Synergistic Effect of Core/Shell‑Structured Composite Fibers:Efficient Recovery of Rare‑Earth Elements from Spent NdFeB Permanent Magnets

NdFeB magnets are third-generation permanent magnets that are employed as indispensable components in various industries.Notably,rare-earth elements(REEs)such as Dy and Nd must be efficiently recovered from end-of-life magnets to enable resource circulation and reinforce unstable supply chains.To that end,this paper reports synergistically performing core/shell-structured composite fibers(CSCFs)containing sodium polyacrylate and nanoporous zeolitic imidazolate framework-8(NPZIF-8)nanocrystals as a readily recoverable adsorbent with an exceptional REE-adsorbing ability.The CSCF core forms an NPZIF-8 nanocrystal shell on the fiber surface as well as draws REEs using its dense sodium carboxylate groups into the NPZIF-8 nanocrystal lattice with high specific surface area.The CSCFs exhibit significantly higher maximum adsorption capacities(468.60 and 435.13 mg·g-1)and kinetic rate constants(2.02 and 1.92 min-1)for the Nd3+and Dy3+REEs than those of previously reported REE adsorbents.Additionally,the simple application of the CSCFs to an adsorption reactor considerably mitigates the adsorbent-shape-induced pressure drop,thereby directly influencing the energy efficiency of the recovery.Moreover,the high REE-recovery ability,tractability,and recyclability of the CSCFs offers a pragmatic pathway to achieving cost-effective REE recovery.Overall,this study provides new insights into designing synergistically performing core/shell architectures for feasible REE recovery.

ANALYSIS OF NONLINEAR PIEZOELECTRIC CIRCULAR SHALLOW SPHERICAL SHELLS BY DIFFERENTIAL QUADRATURE ELEMENT METHOD

The static behavior of piezoelectric circular spherical shallow shells under both electrical and mechanical loads is studied by using the differential quadrature element method (DQEM). Geometrical nonlinearity effect is considered. Detailed formulations and procedures are given for the first time. Several examples are analyzed and accurate results are obtained by the DQEM. Based on the results in this paper, one may conclude that the DQEM is a useful tool for obtaining solutions of structural elements. It can be seen that the shell shape may be theore tically controlled and snap through may occur when the applied voltage reaches a critical value even without mechanical load for certain geometric configurations.

THE CONSTRUCTION OF WAVELET-BASED TRUNCATED CONICAL SHELL ELEMENT USING B-SPLINE WAVELET ON THE INTERVAL

Based on B-spline wavelet on the interval （BSWI）, two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately thick truncated conical shell element with independent slopedeformation interpolation. In the construction of wavelet-based element, instead of traditional polynomial interpolation, the scaling functions of BSWI were employed to form the shape functions through the constructed elemental transformation matrix, and then construct BSWI element via the variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkin method, the elemental displacement field represented by the coefficients of wavelets expansion was transformed into edges and internal modes via the constructed transformation matrix. BSWI element combines the accuracy of B-spline function approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples of conical shells were studied to demonstrate the present element with higher efficiency and precision than the traditional element.

Geochemistry of trace elements and Sr-Nd isotopes of foraminifera shell from the Okinawa Trough

Trace elemental associations and Sr-Nd isotopic compositions are of important to recognition of biogenic material from mixed marine sediments. The foraminifera shell from the Okinawa Trough strongly enriches Sr,P,Mn and Ba, enriches Li,U,Th,Sc,Co,Cu,Pb,Zn,Cr,Rb,Y,Sb and light rare earth elements,slightly enriches V,Ga,Zr,Nb,Cd and middle rare earth elements,is short of Mo,In,Sn,Cs,Hf,Ta,W,Ti,Bi and heavy rare earth elements. The mechanism of elemental enrichment in forminifera is the concentrations of trace elements in sea water and selective absorption of trace elements during foraminifera living, as well as the geochemical affinity between major elements and trace elements.The REE (rare earth elements)partition pattern of foraminifera shell of the Okinawa Trough shows enrichment of middle rare earth elements with slightly negative Ce anomaly,which are different from those of foraminifera of the Pacific Ocean.The Sr,Nd isotopic ratios of the Okinawa Trough foraminifera are 0 709 769 and 0 512 162,respectively, which are different not only from those of oceanic water, but also from those of river water of China's Mainland, the former is slightly higher than those of oceanic water,but much lower than those of river water;the latter is slightly lower than those of oceanic water,but higher than those of river water,demonstrating that the Okinawa Trough sea water has been influenced by river water of China's Mainland.

