler foundation

In this paper, the critical equilibrium of a simply supported compressed column on a Winkler foundation is analyzed based on Koiter’s theory. The exact expression of the potential energy functional is presented. By the Fourier series of the disturbance deflection, the second-order variation of the potential energy is expressed as a quadratic form. At critical equilibrium, the second-order variation of the potential energy is semi-positive definite, so that the stability of the critical equilibrium is determined by the sign of the fourth-order variation or sixth-order variation. It can be seen that only in two small ranges of elastic-foundation stiffness is the corresponding critical state stable and the bifurcation equilibrium upward. Then, the theoretical results of this paper are compared with previous experimental and theoretical results.

Analysis of the Functionally Step-Variable Graded Plate Under In-Plane Compression

A study of the pre- and post-buckling state of square plates built from functionally graded materials (FGMs) and pure ceramics is presented. In contrast to the theoretical approach, the structure under consideration contains a finite number of layers with a step-variable change in mechanical properties across the thickness. An influence of ceramics content on a wall and a number of finite layers of the step-variable FGM on the buckling and post-critical state was scrutinized. The problem was solved using the finite element method and the asymptotic nonlinear Koiter’s theory. The investigations were conducted for several boundary conditions and material distributions to assess the behavior of the plate and to compare critical forces and post-critical equilibrium paths.

Problem behavior in autism spectrum disorders: A paradigmatic self-organized perspective of network structures

Autism spectrum disorder (ASD) subjects can present temporary behaviors of acute agitation and aggressiveness, named problem behaviors. They have been shown to be consistent with the self-organized criticality (SOC), a model wherein occasionally occurring “catastrophic events” are necessary in order to maintain a self-organized “critical equilibrium.” The SOC can represent the psychopathology network structures and additionally suggests that they can be considered as self-organized systems.

The analysis of buckling and post buckling in the compressed composite columns

Purpose: The aim of the study was to analyse the work of a thin-walled C-shaped profile, made of a carbon-epoxy composite, which was subjected to unified axial compression. Design/methodology/approach: The scope of the study included the analysis of the critical and low post-critical state by the use of numerical and experimental methods. As a result of the experimental test, performed on the physical specimen, post-critical equilibrium path had been determined, on the basis of which, with use of the adequate approximation method critical load value was defined. The next stage of the research was devoted to numerical analysis based on the finite element method. The studies were carried out on a scope of the linear analysis of the eigenvalue problem, on the basis of witch the critical value of load for mathematical model was found. The next step of the numerical tests was covering the nonlinear analysis of the low post-critical state for the model with geometrical imperfection, corresponding to the lowest form of buckling. Findings: The result of the study was to determine the value of the critical load, on the basis of the experimentally obtained post-critical equilibrium paths of the structure, with use of two independent methods of Approximation: Koiter's method and the method of the vertical tangent. The results of the analysis were compared with the value of the critical load determined by using finite element method. Research limitations/implications: The obtained results of study provide the important information concerning the modelling techniques of the thin-walled structures made of composite materials, while confirming the adequacy of the numerical models developed both in the calculation of eigenvalue problem, as well as non-linear static analysis in the post-critical range. Originality/value: The research provided the necessary knowledge of the behaviour of the critical and low post-critical of the thin-walled structure made of modern orthotropic material (CFRP).

Nonlinear Modeling and Dynamic Simulation Using Bifurcation and Stability Analyses of Regenerative Chatter of Ball-End Milling Process

A dynamic model for a ball-end milling process that includes the consideration of cutting force nonlinearities and regenerative chatter effects is presented. The nonlinear cutting force is approximated using a Fourier series and then expanded into a Taylor series up to the third order. A series of nonlinear analyses was performed to investigate the nonlinear dynamic behavior of a ball-end milling system, and the differences between the nonlinear analysis approach and its linear counterpart were examined. A bifurcation analysis of points near the critical equilibrium points was performed using the method of multiple scales (MMS) and the method of harmonic balance (MHB) to analyse the local chatter behaviors of the system. The bifurcation analysis was conducted at two subcritical Hopf bifurcation points. It was also found that a ball-end milling system with nonlinear cutting forces near its critical equilibrium points is conditionally stable. The analysis and simulation results were compared with experimental data reported in the literature, and the physical significance of the results is discussed.