Multilayer Shell Model Research Articles

Multi-Layered Shell Model and Seismic Limit States of a Containment Building in Nuclear Power Plant Considering Deterioration and Voids

Multi-Layered Shell Model and Seismic Limit States of a Containment Building in Nuclear Power Plant Considering Deterioration and Voids

Static stability test and simulation of a large-scale modular carbon fiber reinforced polymer wheel-spoke-shaped stiffening ring subjected to multi-point radial loading

To enhance the hoop stiffness of the rigid-flexible integrated airship, a new large-scale wheel-spoke-shaped stiffening ring composed of modular carbon fiber reinforced polymer (CFRP) standard trusses was designed in this work. Particularly, by using the modular assembly technology, the CFRP stiffening ring with a diameter of 40.0 m was integrated assembly, which verified the feasibility of the proposed structural design method. Based on the applied uniformly distributed load form of the CFRP wheel-spoke-shaped stiffening ring during the flight of the rigid-flexible integrated airship, the standard truss module was subjected to a multi-point loading static stability test through a self-developed loading device, while the in-plane buckling failure position and buckling load of the CFRP wheel-spoke-shaped stiffening ring were also determined. Based on the refined multi-layered shell model, the combined eigenmode imperfection method was used for the nonlinear buckling analysis of the CFRP truss module. The buckling failure mode and the buckling load obtained from the simulation results were in good agreement with the test results. The proposed and verified large-scale modular CFRP wheel-spoke-shaped stiffening ring improved the hoop stiffness of the rigid-flexible integrated airship and achieved structural weight reduction and the design goal of the large-scale structure. The refined multi-layered shell model based on the combined eigenmode imperfection method has an important application value and guiding significance for investigating the buckling property of CFRP wheel-spoke-shaped stiffening rings, which provides valuable technical support for the structural design of rigid-flexible integrated airships.

Precise mix-design of Ultra-High Performance Concrete (UHPC) based on physicochemical packing method: From the perspective of cement hydration

• A physicochemical packing method to optimize the design of UHPC is proposed. • A new equivalent particle size distribution of hydrated cement is calculated. • The macro characteristics of the newly developed UHPC is evaluated. • The hydration kinetics of the newly developed UHPC is evaluated. • The microstructure development of the newly developed UHPC is evaluated. It is widely accepted that Ultra-High Performance Concrete (UHPC) could be designed by the employment of Modified Andreasen and Andersen (MAA) particle packing model. However, the traditional MAA model only takes into account that dry particles reach the dense packing status under physical conditions, without considering the chemical hydration of wet cement particles. To solve this problem, this study adopts a physicochemical packing method to optimize the mix-design of UHPC through establishing a new equivalent particle size distribution of hydrated cement by applying a multilayer spherical shell model. Based on this, the mix proportion of UHPC is redesigned and the properties of the optimized UHPC are evaluated afterwards. The results show that the optimized mix-design leads to higher particle packing density of UHPC, thereby improving the durability on the premise of guaranteeing the workability and mechanical properties. Meanwhile, the optimized mix-design can also achieve denser micro structures of UHPC matrix, which provides a valuable reference to design UHPC more scientifically and reasonably.

An innovative multi-layer shell model for in-pile thermo-mechanical behavior analysis of plate-type fuel assemblies

In this study, an innovative large-deformation multi-layer shell model is developed. In order to improve the efficiency of simulating the thermo-mechanical coupling behavior in complex plate-type fuel assemblies, the fuel plates are simulated by 2D shell element, with the irradiation swelling and creep effects involved. The specific theoretical frame for the kinematic models and three-dimensional constitutive models is presented, together with the generalized force update algorithm. The application of the developed shell model in the thermal–mechanical behavior simulation of a monolithic U-Mo/Al fuel assembly indicates that (1) the out-of-plane displacements of the side plates can be precisely calculated, with the calculation time ∼92% shorter than that of a full 3D simulation of 308-day irradiation behavior; (2) the out-of-plane displacements of the fuel plates excluding the peripheral ones can also be well obtained, with small relative deviations to the full 3D simulation results; (3) using 3D solid models for the peripheral fuel plates, a fuel assembly finite element (FE) model with 2D&3D geometric models for the fuel plates is proposed with a total computation time decrease of 64%, and the precise of deformation simulation results can be improved comprehensively. This research provides important theoretical models and algorithms for the irradiation-induced deformation analysis of complex plate-type fuel assemblies.

