Existing Shell Models Research Articles

Application of a Custom Fe Simulation Technique for the Analysis of Hybrid Double-Cover Butt Joints

The simulation of hybrid composite-metal bolted joints using finite element analysis necessitates balancing the accuracy of the results and the simulation time. Accurately analyzing a bolted joint involves understanding various linear and non-linear phenomena. To simplify this process, the Composite Bolted Joint Element (CBJE) technique can be used as a modeling tool within an existing shell model. The CBJE technique uses basic finite elements featuring stiffness characteristics evaluated from the theoretical reference model of the bolted joint to provide precise results in a short time. In this study, the effectiveness of the CBJE technique is examined in the modeling of hybrid double-cover butt joints by comparing the outcomes of stiffness prediction and bolt-load distribution with those generated from a refined 3D model.

Independent cover isogeometric Reissner‐Mindlin shell model for the simulation of the fabricated lining

AbstractThe fabricated lining is widely used in the underground rail transit, water conveyance system and river‐crossing tunnel. It is generally composed of the precast concrete segments, joints, bolts and reinforcements. Compression and separation often coexist in a single joint, which brings great challenges to the modeling and calculation of the fabricated lining. In this paper, an independent cover isogeometric Reissner‐Mindlin shell model (denoted as the ICI‐R shell model) is proposed for the simulation of the fabricated lining. In the ICI‐R shell model, each segment is regarded as an independent cover, whose geometry is described with the nonuniform rational B‐splines (NURBS) surface, and an isogeometric displacement function is defined based on the Reissner‐Mindlin shell deformation theory. The adjacent segments are connected with the fictitious thin layers, of which the normal and tangential deformations and stresses can be correctly calculated. Within this framework, the difficulties in the continuity‐discontinuity coupling analysis occurring when using the existing shell models are well solved, and the fabricated lining can be simulated expediently. The ICI‐R shell model has the advantages of clear physical meaning, concise formulas and convenient implementation. Benefiting from the strong capability of representing geometries of NURBS and the simplicity of the formulation of the ICI‐R shell model, the parameterized modeling and automatic calculation of the fabricated lining can be easily achieved for simplifying the analysis process and reducing user cost for geotechnical engineers. The successful application in the benchmark tests and engineering example shows the versatility, efficiency and robustness of the ICI‐R shell model.

Two Dimensional Static Mechanical Analysis of Laminated Composite Tube Using ABCDE Matrix with No Correction Factor

Accurate modeling and prediction of materials properties is of utmost importance to design engineers. In this study, newly developed two-dimensional laminate constitutive equations (LCE) were derived directly from an existing shell model without using a classical correction factor. The resulted LCEs were subsequently used for the first time to analyze a laminated composite tube (LCT) subjected to in plane-loading. This led to additional composite-shell stiffness coefficients which are not currently available in some LCEs. The strains and stresses distribution fields were computed via Matlab. The accuracy and robustness of our analytical method were proven by opposing the as-obtained results of thick and thin LCTs with that of existing theories which use a correction factor. An excellent convergence was observed. Whereas a lower convergence was observed in the case of a laminated shell plate. Results also showed that the thickness ratio χ (2χ=h/R ) considerably influences the mechanical behavior of the LCT. In fact when χ<0.1, the distribution of stresses and strains of the tube were the same for the two opposed theories. When χ>0.1, the distribution of stresses and strains were not the same, hence the contribution of our ABCDE matrix. The new mechanical couplings in our LCE could be well illustrated in a finite element package with visualization tools to observe some intricate deformations which are yet to be seen. Thus the outcome of this work will be of particularly interest to promote advanced scientific and structural engineering applications.

Shell Model for Atomistic Simulation of Lithium Diffusion in Mixed Mn/Ti Oxides

Mixed Mn/Ti oxides present attractive physicochemical properties such as their ability to accommodate Li for application in Li-ion batteries. In this work, atomic parameters for Mn were developed to extend an existing shell model of the Li–Ti–O system and allow simulations of pure and lithiated Mn and mixed Mn/Ti oxide polymorphs. The shell model yielded good agreement with experimentally derived structures (i.e., lattice parameters and interatomic distances) and represented an improvement over existing potential models. The shell model was employed in molecular dynamics (MD) simulations of Li diffusion in the 1 × 1 c-direction channels of LixMn1–yTiyO2 with the rutile structure, where 0 ≤ x ≤ 0.25 and 0 ≤ y ≤ 1. In the infinite dilution limit, the arrangement of Mn and Ti ions in the lattice was found to have a significant effect on the activation energy for Li diffusion in the c channels due to the destabilization of half of the interstitial octahedral sites. Anomalous diffusion was demonstrated for Li ...