Difference in Number of Electrons in Inner Shells of Charged or Uncharged Elements in Organic and Inorganic Chemistry: Compatibility with the Even-Odd Rule

The recently introduced even-odd rule has been shown to successfully represent chemical structures of ions and molecules. While comparing available drawings in the scientific literature with the list of compounds predicted by the even-odd rule, it became however obvious that existing compounds are fewer than expected. Several predicted compounds involving many covalent bonds have apparently never been experimentally observed. Neutral oxygen for instance is expected to have 6 valence electrons, whereas oxygen can only build a maximum of two bonds, as in water. This specificity is observed for elements in the top-right corner of the periodic table. For compounds to contain only single covalent bonds, and thus follow the even-odd rule, further explanations are necessary. The present paper proposes that those specific elements experience a transfer of electrons from the valence shell into the inner shell, making them unavailable for further bonding. These elements will be described as organic, hereby providing a clear and hopefully unifying definition of the term. In opposition, inorganic elements have a constant inner shell no matter their electrical state or the number of bonds they maintain. More than 70 compounds involving 11 elements of the main group are studied, revealing a progression from fully inorganic elements at the left of the periodic table to fully organic elements. The transition between inorganic or organic elements is made of few elements that take an organic form when negatively charged;they are labelled semi-organic. The article concludes that the fully organic elements of the main group are Oxygen and Fluorine, whereas semi-organic elements are more numerous: C, N, S, Cl, Se, Br and I. Thus, the even-odd rule becomes fully compatible with scientific knowledge of compounds in liquid or gaseous phase.

ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL—II:FINITE ELEMENT MODELING AND APPLICATION

Based on the generalized vaxiational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established （see, Analyses on nonlinear coupling of magneto-thermo- elasticity of ferromagnetic thin shell--I）, the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.

Enriched goal-oriented error estimation for fracture problems solved by continuum-based shell extended finite element method

An enriched goal-oriented error estimation method with extended degrees of freedom is developed to estimate the error in the continuum-based shell extended finite element method. It leads to high quality local error bounds in three-dimensional fracture mechanics simulation which involves enrichments to solve the singularity in crack tip. This enriched goal-oriented error estimation gives a chance to evaluate this continuum- based shell extended finite element method simulation. With comparisons of reliability to the stress intensity factor calculation in stretching and bending, the accuracy of the continuum-based shell extended finite element method simulation is evaluated, and the reason of error is discussed.

Development and Application of a High-Performance Triangular Shell Element and an Explicit Algorithm in OpenSees for Strongly Nonlinear Analysis

The open-source finite element software,OpenSees,is widely used in the earthquake engineering community.However,the shell elements and explicit algorithm in OpenSees still require further improvements.Therefore,in this work,a triangular shell element,NLDKGT,and an explicit algorithm are proposed and implemented in OpenSees.Specifically,based on the generalized conforming theory and the updated Lagrangian formulation,the proposed NLDKGT element is suitable for problems with complicated boundary conditions and strong nonlinearity.The accuracy and reliability of the NLDKGT element are validated through typical cases.Furthermore,by adopting the leapfrog integration method,an explicit algorithm in OpenSees and a modal damping model are developed.Finally,the stability and efficiency of the proposed shell element and explicit algorithm are validated through the nonlinear time-history analysis of a highrise building.

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

The finite_element_displacement_perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first_order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C_shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.

A 3-Node Co-Rotational Triangular Finite Element for Non-Smooth,Folded and Multi-Shell Laminated Composite Structures

Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.

LOCKING-FREE DEGENERATED ISOPARAMETRIC SHELL ELEMENT

An 8-noded locking-free degenerated isoparametric shell element is presented. A revised interpolation for shear strain terms was constructed in natural co-ordinate system such that all necessary modes (translation, rotation and constant curvature) are preserved, which can be used to eliminate shear locking. A revised interpolation for membrane strains was produced in the local Cartesian co-ordinate system to overcome membrane locking behavior. The new 8-noded element has the proper rank, with the requisite number of zero eigenvalues each associated with a rigid mode. The element does not exhibit membrane or shear locking for large span-thickness ratio. The element does not form element mechanisms or extra spurious zero energy modes. Therefore, it can be used for both thin and thick shells.

ON THE STABILITY ANALYSIS OF PLATES AND SHELLS USING A QUADRILATERAL,16-DEGREES OF FREEDOM PLAT SHELL ELEMENT DKQ16

The linear buckling problems of plates and shells were analysed using a recently developped quadrilateral,16-degrees of freedom flat shell element (called DKQ16).The geometrical stiffness matrix was established.Comparison of the numerical results for several typical problems shows that the DKQ16 element has a very good precision for the linear buckling problems of plates and shells.

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

In order to analyze bellows effectively and practically, the finite_element_displacement_perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba_ tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root_mean_square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander's nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.