Generation of fast neutron removal cross sections using a multi-layered spherical shell model

A new method is explored for estimating the fast or fission neutron removal cross sections in single-element or multi-element media. A spherical Monte Carlo model conforming to the removal theory for fission neutrons was used. The MCNP5 code coupled with ENDF/B-VII.0 library was used to simulate the transport of U-235 fission neutrons within the model. Several removal cross sections were generated for abundant elements in construction and nuclear materials including H, Li, Be, B, C, O, F, Al, Cl, Fe, Ni, Cu, W, Pb, Bi, and U, and multi-element materials such as several compounds and composites. Validations were made using experimentally produced fast neutron removal cross section values, and those given by Phy-X/PSD and MRCsC software, and an empirical method. The comparison of the Monte Carlo generated removal cross sections showed good agreements with experimental values and those by theoretical methods. For multi-element media, the Monte Carlo generated removal cross sections were found to best fit the experimental values, in comparison with those produced by other available methods. Furthermore, a comparison of the thermal fluence trends obtained between the Monte Carlo simulations and several neutron removal experiments resulted in good agreement. The proposed method is highly useful in the generation of ENDF/B based removal cross sections, for point-kernel applications and fast neutron shielding materials comparisons.

A Short Review on Numerical Modelling Approaches for Seismic Evaluation Performance of Nuclear Power Plant Structures

Nuclear power plant (NPP) structures play a crucial role in protecting the safety of the whole plant. Overall, NPP structures have complex shapes and large dimensions. Therefore, the decision of an appropriate finite element model for seismic response analysis is important. This study presents a brief review of various numerical modelling approaches for seismic evaluation performance of NPP structures. Different conventional models, i.e. lumped-mass stick model (LMSM), full three-dimensional finite element model (3D FEM), elastic solid element model (ESM), and multi-layer shell model (MLSM), which have been applied in modelling nuclear structures, are introduced. Also, the advantages and drawbacks of those models are analysed. Furthermore, a new model namely, beam-truss model (BTM), which is recently proposed, is highlighted. It reveals that LMSM is the most simplified approach for structural modelling of NPP structures. However, it is normally used for linear analyses and not able to simulate the local behaviours and vertical responses of the complex NPP structures. Even though 3D FEM is the most sufficient method for nonlinear seismic response analyses, this approach is very time-consuming and costly computation. MLSM and BTM are recommended as practical and efficient models for nonlinear analyses of NPP structures.

Efficiency of various structural modeling schemes on evaluating seismic performance and fragility of APR1400 containment building

The purpose of this study is to investigate the efficiency of various structural modeling schemes for evaluating seismic performances and fragility of the reactor containment building (RCB) structure in the advanced power reactor 1400 (APR1400) nuclear power plant (NPP). Four structural modeling schemes, i.e. lumped-mass stick model (LMSM), solid-based finite element model (Solid FEM), multi-layer shell model (MLSM), and beam-truss model (BTM), are developed to simulate the seismic behaviors of the containment structure. A full three-dimensional finite element model (full 3D FEM) is additionally constructed to verify the previous numerical models. A set of input ground motions with response spectra matching to the US NRC 1.60 design spectrum is generated to perform linear and nonlinear time-history analyses. Floor response spectra (FRS) and floor displacements are obtained at the different elevations of the structure since they are critical outputs for evaluating the seismic vulnerability of RCB and secondary components. The results show that the difference in seismic responses between linear and nonlinear analyses gets larger as an earthquake intensity increases. It is observed that the linear analysis underestimates floor displacements while it overestimates floor accelerations. Moreover, a systematic assessment of the capability and efficiency of each structural model is presented thoroughly. MLSM can be an alternative approach to a full 3D FEM, which is complicated in modeling and extremely time-consuming in dynamic analyses. Specifically, BTM is recommended as the optimal model for evaluating the nonlinear seismic performance of NPP structures. Thereafter, linear and nonlinear BTM are employed in a series of time-history analyses to develop fragility curves of RCB for different damage states. It is shown that the linear analysis underestimates the probability of damage of RCB at a given earthquake intensity when compared to the nonlinear analysis. The nonlinear analysis approach is highly suggested for assessing the vulnerability of NPP structures.