Efficient approach to simulate EM loads on massive structures in ITER machine

Operation of the ITER machine is associated with high electromagnetic (EM) loads. An essential contributor to EM loads is eddy currents induced in passive conductive structures. Reasoning from the ITER construction, a modelling technique has been developed and applied in computations to efficiently predict anticipated loads. The technique allows us to avoid building a global 3D finite-element (FE) model that requires meshing of the conducting structures and their vacuum environment into 3D solid elements that leads to high computational cost. The key features of the proposed technique are: (i) the use of an existing shell model for the system “vacuum vessel (VV), cryostat, and thermal shields (TS)” implementing the magnetic shell approach. A solution is obtained in terms of a single-component, in this case, vector electric potential taken within the conducting shells of the “VV+cryostat+TS” system. (ii) EM loads on in-vessel conducting structures are simulated with the use of local FE models. The local models use either the 3D solid body or shell approximations. Reasoning from the simulation efficiency, the local boundary conditions are put with respect to the total field or an external field. The use of an integral-differential formulation and special procedures ensures smooth and accurate simulated distributions of fields from current sources of any geometry. The local FE models have been developed and applied for EM analyses of a variety of the ITER components including the diagnostic systems, divertor, test blanket modules, cryopumps, blanket modules. (iii) Two integration algorithms can be applied to an ordinary differential equation system (ODES) describing a discrete problem. First, a direct integration of ODES can be performed in accordance with operating scenarios (variations of field sources). Second, complex variations of field sources can be decomposed for each source into individual components via a set of basic (influence) functions. A generalized solution is obtained as a superposition of individual solutions. (iv) The use of a combination of different computer codes implementing the shell models and 3D solid-body models. The codes and developed models were validated and approved, particularly, in the course of an ITER-initiated extensive benchmark to support of the blanket modules design.

Nonlinear viscous stress modification in the lipid-coated contrast agent microbubble dynamic model

In the existing shell models for lipid-encapsulated microbubbles, the viscous shell terms always have the linear form, which assumes that the viscous stresses acting inside the lipid shell are proportional to the shell shear rate with constant coefficient of proportionality. In the present work, a modified dynamic model is proposed for the lipid-coated ultrasound contrast agent (UCA) bubbles by taking into account the nonlinear viscous properties of a lipid monolayer coating. The dynamic responses of the UCA bubbles exposed to 1-MHz ultrasound pulses with varied driving pressures were measured using a modified flowcytometry system. By fitted the measured bubble dynamic curves with the proposed model, it has been verified that the use of the nonlinear theory for shell viscosity allows one to more accurately model the complicated UCA microbubble rheological properties.

A finite element modelling methodology for the non-linear stiffness evaluation of adhesively bonded single lap-joints: Part 2. Novel shell mesh to minimise analysis time

A new modelling methodology is presented that enables the stiffness of adhesively bonded single lap-joints to be included in the finite element analysis of whole vehicle bodies. This work was driven by the need to significantly reduce computing resources for vehicle analysis. To achieve this goal the adhesive bond line and adherends are modelled by a relatively ‘small’ number of shell elements to replace the usual solid element mesh for a reliable analysis. Previous work in Part 1 has provided the necessary background information to develop and verify the new finite element analysis that reduces the solution runtime by a factor of 1000. Although a joint’s non-linear stiffness is reliably simulated to failure load, it is recognised by the authors that the coarse shell mesh cannot provide accurate peak stresses or peak strains for the successful application of a numerical failure criterion. Given that the new modelling methodology is very quick to apply to existing shell models of vehicle bodies, it is recommended for use by the stress analyst who requires, say at the preliminary design stage, whole vehicle stiffness performance in a significantly reduced timeframe.

Energy transfers in shell models for magnetohydrodynamics turbulence

A systematic procedure to derive shell models for magnetohydrodynamic turbulence is proposed. It takes into account the conservation of ideal quadratic invariants such as the total energy, the cross helicity, and the magnetic helicity, as well as the conservation of the magnetic energy by the advection term in the induction equation. This approach also leads to simple expressions for the energy exchanges as well as to unambiguous definitions for the energy fluxes. When applied to the existing shell models with nonlinear interactions limited to the nearest-neighbor shells, this procedure reproduces well-known models but suggests a reinterpretation of the energy fluxes.

