Properties of the free boundary near the fixed boundary of the double obstacle problems

In this paper, we study the tangential touch and [Formula: see text] regularity of the free boundary near the fixed boundary of the double obstacle problem for Laplacian and fully nonlinear operator. The main idea to have the properties is regarding the upper obstacle as a solution of the single obstacle problem. Then, in the classification of global solutions of the double problem, it is enough to consider only two cases for the upper obstacle, [Formula: see text] The second one is a new type of upper obstacle, which does not exist in the study of local regularity of the free boundary of the double problem. Thus, in this paper, a new type of difficulties that come from the second type upper obstacle is mainly studied.

Influence of Different Sites on Impact Response of Steel-Plate Concrete Containment against a Large Commercial Aircraft

This paper aimed at evaluating the influence of different site conditions on the impact response of the structure of nuclear power plants (NPPs) against a large commercial aircraft. The lumped parameter site dynamic model recommended by the code of ASCE 4-98 was used to consider the different homogeneous sites. With respect to the excellent impact resistant performance of steel-plate concrete (SC) structure, the full SC containment is selected as the research object. The impact analysis of the full SC containment against a large commercial aircraft under different site conditions was carried out, based on the force time-history analysis method. The numerical results in terms of the displacement, plastic strain, local concrete damage, and different values of energy were evaluated. The results showed that: (1) For the relatively thin full SC containment, the impact response under the fixed boundary is the largest, while that calculated by other, different sites varies greatly, and there is no consistent rule, the boundary condition which is assumed to be fixed is relatively conservative. (2) For the thicker full SC containment, the displacement response decreased with the increasing of the site shear wave velocity, which is the smallest when the fixed boundary is considered. When the shear wave velocity of the site is large enough, its boundary condition which is assumed to be the fixed constraint is reasonable. (3) For the relatively thin full SC containment, the site damping effect has a significant effect on the structural impact response. Nevertheless, the impact response of the thicker containment is slightly influenced by the site damping effect. (4) For the impact analysis of the structures of NPPs against a large commercial aircraft, it is suggested that both the specific site condition and fixed boundary should be considered.

A new time-delayed periodic boundary condition for discrete element modelling of railway track under moving wheel loads

A new time-delayed periodic boundary condition (PBC) has been proposed for discrete element modelling (DEM) of periodic structures subject to moving loads such as railway track based on a box test which is normally used as an element testing model. The new proposed time-delayed PBC is approached by predicting forces acting on ghost particles with the consideration of different loading phases for adjacent sleepers whereas a normal PBC simply gives the ghost particles the same contact forces as the original particles. By comparing the sleeper in a single sleeper test with a fixed boundary, a normal periodic boundary and the newly proposed time-delayed PBC (TDPBC), the new TDPBC was found to produce the closest settlement to that of the middle sleeper in a three-sleeper test which was assumed to be free of boundary effects. It appears that the new TDPBC can eliminate the boundary effect more effectively than either a fixed boundary or a normal periodic cell. Graphic abstract

Bending Vibration Characteristics of a Novel Piezoelectric Composite Trilaminar Vibrator

In this work, the bending vibration characteristics of the 2-2 piezoelectric composite trilaminar vibrator are studied by the finite element simulation and experiment. The simulation results show that the trilaminar vibrator has lower resonant frequency and larger vibration displacement under the fixed boundary condition compared with that of the free boundary condition, and its performance is relatively good. Then, the 2-2 piezoelectric composite and piezoelectric ceramic trilaminar vibrators are fabricated and their performances are tested under the fixed boundary condition. The experimental and simulation results show that the vibrator has pure bending vibration characteristics in the frequency band of 1.2–1.4 kHz, especially the 2-2 piezoelectric composite vibrator, which has lower frequency, higher electromechanical coupling coefficient and larger bending vibration displacement; thus, the 2-2 piezoelectric composite trilaminar vibrator is a better choice for the fabrication of a low-frequency transducer.