3D Shell Model Research Articles

Research on topology optimization of carbon fiber reinforced composite electric vehicle helmet based on deep learning

Abstract To study the topology optimization of carbon fiber composite helmets, a method of optimizing the three-dimensional (hereinafter referred to as 3D) model based on a deep learning network after dimensionality reduction is proposed. In this method, the 3D shell model is expanded and tiled into two-dimensional (hereinafter referred to as 2D) grids based on the one-step inverse forming method. The variable density method (Isotropic Material Penalty Density method) is used to collect the data set required for deep learning training, and the U-Net neural network is built to complete the training. To obtain the input tensor of the neural network, the mechanical analysis of the 3D model is carried out, and the physical properties are imported into the network for learning. In this way, the 2D optimization results of the helmet model are obtained and then reflected in the 3D model according to the unit topology relationship to obtain the final optimization results. Then, the ordinary helmet and the optimized helmet are simulated and compared under the same quality to test their mechanical properties. The results show that the stiffness performance and energy absorption effect of the optimized helmet are stronger when the quality of the two helmets is the same.

Reconciling Mars InSight Results, Geoid, and Melt Evolution With 3D Spherical Models of Convection

AbstractWe investigate the geodynamic and melting history of Mars using 3D spherical shell models of mantle convection, constrained by the recent InSight mission results. The Martian mantle must have produced sufficient melt to emplace the Tharsis rise by the end of the Noachian–requiring on the order of 1–3 × 109 km3 of melt after accounting for limited (∼10%) melt extraction. Thereafter, melting declined; however, abundant evidence for limited geologically recent volcanism necessitates some present‐day melt even in the cool mantle inferred from InSight data. We test models with two mantle activation energies and a range of crustal Heat Producing Element (HPE) enrichment factors and initial core‐mantle boundary temperatures. We also test the effect of including a hemispheric (spherical harmonic degree‐1) step in lithospheric thickness to model the Martian dichotomy. We find that a higher activation energy (350 kJ mol−1) rheology produces present‐day geotherms consistent with InSight results, and crustal HPE enrichment factors of 5–10‐times produce localized melting near or up to present‐day. The 10‐times crustal HPE enrichment is consistent with both InSight and geochemical results and also produces present‐day geoid power spectra consistent with Mars. However, calculations that match the present‐day geoid power spectra require more than 60% melt extraction to produce the Tharsis swell. The addition of a degree‐1 hemispheric dichotomy, as an equatorial step in lithospheric thickness, does not significantly improve upon melt production or the geoid.

An assessment of PWR fuel assembly spacer grid strength by FEM models

Since Fukushima accident, integrity of fuel assembly for seismic load became very important. This study assesses the structural integrity of mid spacer grid (SG) of PLUS7 fuel assembly (FA) which is the weakest part of fuel assembly structural components. Spacer grid FEM models were developed by 3D solid element and 3D shell element. From the FEM analysis, it was found that the structural strength for normal direction was much larger than for shear direction. At core outlet, the normal stiffness was estimated to 36kN/mm for 3D solid model and 33kN/mm for 3D shell model, and the shear stiffness was estimated to 49 N/mm for 3D solid model and 75 N/mm for 3D shell model. From this result normal stiffness is a lot bigger than shear stiffness, and spacer grid structure is more vulnerable against shear loads. It is recommended to do shear test or analysis of fuel assembly in the development stage.

Development of modular and reusable AI models for fast predicting fire behaviour of steel columns in structural systems

It is important to model the local failure of structural members as well as the global responses of a structural system when it is exposed to fire. The local failure of columns such as buckling requires high-resolution models, which could be not used for modelling a structural system for its computational cost. Inspired by the hybrid simulation technique, this paper aims to develop modular AI models as a first attempt to predict the local performance of a specific steel column exposed to fires and to enable the future communication with structural system model. Two kinds of machine learning methods namely artificial neural network (ANN) and support vector regression (SVR) are utilized to train AI models based on a large numerical dataset extended from a 3D detailed shell model of columns after validation against fire test results. The excellent prediction performance of AI models is shown regarding the mean squared error (MSE), mean absolute error (MAE), coefficient of the variation of the root mean square error (cvRMSE), variance accounting for (VAL) and coefficient of determination (R2). Moreover, the capability of AI models is demonstrated in predicting fire behaviour of columns in untrained steady heating and transient heating scenarios. A further demonstration is performed within a plane-frame structure simulated with a hybrid-scale model and considering standard fire heating on columns, which shows great potential of the AI models towards further implementation in hybrid simulation.

