Efficient Numerical Solution of Dynamical Ginzburg-Landau Equations under the Lorentz Gauge

In this paper, a new numerical scheme for the time dependent Ginzburg-Landau (GL) equations under the Lorentz gauge is proposed. We first rewrite the original GL equations into a new mixed formulation, which consists of three parabolic equations for the order parameter ψ, the magnetic field σ=curlA, the electric potential θ=divA and a vector ordinary differential equation for the magnetic potential A, respectively. Then, an efficient fully linearized backward Euler finite element method (FEM) is proposed for the mixed GL system, where conventional Lagrange element method is used in spatial discretization. The new approach offers many advantages on both accuracy and efficiency over existing methods for the GL equations under the Lorentz gauge. Three physical variables ψ, σ and θ can be solved accurately and directly. More importantly, the new approach is well suitable for non-convex superconductors. We present a set of numerical examples to confirm these advantages.

NUMERICAL SIMULATION OF AL-SI ALLOYS WITH AND WITHOUT A DIRECTIONAL SOLIDIFICATION

Numerical simulations are presented to analyze the influence of the casting process on the resulting strength of Strontium modified Al–Si alloys. A relationship is identified between the mechanical behavior and the different 3D morphologies of the eutectic silicon of the samples obtained by the die cast procedure and the directional solidification. It is shown that the mechanical behavior of the die cast alloy is isotropic in all three directions. In contrary, for the directional solidified alloy, the mechanical strength in the direction of the temperature gradient is higher than in the transverse direction. This fact has to be taken into account when analyzing structures issued from different casting processes. The volume meshes for the simulations are generated from experimental 3D FIB/SEM data sets. The influence of several levels of coarsening of the meshes as well as the order of the Lagrange element in the finite element setup are also analyzed.

Finite Element Formulation for the Vibration Analysis of Couple-Stress Continuum

This paper proposed a finite element formulation to analysis the vibration of couple-stress continuum. A four-node discrete couple-stress element relaxed the requirement of C1 continuity is developed. This element is modified by a bubble function, based on the classical four-ode Lagrange element. The element includes the internal bending constants and the internal initial moment of rotation. Numerical examples show that the present FE scheme is accurate for the eigenvalue analysis of couple-stress continuum structures, especially for the low order frequency analysis.

Study on the Influence of Stability for Higher Precipitous Open Pit Slope under Mining Blasting

Based on the hydrological, geologies and slope features of Jianshan phosphate mine in Yunnan province, the geomechanics model of slope was established. Then the static stability of different elevations in mining section was studied by using methods such as the rigid body limit equilibrium method, finite element method, continuum large deformation Lagrange element method. According to the supervise data of the mining blasting, the dynamic response of the slope in blasting was studied by continuum large deformation Lagrange element method, and some suggestions were proposed for following mining blasting. The research results show that the slope was in the stable status before blasting vibration. Current mining blasting vibration has little effect on the stability of slope, but would reduce the safety factor of the top of the slope. Single blasting would enlarge the instantaneous acceleration of the top of the slope in a ratio of 8.8% and 10.8%.

Enhanced Elastic Buckling Loads of Composite Plates With Tailored Thermal Residual Stresses

Thermal residual stresses introduced during the manufacturing process and their effect on the buckling load of stringer reinforced composite plates is investigated. The principal idea is to include stiffeners on the perimeter of the plate and thereby, during manufacture, induce a favorable thermal residual-stress state in the structure; these stresses arise by considering the difference in thermal expansion coefficients and elastic properties of the plate and the stiffeners. In this manner, it is shown that thermal residual stresses can be tailored to significantly enhance the performance of the structure. The analysis is taken within the context of an enhanced Reissner-Mindlin plate theory and the finite element technique is used to analyze the problem. A 16 node bi-cubic Lagrange element is implemented in a FORTRAN code to determine the buckling load of the composite plate in the presence of thermal residual stresses. Three different plate-stiffener geometries are used as illustrations. The analyses indicate that buckling loads can be significantly increased by properly tailoring the thermal residual stresses. Therefore it may be concluded that an evaluation of these stresses and a judicious analysis of their effects must be included in the design procedure for this class of composite structure.