Modeling of nonlinear viscous stress in encapsulating shells of lipid-coated contrast agent microbubbles

A general theoretical approach to the development of zero-thickness encapsulation models for contrast microbubbles is proposed. The approach describes a procedure that allows one to recast available rheological laws from the bulk form to a surface form which is used in a modified Rayleigh–Plesset equation governing the radial dynamics of a contrast microbubble. By the use of the proposed procedure, the testing of different rheological laws for encapsulation can be carried out. Challenges of existing shell models for lipid-encapsulated microbubbles, such as the dependence of shell parameters on the initial bubble radius and the “compression-only” behavior, are discussed. Analysis of the rheological behavior of lipid encapsulation is made by using experimental radius-time curves for lipid-coated microbubbles with radii in the range 1.2–2.5 μm. The curves were acquired for a research phospholipid-coated contrast agent insonified with a 20 cycle, 3.0 MHz, 100 kPa acoustic pulse. The fitting of the experimental data by a model which treats the shell as a viscoelastic solid gives the values of the shell surface viscosity increasing from 0.30 × 10 −8 kg/s to 2.63 × 10 −8 kg/s for the range of bubble radii, indicated above. The shell surface elastic modulus increases from 0.054 N/m to 0.37 N/m. It is proposed that this increase may be a result of the lipid coating possessing the properties of both a shear-thinning and a strain-softening material. We hypothesize that these complicated rheological properties do not allow the existing shell models to satisfactorily describe the dynamics of lipid encapsulation. In the existing shell models, the viscous and the elastic shell terms have the linear form which assumes that the viscous and the elastic stresses acting inside the lipid shell are proportional to the shell shear rate and the shell strain, respectively, with constant coefficients of proportionality. The analysis performed in the present paper suggests that a more general, nonlinear theory may be more appropriate. It is shown that the use of the nonlinear theory for shell viscosity allows one to model the “compression-only” behavior. As an example, the results of the simulation for a 2.03 μm radius bubble insonified with a 6 cycle, 1.8 MHz, 100 kPa acoustic pulse are given. These parameters correspond to the acoustic conditions under which the “compression-only” behavior was observed by de Jong et al. [Ultrasound Med. Biol. 33 (2007) 653–656]. It is also shown that the use of the Cross law for the modeling of the shear-thinning behavior of shell viscosity reduces the variance of experimentally estimated values of the shell viscosity and its dependence on the initial bubble radius.

Resonance frequencies of lipid-shelled microbubbles in the regime of nonlinear oscillations

Knowledge of resonant frequencies of contrast microbubbles is important for the optimization of ultrasound contrast imaging and therapeutic techniques. To date, however, there are estimates of resonance frequencies of contrast microbubbles only for the regime of linear oscillation. The present paper proposes an approach for evaluating resonance frequencies of contrast agent microbubbles in the regime of nonlinear oscillation. The approach is based on the calculation of the time-averaged oscillation power of the radial bubble oscillation. The proposed procedure was verified for free bubbles in the frequency range 1–4 MHz and then applied to lipid-shelled microbubbles insonified with a single 20-cycle acoustic pulse at two values of the acoustic pressure amplitude, 100 kPa and 200 kPa, and at four frequencies: 1.5, 2.0, 2.5, and 3.0 MHz. It is shown that, as the acoustic pressure amplitude is increased, the resonance frequency of a lipid-shelled microbubble tends to decrease in comparison with its linear resonance frequency. Analysis of existing shell models reveals that models that treat the lipid shell as a linear viscoelastic solid appear may be challenged to provide the observed tendency in the behavior of the resonance frequency at increasing acoustic pressure. The conclusion is drawn that the further development of shell models could be improved by the consideration of nonlinear rheological laws.

Transition probabilities and isospin structure in theN=Znucleus46V

Picosecond lifetimes in ${}^{46}\mathrm{V}$ and ${}^{46}\mathrm{Ti}$ were determined using the recoil distance Doppler-shift technique with a plunger device coupled to a setup of five HP Ge detectors enhanced by one EUROBALL CLUSTER detector. The experiment was carried out using the ${}^{32}\mathrm{S}{(}^{16}\mathrm{O},pn)$ reaction at 38 MeV at the Cologne FN TANDEM facility. The differential decay curve method in coincidence mode was employed to derive lifetimes for five excited states in each nucleus. The resulting $E2$ transition probabilities are compared with existing shell model calculations and a comparison within the $T=1$ isospin triplet is given. Absolute $E1$ strengths of the ${2}^{\ensuremath{-}}$ decay in ${}^{46}\mathrm{V}$ are discussed.