Finite Element Modeling of a Fluid Filled Cylindrical Shell with Active Constrained Layer Damping

On the basis of the piezoelectric theory, Mindlin plate theory, viscoelastic theory and ideal fluid equation, the finite element modeling of a fluid-filled cylindrical shell with active constrained layer damping (ACLD) was discussed. Energy methods and Lagrange’s equation were used to obtain dynamic equations of the cylindrical shell with ACLD treatments, which was modeled as well with the finite element method. The GHM (Golla-Hughes-McTavish) method was applied to model the frequency dependent damping of viscoelastic material. Ideal and incompressible fluid was considered to establish the dynamic equations of the fluid-filled cylindrical shell with ACLD treatments, Numerical results obtained from the finite element analysis were compared with those from an experiment. The comparison shows that the proposed modeling method is accurate and reliable.

THE RATIONALISM THEORY AND ITS FINITE ELEMENT ANALYSIS METHOD OF SHELL STRUCTURES

In this paper, a kind of rationalism theory of shell is established which is of different mechanic characters in tension and in compression, and the finite element numerical analysis method is also described.

A Smoothed Finite Element Method for the Static and Free Vibration Analysis of Shells

A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples.

Finite Element Analysis of Polygon Shaped Shell Roof

A new spherical triangular finite element based on shallow shell formulation is developed in this paper. The element has six degrees of freedom at each comer node, five of which are the essential external degrees of freedom and the additional sixth is associated with the in-plane shell rotation. The displacement fields of the element satisfy the exact requirement of rigid body modes of motion. The element is based on independent strain assumption insofar as it is allowed by the compatibility equations. The element developed herein is first validated by applying it to the analysis of a benchmark problem involving a standard spherical shell with simply supported edges. The results of the analysis showed that reasonably accurate results were obtained even when modeling the shells using fewer elements compared to other shell element types. The element is then used in a finite element model to analyze polygon shaped spherical roof structures. The distribution of the various components of deflection and stress is obtained. Furthermore, the effect of introducing circular arched beams as stiffeners spanning the two diagonally opposite end comers is investigated. It is found that the stiffeners reduced the deflections and the stresses in the roof structure by considerable value.

Stochastic Finite Element Analysis of Plate and Shell Construction

The response of random plate and shell construction is analyzed with the stochastic finite element method (SFEM). Random material properties and geometric dimensions of construction are involved in this paper. A simplified isoparametric local average model is used to describe the random field. Numerical results of the examples indicate that the approach presented herein is an economical and efficient solution for such an analysis compared with Monte Carlo simulation (MCS).

The New Rigid Element for Laminated Cylindrical Shell

Thermal effects are incorporated into developed discrete layer mechanics for two-dimensional cylindrical shells structures. Finite element equations are developed according to layerwise theory of laminated structure. Following the layerwise theory, a variable kinematic model that incorporates mechanics and thermal conditions is also presented. The new element has a field of displacement compatible with the cylindrical shell element or plate and it can be used as a rigid element for this structural element.ln the laminate model construction, adjacent layers are arranged as bonded layers. The layer has a unique constant thickness that can be different to each layer. The fiber reinforced is used and the fibers in a laminate may be oriented arbitrarily. The shear stress is adopted equal to zero because the thin thickness, on the other hand, the normal stress is maintained in order to ensure the compatibility of stress in material. The previously authors of this methods neglect the implications of thermal effects on cylindrical shells structures. Thermal effects become important when the structure has to operate in either extremely hot or cold temperature environments. These extreme conditions may severely affect the response of structure in two distinct ways： （1） induction of thermal stresses due to differences in the coefficients of thermal expansion between the various composite plies and layers and （2） temperature dependence of the elastic properties. Only a limited amount of work has been reported concerning this topic. All in all, the main contribution of this work is the consideration of this kinematic for cylindrical shells that incorporate mechanics and thermal conditions. In addition, numerical results are presented to demonstrate the capability of the current formulation to represent the behavior of cylindrical shells with these characteristics.

A Wave Superposition-Finite Element Method for Calculating the Radiated Noise Generated by Volumetric Targets in Shallow Water

A combined method of wave superposition and finite element is proposed to solve the radiation noise of targets in shallow sea.Taking the sound propagation of spherical sound source in shallow sea as an example,the radiation sound field of the spherical sound source is equivalent to the linear superposition of the radiation sound field of several internal point sound sources,and then the radiated noise induced by spherical sound source can be predicted quickly.The accuracy and efficiency of the method are verified by comparing with the numerical results of finite element method,and the rapid prediction of underwater radiated noise of cylindrical shell is carried out based on the method.The results show that compared with the finite element method,the relative error of the calculation results under different simulation conditions does not exceed 0.1%,and the calculation time is about 1/10 of the finite element method,so this method can be used to solve the radiated noise of shallow underwater targets.