Experimental and numerical studies on failure and energy absorption of composite thin-walled square tubes under quasi-static compression loading

Abstract To analysis the failure and energy absorption of carbon fiber reinforced polymer (CFRP) thin-walled square tube, the quasi-static axial compression loading tests are conducted for [±45]3s square tube, and the square tube after test is scanned to further investigate the failure mechanism. Three different finite element models, i.e. single-layer shell model, multi-layer shell model and stacked shell mode, are developed by using the Puck 2000 matrix failure criterion and Yamada Sun fiber failure criterion, and three models are verified and compared according to the experimental energy absorption metrics. The experimental and simulation results show that the failure mode of [±45]3s square tube is the local buckling failure mode, and the energy are absorbed mainly by intralaminar and interlaminar delamination, fiber elastic deformation, fiber debonding and fracture, matrix deformation cracking and longitudinal crack propagation. Three different finite element models can reproduce the collapse behaviours of [±45]3s square tube to some extent, but the stacked shell model can better reproduce the failure mode, and the difference of specific energy absorption (SEA) is minimum, which shows the numerical simulation results are in better agreement with the test results.

Hysteretic performance of reinforced concrete cavity shear walls

AbstractCavity shear wall, as a kind of precast wall with internal cavity, is divided into strong and weak areas. It is hoped that the structure stiffness, lateral load capacity, and ductility could be better matched in the cavity shear wall. Therefore, the quasi‐static tests were carried out to study the hysteretic performance of reinforced concrete cavity shear walls. Test results indicated that the regular squat shear wall's failure mode is dominated by shear and the setting of the cavity can effectively reduce the stiffness and lateral load capacity. The cavity makes the development and distribution of cracks in the sidewalls more uniform and finer, which is more conducive to energy dissipation. The rational match of the stiffness, lateral load capacity, and ductility can be achieved by arranging reasonable cavity in the shear wall. The purpose of improving the ductility and optimizing the failure mode of shear wall can also be achieved by relaxing the constraints of the bottom of the shear wall or setting several cavities. In addition, the multilayer shell model was adopted to simulate the specimens and parametric analysis was also carried out. The verification shows that the numerical model can predict the lateral responses of the cavity shear wall with reasonable accuracy. The parametric analysis shows that the initial stiffness and peak load of the shear wall would be reduced if there is cavity or horizontal seam at the bottom. However, the ductility could be improved if the cavity or horizontal seam is arranged in a reasonable combination. The influence of cavity and horizontal seam on the strain arch leads to the change of lateral capacity and response.

Isogeometric analysis for simulation of progressive damage in composite laminates

The increasing popularity of composite materials in aerospace applications is creating the need for a new class of predictive methods and tools for the simulation of progressive damage in laminated fiber-reinforced composite structures. The unique challenges associated with modeling damage in these structures may be addressed by means of thin-shell formulations which are naturally developed in the context of Isogeometric Analysis. In this paper, we further validate our recently developed Isogeometric Analysis-based multi-layer shell model for progressive damage simulations using experimental data for low-velocity impact on a 24-ply flat panel. The validation includes a careful comparison of delamination and matrix damage patterns predicted by the Isogeometric Analysis-based simulation and those obtained from post-impact non-destructive evaluation of the damaged coupon. The Isogeometric Analysis-based formulation is then deployed on two additional examples: a stiffened panel and a full-scale UAV wing, to demonstrate its suitability for, and ease of application to, typical aerospace composite structures.

