Nonlocal strain gradient continuum mechanics is a methodology widely employed in the literature to assess size effects in nano-structures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems. In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation. The treatment, developed in the framework of torsion of elastic beams, provides an effective approach to evaluate scale phenomena in smaller and smaller devices of engineering interest. Both elastostatic torsional responses and torsional-free vibrations of nano-beams are investigated by applying a simple analytical method. It is also underlined that the nonlocal strain gradient model, if equipped with the inappropriate HOBC, can lead to torsional structural responses which unacceptably do not exhibit nonlocality. The presented variational strategy is instead able to characterize significantly peculiar softening and stiffening behaviors of structures involved in modern nano-electro-mechanical systems.

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

Nonlocal strain gradient continuum mechanics is a methodology widely employed in literature to assess size effects in nanostructures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems. In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation. The treatment, developed in the framework of torsion of elastic beams, provides an effective approach to evaluate scale phenomena in smaller and smaller devices of engineering interest. Both elastostatic torsional responses and torsional free vibrations of nano-beams are investigated by applying a simple analytical method. It is also underlined that the nonlocal strain gradient model, if equipped with the inappropriate HOBC, can lead to torsional structural responses which unacceptably do not exhibit nonlocality. The presented variational strategy is instead able to characterize significantly peculiar softening and stiffening behaviours of structures involved in modern Nano-Electro-Mechanical-Systems (NEMS).

In this work, a new displacement-based Trefftz plate element is developed for size-dependent bending analysis of the thin plate structures in the context of the modified couple stress theory. This is achieved via two steps. First, the Trefftz functions, that are derived by introducing the thin plate bending assumptions into the three-dimensional governing equations of the modified couple stress elasticity, are adopted as the basis functions for designing the element's displacement interpolations. Second, the generalized conforming theory is employed to meet the interelement compatibility requirements in weak sense for ensuring the convergence property. The resulting 4-node displacement-based plate element performs like nonconforming models on coarse meshes and gradually converges into a conforming one with the mesh refinement. Numerical tests reveal that the new element can efficiently capture the size-dependent mechanical responses of thin microplates and exhibits satisfactory numerical accuracy and distortion tolerance. Moreover, as the element has only three degrees of freedom (DOF) per node, it can be easily incorporated into the commonly available finite element programs.

Generalized conforming Trefftz element for size-dependent analysis of thin microplates based on the modified couple stress theory

Nano-sized batteries composed of nanostructured electrode materials stand as one of the most promising candidates for next-generation rechargeable charging devices which have been widely used in the energy storage systems for advanced power applications. Buckling analysis of nanobeam under non-uniform concentration is significantly important for the design of nano-sized batteries under the rapid charging mode. In this work, such issue is investigated in the framework of the size-dependent mechanical–diffusion model, and size effect of mass transfer on buckling property is considered for the first time. By using the eigenvalue method, the critical buckling loads of Euler–Bernoulli nanobeam under the conditions of clamped–clamped, clamped–free, simply supported–simply supported and clamped–simply supported are analytically obtained. The derived results are compared with those of non-gradient nonlocal elastic stress theory, classical elasticity theory and classical theory of mass transfer. It is also found that the value of critical buckling load will be reduced if diffusive nonlocal parameter becomes larger.

Size-dependent buckling analysis of Euler-Bernoulli nanobeam under non-uniform concentration

High-performance alloy materials are increasingly considered for various engineering applications due to their combination of desirable properties. However, the guided wave-based structural health monitoring of alloys is often challenged by their strong anisotropic nature, which makes it difficult to calculate the guided wave behavior and associate mode shapes. In this article, Lamb mode waves of Cu–Al–Ni alloy under uniaxial stresses are characterized by developing a novel numerical polynomial approach, which may provide an efficient way to solve problems concerning acoustic wave propagations. To facilitate understanding of the dispersion curve trajectories, the anisotropic phase transformation from cubic phase (austenite) to orthorhombic plate (martensite) is considered. The comparison of the evanescent mode trajectories between the cubic and orthorhombic alloys shows the presence of imaginary modes in the cubic phase, although they may not exist in the orthorhombic phase at specific frequencies. In the case of Lamb propagation in the cubic alloy, the dispersion curves oscillate strongly, creating crossings among multiple symmetric and antisymmetric modes. This study also concerns the second harmonic generation of Lamb mode pairs in cubic and orthorhombic alloys. Furthermore, effect of uniaxial stresses on Lamb dispersion curves in both phases are also identified and discussed. The results obtained may promote understanding and optimization of novel acoustic devices made of anisotropic materials.

Propagating, evanescent and ZGV Lamb modes in high-performance anisotropic Cu–Al–Ni alloy plates

The present paper develops a size-dependent Kirchhoff microplate model with surface effects by using simplified strain gradient elasticity theory and surface elasticity theory. This new model is able to capture size-dependent behaviors and surface effects. The most noticeable difference of the proposed model from the existing plate models about microplates is that not only strain gradient and surface stress are taken into account, but also the surface-induced internal residual stresses are considered. Based on whether the plates having surface-induced internal residual stress or not, their governing equations have distinct differences. An extended Kantorovich method is employed to provide approximate closed-form solution for the rectangular microplate with simply supported boundary conditions. For the microplate with biaxial initial residual surface stress, the numerical results reflect that when the simply supported microplates do not have surface-induced internal residual stresses, internal length scale and biaxial surface residual stress have significant influence on the static bending of the microplates. However, when the simply supported microplates have nonzero surface-induced internal residual stresses, the effects of internal length scale and biaxial surface residual stress become very weak. It indicates that the effect of surface-induced internal residual stresses can counteract most of the effects of internal length scale and surface residual stress. This work provides a more general model for the analysis of microplate problems.

The influence of surface stress and surface-induced internal residual stresses on the size-dependent behaviors of Kirchhoff microplate

International Thermonuclear Experimental Reactor (ITER), the world&apos; largest fusion facility, has officially began assembly work at July 28, 2020 and plan to operation at December 2025. If ITER can operate successfully, which means the people step forward on the road to peaceful use of fusion energy. Meanwhile, how safe about ITER and whether the ITER will cause radiation harm to the surrounding environment and personnel is our concern. A lot of safety assessment work had been done for ITER using a deterministic approach through conservative assumptions and calculations. But it&apos;s not enough. This paper aims to estimate the radiological risk of ITER. The first, the probabilistic safety assessment (PSA) progress for ITER was proposed in this paper and then, the preliminary PSA was applied on ITER and the results shows that ITER has a high frequency of accidents in the range of small dose. But the large-scale radiological consequences are unlikely. The reasons for those results are also analyzed in this paper. Those result could provide some valuable reference for risk assessment and safety supervision of fusion commercial reactor in the near future. 

A preliminary probabilistic safety assessment for ITER

In this paper, based on the correlation matrix, the fault detection method of controller is studied based on the fault diagnosis characteristics of environment control and life support system(ECLSS). Combined with the characteristics of actual system fault diagnosis, the reasons for the existence of the feedback loop are analyzed, the different diagnostic effects caused by voltage and current detection methods are compared, and the detection method of breaking the feedback loop by manual testing is proposed. Through modeling and analysis, complete design ideas and methods are provided for improving testability design of controller products, which can help guide Built-In-Test(BIT) design of controllers. 

W. J. Wang

Papers

The influence of surface stress and surface-induced internal residual stresses on the size-dependent behaviors of Kirchhoff microplate

A preliminary probabilistic safety assessment for ITER

Research on a system controller fault detection method based on correlation matrix