Beam model for calculating magnetostriction strains in thin films and multilayers

A standard technique to measure the magnetostriction strain in thin films involves measurement of the end deflection or slope of cantilever beams using optical deflectometry or capacitive methods. This article presents a general beam model for inferring magnetostriction strain from the end deflection or slope data. This model greatly extends the range of applicability over existing shell models, allowing for inference of magnetostriction strains for practical film/substrate thickness ratios that are important in microelectromechanical systems (MEMS) and bio-microelectromechanical systems (bio-MEMS). If the properties of individual layers are known, the beam theory can be used to design multilayer MEMS or bio-MEMs beams over a full range of thickness ratios.

An engineering method for constraint based fracture assessment of welded structural components with surface cracks

In this study it has been shown that accurate descriptions of crack-tip stress-fields in surface cracked welded plates can be obtained without large 3D FEA models. When a fracture mechanics FE analysis is required in a large construction, existing shell models can be used in combination with a plane strain submodel. The 2D plane strain model is driven by displacements from the global shell model. This technique has been used to simulate crack-tip stress-fields in a surface cracked plate. The crack-tip stress fields are characterised with the J-integral and the constraint parameter, Q. The crack in the global shell model was simulated with line-spring elements. The global behaviour as well as the crack-tip stress-fields of the plane strain submodel have been compared to a 3D solid model. Initially, the crack-tip stress-fields in the plane strain model and the 3D model with surface crack were compared, using the same in-plane mesh and element type. It was found that when first order elements were used, the constraint was higher in 3D than in plane strain. For second order elements, however, the trend was the opposite. By using a correction factor for the load, the load vs. J behaviour and the crack-tip stress-fields of a surface cracked plate can be predicted from a shell analysis with line-spring elements and a plane strain model. Accurate predictions of J and Q were obtained using the shell + submodel technique for homogeneous material and for a weldment with fusion line crack. The shell + submodelling technique was used to assess brittle fracture in two steel weldments with a surface crack using the RKR failure criterion by Ritchie et al. [16]. For the investigated case, the toughness requirements could be relaxed significantly based on the two parameter analysis compared to conventional fracture mechanics analyses.

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Differential cross sections and analyzing powers for the (p\ensuremath{\rightarrow},n) reaction on carbon isotopes have been measured for angles up to ${\ensuremath{\theta}}_{\mathrm{lab}=50}$\ifmmode^\circ\else\textdegree\fi{} using 160 MeV protons. The angular distributions for the stronger transitions are compared with the results of distorted-wave impulse approximation calculations which utilize transition densities from existing shell model calculations. The total observed Gamow-Teller strength is also compared with the shell model predictions. In addition, the shapes of these angular distributions are discussed emphasizing decomposition into longitudinal, transverse, and non-normal-parity-transfer components. Some comparisons of the present (p,n) data with corresponding (p,p') data and with other relevant (p,n) data are also made.

Electromagnetic and angular momentum properties of states in25Mg below 6.05 MeV in excitation

The reaction 22Ne ( alpha ,n)25Mg was used to populate levels in 25Mg at alpha -particle energies of 8.00 and 9.15 MeV. The analysis of angular distributions and linear polarizations gave unique spin and parity assignments of 1/2-, 9/2+, 1/2-, 13/2+, 11/2+, 9/2+ and 7/2+ to the levels at 4277, 4712, 5116, 5461, 5533, 5971 and 5977 keV and strongly favoured values of 11/2- and 11/2+ for the levels at 5793 and 6041 keV respectively. Also, gamma -ray multipole mixing ratios were accurately determined for many transitions from states below 6.05 MeV in excitation. The experimental measurements are discussed in terms of rotational model structure built on both single particle and 2 particle-1 hole excitations. The properties of the positive parity states are compared with predictions of existing shell model calculations, and are found to be well reproduced by a model calculation which used the full 2s-1d space.

Two particle intrinsic excitations in 22Ne and 26Mg

A basis of two particle intrinsic states for 22Ne and 26Mg is defined in terms of the Hartree-Fock solutions for 20Ne and 24Mg. Mixing between the different intrinsic states is estimated from a deformed shell model. The model proceeds to describe the lowest 12 positive parity states in 22Ne and the lowest 15 in 26Mg. Spin, parity and K-quantum number assignments are proposed. These results are also compared with the existing shell model and projection model interpretations of 22Ne and 26Mg.