Global seismic performance of a new precast CFST column to RC beam braced frame: Shake table test and numerical study

A new type of precast CFST column to RC beam braced frame is proposed in this paper. A series of shake table tests were conducted to excite a one-third scale six-story model for investigating the global seismic performance of this type of structure against earthquake actions. Particular emphasis was given to its dynamic property, global seismic responses and failure path. Correspondingly, a numerical model built on the basis of fiberbeam- element model, multi-layer shell model and element-deactivation method was developed to simulate the seismic performance of the prototype structure. Numerical results were compared with the measured values from shake table tests to verify the validity and reliability of the numerical model. The results demonstrated that the proposed novel precast CFST column to RC beam braced frame performs excellently under strong earthquake excitations; the "strong CFST column-weak RC beam" and "strong connection-weak member" anti-seismic design principles can be easily achieved; the maximum deflections of precast CFSTC-RCB braced frame satisfied the deflection limitations proposed in national code; the numerical model can properly simulate the dynamic property and responses of the precast CFSTC-RCB braced frame that are highly concerned in engineering practice.

Estimating Brown-Korringa constants for fluid substitution in multimineralic rocks

Brown and Korringa extended Gassmann’s equations for fluid substitution in rocks to allow for arbitrarily mixed mineralogy. This extension was accomplished by adding just one additional constant—replacing the mineral bulk modulus with two less intuitive constants. Even though virtually all rocks have mixed mineralogy, the Brown and Korringa equations are seldom used because values for the constants are unknown. We estimate plausible values for the Brown-Korringa constants, based on effective medium models. The self-consistent formulation is used to describe a rock whose mineral and pore phases are randomly distributed ellipsoids—a plausible representation of randomly mixed mineral grains, as with dispersed clay in sandstone. Using the self-consistent model, the two constants are predicted to be nearly identical, justifying the use of an average mineral modulus in Gassmann’s equations. For small contrasts in mineral stiffness, the Brown-Korringa constants are approximately equal to the Voigt-Reuss-Hill average of the individual mineral bulk moduli. In a second approach, a multilayered spherical shell model is used to describe a rock where a particular solid phase preferentially coats grains or lines pores. In this case, the constants can differ substantially from each other, demonstrating the need for the Brown-Korringa equation. A third model represents weak pore-lining or pore-filling clay within an arbitrary pore geometry. The clay-fluid mix can be replaced exactly with an average fluid or “mud.” When the nonclay minerals have similar moduli, then the replacement of the clay-fluid mix causes the Brown-Korringa equation to revert to Gassmann’s equation.

Pitfalls in the finite element modeling of the buckling of sandwich shells of revolution

The objective of this work is to answer the following question: Is a multilayer shell model always appropriate for the prediction of the buckling of a thin structure? In order to do that, we chose to analyze the buckling of a three-layer cylindrical tube in uniform axial compression. We compared three approaches for the calculation of the theoretical buckling load: a fully analytical formula, a Fourier series buckling model of a multilayer axisymmetric shell and a calculation based on a mechanical mesh of the axisymmetric medium of the middle layer. This analysis shows that two buckling modes are in competition: a global beam mode and a local skin buckling mode (wrinkling) which develops when the stiffness of the middle layer is quite small. The critical loads can be estimated analytically for both types of modes, leading to a critical length under which the cylinder fails by skin buckling; otherwise, it fails in beam mode. Then the problem was solved by finite elements using two models: first, a multilayer axisymmetric shell model, then a model with two types of elements in each section (an 8-node axisymmetric element for the middle layer, and axisymmetric shell elements for the two skins). We showed that both models can predict the beam mode, but only the latter was capable of predicting the skin buckling mode. Similar results are proposed for the prediction of the buckling of a three-layer cone under internal pressure. We also compared the formulations for geometrically nonlinear problems with nonlinear materials and showed that in such problems the nonlinearities cause even more pronounced differences. This clearly raises the question of the choice of the type of finite element for the prediction of buckling in a multilayer structure in which some layers have only a small relative stiffness. The analytical solution and the analysis of the nonlinear response in the case of the cone confirm that the poor prediction of the skin buckling mode is due to a failure to account for the flexibility perpendicular to the mean surface.

