Quasi-static thermal stresses in a thick circular plate

The present paper deals with the determination of a quasi-static thermal stresses in a thick circular plate subjected to arbitrary initial temperature on the upper face with lower face at zero temperature and the fixed circular edge thermally insulated. The results are obtained in series form in terms of Bessel’s functions and they are illustrated numerically.     

Time-discretization scheme for quasi-static Maxwell's equations with a non-linear boundary condition

We study a time dependent eddy current equation for the magnetic field H$\mathit{H}$ accompanied with a non-linear degenerate boundary condition (BC), which is a generalization of the classical Silver–Müller condition for a non-perfect conductor. More exactly, the relation between the normal components of electrical E$\mathit{E}$ and magnetic H$\mathit{H}$ fields obeys the following power law ν×E=ν×(|H×ν|^α-1H×ν)$\mathit{\nu }\times \mathit{E}=\mathit{\nu }\times (|\mathit{H}\times \mathit{\nu }{|}^{\alpha -1}\mathit{H}\times \mathit{\nu })$ for some α∈(0,1]$\alpha \in (0,1]$. We establish the existence and uniqueness of a weak solution in a suitable function space under the minimal regularity assumptions on the boundary Γ$\Gamma$ and the initial data _H0${\mathit{H}}_0$. We design a non-linear time discrete approximation scheme based on Rothe's method and prove convergence of the approximations to a weak solution. We also derive the error estimates for the time-discretization.     

Exact Null Controllability of a Nonlinear Thermoelastic Contact Problem

We study the controllability properties of a nonlinear parabolic system that models the temperature evolution of a one-dimensional thermoelastic rod that may come into contact with a rigid obstacle. Basically the system dynamics is described by a one-dimensional nonlocal heat equation with a nonlinear and nonlocal boundary condition of Newmann type. We focus on the control problem and treat the case when the control is distributed over the whole space domain. In this case the system is proved to be exactly null controllable provided the parameters of the system are smooth. The proof is based on changing the control variable and using Aubins Compactness Lemma to obtain an invariant set for the linearized controllability map. Then, by proving that the found solution is sufficiently smooth, we get the null controllability for the original system.     

Strength predictions by applied effective volume theory in short-glass-fibre-reinforced plastics

Uniaxial stresses were evaluated under flexural, tensile and torsional tests with various fibre volume fractions, v_f, and specimen sizes to develop simple and effective predictions on the quasi-static strength of compression-moulded short-glass-fibre-reinforced phenolic resin. The distributions in fibre orientation and fibre length were represented by Weibull and normal distributions, regardless of v_f. The size effect was characterized by uniaxial stress testing and Weibull statistical analysis. The effective volume theory (EVT) was used to predict the quasi-static strength for v_f of 0.0 with a scale parameter of 108.2 MPa and a shape parameter of 8.92. Strength prediction while considering V_eff and v_f was proposed by applying the EVT of the resin matrix to a method that combined a modified rule of mixtures and the Thai-Hill failure criterion. The measured value agreed well with the prediction for each V_eff and v_f, regardless of manufacturing defects in the matrix resin.     

Quasi-static simulations of compact polydisperse particle systems

The Discrete Element Method (DEM) was originally devised by Cundall and Strack (1979), as a technique to examine the micromechanics of granular media with the anticipation that this would lead to more physically reliable continuum theories to describe the quasi-static deformation of granular material such as sand. However, the methodology models the evolution of a system of particles as a dynamic process. Consequently there have been numerous publications of the application of DEM to an increasingly wider v...     

The propagation of Quasi-static region during granular impact

In this paper, through experiments and DEM simulations, it is found that there is a ring-shaped region named Quasi-static Region between the particles expanding outward and the particles collapsing inward during the impact process. Quasi-static Region is always generated from the impact point at the same time, and then spreads out at a uniform speed. During the propagation of Quasi-static Region, the velocity of the particles in the particle extend region varies linearly in space and time. And the change rate is only related to the properties of the particle system. The simulation results show that the particle flow in Quasi-static Region is elastic-inertial flow, while the particle flow expanding outward and collapsing inward is inertial flow.