Collapse simulation of reinforced concrete high‐rise building induced by extreme earthquakes

SUMMARYCollapse resistance of high‐rise buildings has become a research focus because of the frequent occurrence of strong earthquakes and terrorist attacks in recent years. Research development has demonstrated that numerical simulation is becoming one of the most powerful tools for collapse analysis in addition to the conventional laboratory model tests and post‐earthquake investigations. In this paper, a finite element method based numerical model encompassing fiber‐beam element model, multilayer shell model, and elemental deactivation technique is proposed to predict the collapse process of high‐rise buildings subjected to extreme earthquake. The potential collapse processes are simulated for a simple 10‐story RC frame and two existing RC high‐rise buildings of 18‐story and 20‐story frame–core tube systems. The influences of different failure criteria used are discussed in some detail. The analysis results indicate that the proposed numerical model is capable of simulating the collapse process of existing high‐rise buildings by identifying potentially weak components of the structure that may induce collapse. The study outcome will be beneficial to aid further development of optimal design philosophy. Copyright © 2012 John Wiley & Sons, Ltd.

Extension of the Strain Energy Updating Technique to a Multilayered Shell Model with Adaptive Displacements and Fixed DOF

AbstractThe strain energy updating technique (SEUPT) is extended to a new zigzag shell model with a hierarchical piecewise representation of displacements, which can adapt to a variation of solutions across the thickness. This model has the capability of being refined across the thickness without increasing the number of functional degrees of freedom (DOF) (the traditional midplane displacements and shear rotations). The purpose of the SEUPT is to improve the accuracy of standard finite elements based on equivalent single-layer models with transverse shear deformations up to the level of the zigzag model. The strain and kinetic energies and the work of external forces are updated through a postprocessing iterative procedure by starting from a local interpolation of the results of the finite-element analysis. Because no derivatives of in-plane stresses are involved, updating is fast. The current version of the SEUPT obtains accurate predictions of interlaminar stresses from constitutive equations; thus, it...

Multilayered shell model with variable representation of displacements across the thickness

A multilayered zig-zag shell model is developed; it has a hierarchic representation of displacements across the thickness that a priori fulfils the interfacial stress contact conditions on interlaminar shear and normal stresses. Like for classical models, the functional d.o.f. are the mid-plane displacements and the shear rotations. Characteristic feature, the representation can vary from point to point across the thickness, in order to adapt to the variation of solutions. The coefficients of the higher-order terms are determined as functions of the d.o.f. by enforcing equilibrium conditions at discrete points across the thickness. The Lame’s coefficients are expanded up to the second order. As shown by the numerical tests, it accurately predicts the stress fields of thick laminated and sandwich shells with abruptly changing material properties with a lower overall processing time than for the fixed representation, since post-processing is unnecessary.

Verification, validation and variability for the vibration study of a car windscreen modeled by finite elements

The main purpose of this paper is to investigate verification, validation and variability issues applied to an industrial component: a car windscreen. The windscreen is a sandwich structure whose stacking sequence contains five layers. The two external thick layers are made of glass, while the three thin intermediate layers are made of appropriate polymers. In this framework, two main objectives are identified for this paper. The paper focuses the attention on the study of the dynamics of an acoustic windscreen under free–free and real boundary conditions. An application of the verification and validation methodology is presented to assess the capability of finite element models to predict the natural frequencies of the acoustic windscreen, in presence of intra variability due to temperature variation. Indeed, intra variability of glue and polymers’ elastic properties leads to intra variability of the dynamic behaviour of the windscreen. Experimental campaigns, in free–free and real boundary conditions, have been performed in a climatic chamber. The effect of the temperature changes on the windscreen vibration behaviour has been evaluated and the component experimental intra variability estimated. A numerical study has been performed as well. Three different numerical models have been considered: a simplified model in free or clamped conditions, a trimmed body model. The verification stage, including convergence studies, concludes that the multilayer shell model approach is valid at low temperature, when polymers are relatively stiff. On the contrary, at higher temperature, polymers are very flexible and shell models lead to significant errors due to considerable transverse shear effects. Finally, the main result is that a solid model must be used for the windscreen to correctly reproduce the physics at different temperatures. A validation stage, involving numerical and experimental results, has been performed to evaluate the predictive capability of the developed numerical models. Validation metrics, which assess the mean value and the variability level of the frequencies, are proposed. The finite element models lead to very satisfactory results for the mean values of the frequencies. The general trends of the experimentally observed intra variability are also well reproduced. Nevertheless, further investigations are necessary to improve the predictive capability of the numerical model that currently underestimates the experimental intra variability. This discrepancy is essentially due to the complex non-linear behaviour of polymers.

Influence of Multilayer vdW Interaction on Torsional Buckling of Multi-walled Carbon Nanotube under Thermal Fields

Torsional buckling of multi-walled carbon nanotube embedded in an elastic matrix subjected to thermal fields is studied using a continuum-based multilayered shell model. The model takes into account the multilayer van der Waals (vdW) interaction between any two layers of the MWCNT as radius dependent function. The elastic matrix surrounding the outermost tube is modeled as Pasternak foundation to account for not only the normal stresses, but also the shear stress between the outermost tube and the surrounding medium. The effect of inner tube radius, number of tubes, stiffness of surrounding elastic medium and temperature change on the critical torsional load is examined. Numerical results show that the vdW interaction will lead to a higher critical torsional load and at room or lower temperature the critical torsional load for infinitesimal buckling of a multi-walled carbon nanotube increases as the value of temperature change increases, while at a temperature higher than room temperature the critical torsional load for infinitesimal buckling of a multi-walled carbon nanotube decreases as the value of temperature change increases.

Torsional buckling of carbon nanopeapods

Torsional buckling of carbon nanopeapods (carbon nanotubes filled with fullerenes) is studied using a continuum-based multi-layered shell model. The model takes into account non-bonded van der Waals interactions between nested fullerenes and the innermost layer of host nanotube. For nanopeapods with linearly arranged nested fullerenes, equivalent pressure distribution is proposed to model these interactions. Deriving explicit equations governing the torsional stability, it is concluded that the critical torsional load of a carbon nanopeapod is less than that of a carbon nanotube under otherwise identical geometric and mechanical conditions. Performing numerical calculations, it is also shown that increasing the number of layers of the host carbon nanotube decreases the weakening effect of encapsulated fullerenes on torsional stability of the nanopeapod.

Eccentric compression stability of multi-walled carbon nanotubes embedded in an elastic matrix

This paper reports the results of an investigation on the eccentric compression stability of multi-walled carbon nanotubes embedded in an elastic matrix. Based on continuum modeling, a multilayer shell model is presented for the eccentric compression buckling of multi-walled carbon nanotubes embedded in an elastic matrix, in which the effect of van der Waals forces between two adjacent tubes is taken into account. The critical bending moment and the eccentric compression mode for three types of multi-walled carbon nanotubes with different layer numbers and ratios of radius to thickness are calculated. Results obtained show that the eccentric compression buckling mode corresponding the critical bending moment is unique, and is different from the purely axial compression buckling of an individual multi-walled carbon nanotube. For different types of multi-walled carbon nanotubes, the effect of matrix stiffness on the critical bending moment of multi-walled carbon nanotubes under eccentric compression loading is obviously different, and is dependent on the innermost radius and layer numbers of the multi-walled carbon nanotubes. The critical bending stress exerted on the center tubes of nearly solid multi-walled carbon nanotubes does not change as the ratio of the axial compression loading to the bending membrane force increases. The new features and meaningful numerical results in this paper are helpful for the application and the design of nanostructures in which multi-walled carbon nanotubes act as basic elements.