Visual prediction and parameter optimization of viral dynamics in the mucus milieu of the upper airway based on CFPD-HCD analysis

Background and ObjectiveRespiratory diseases caused by viruses are a major human health problem. To better control the infection and understand the pathogenesis of these diseases, this paper studied SARS-CoV-2, a novel coronavirus outbreak, as an example. MethodsBased on coupled computational fluid and particle dynamics (CFPD) and host-cell dynamics (HCD) analyses, we studied the viral dynamics in the mucus layer of the human nasal cavity-nasopharynx. To reproduce the effect of mucociliary movement on the diffusive and convective transport of viruses in the mucus layer, a 3D-shell model was constructed using CT data of the upper respiratory tract (URT) of volunteers. Considering the mucus environment, the HCD model was established by coupling the target cell-limited model with the convection-diffusion term. Parameter optimization of the HCD model is the key problem in the simulation. Therefore, this study focused on the parameter optimization of the viral dynamics model, divided the geometric model into multiple compartments, and used Monolix to perform the nonlinear mixed effects (NLME) of pharmacometrics to discuss the influence of factors such as the number of mucus layers, number of compartments, diffusion rate, and mucus flow velocity on the prediction results. ResultsThe findings showed that sufficient experimental data can be used to estimate the corresponding parameters of the HCD model. The optimized convection-diffusion case with a two-layer multi-compartment low-velocity model could accurately predict the viral dynamics. ConclusionsIts visualization process could explain the symptoms of the disease in the nose and contribute to the prevention and targeted treatment of respiratory diseases.

Hygro-Elastic Coupling in a 3D Exact Shell Model for Bending Analysis of Layered Composite Structures

In this work, a 3D fully coupled hygro-elastic model is proposed. The moisture content profile is a primary variable of the model’s displacements. This generic fully coupled 3D exact shell model allows the investigations into the consequences arising from moisture content and elastic fields in terms of stresses and deformations on different plate and shell configurations embedded in composite and laminated layers. Cylinders, plates, cylindrical and spherical shells are analyzed in the orthogonal mixed curvilinear reference system. The 3D equilibrium equations and the 3D Fick diffusion equation for spherical shells are fully coupled in a dedicated system. The main advantage of the orthogonal mixed curvilinear coordinates is related to the degeneration of the equations for spherical shells to simpler geometries thanks to basic considerations of the radii of curvature. The exponential matrix method is used to solve this fully coupled model based on partial differential equations in the thickness direction. The closed-form solution is related to simply supported sides and harmonic forms for displacements and the moisture content. The moisture content amplitudes are directly applied at the top and bottom outer faces through steady-state hypotheses. The final system is based on a set of coupled homogeneous second-order differential equations. A first-order differential equation system is obtained by redoubling the number of variables. The moisture field implications are evaluated for the static analysis of the plates and shells in terms of displacement and stress components. After preliminary validations, new benchmarks are proposed for several thickness ratios, geometrical and material data, lamination sequences and moisture values imposed at the external surfaces. In the proposed results, there is clearly accordance between the uncoupled hygro-elastic model (where the 3D Fick diffusion law is separately solved) and this new fully coupled hygro-elastic model: the differences between the investigated variables (displacements, moisture contents, stresses and strains) are always less than 0.3%. The main advantages of the 3D coupled hygro-elastic model are a more compact mathematical formulation and lower computational costs. Both effects connected with the thickness layer and the embedded materials are included in the conducted hygro-elastic analyses.

On the Springback and Load in Three-Point Air Bending of the AW-2024 Aluminium Alloy Sheet with AW-1050A Aluminium Cladding.

This article presents the results of an analysis of the bending load characteristics and the springback phenomenon occurring during three-point bending of 1.0 and 2.0 mm thick AW-2024 aluminium alloy sheets with rolled AW-1050A cladding. A new proprietary equation was proposed for determining the bending angle as a function of deflection, which takes into account the influence of the tool radius and the sheet thickness. The experimentally determined springback and bending load characteristics were compared with the results of numerical modelling using different models: Model I, a 2D model for a plane deformation state, disregarding the material properties of the clad layers; Model II, a 2D model for a plane deformation state, taking into account the material properties of the cladding layers; Model III, a 3D shell model with the Huber-von Mises isotropic plasticity condition; Model IV, a 3D shell model with the Hill anisotropic plasticity condition; and Model V, a 3D shell model with the Barlat anisotropic plasticity condition. The effectiveness of these five tested FEM models in predicting the bending load and springback characteristics was demonstrated. Model II was the most effective in predicting bending load, while Model III was the most effective in predicting the amount of springback after bending.

Investigation of the synergistic effect of platelet-rich plasma and polychromatic light on human dermal fibroblasts seeded chitosan/gelatin scaffolds for wound healing.

Conventional wound healing treatments are insufficient for chronic wounds caused by factors such as senescence of fibroblasts, reduced growth factor synthesis, and poor angiogenesis. Recently, tissue engineering approaches have been investigated to develop effective therapies. In this study, a biochemical/biophysical stimulant-based 3D system was developed for the healing of chronic wounds. In this direction, genipin crosslinked chitosan (CHT)/gelatin (GEL) scaffolds were fabricated by freeze-drying and loaded with platelet-rich plasma (PRP). The scaffolds were seeded with human dermal fibroblasts and then, polychromatic light in near infrared region (NIR) was applied to the scaffolds for activating the platelets and stimulating the fibroblasts (photoactivation, PAC). Thus, fibroblasts were stimulated both chemically and physically by PRP and light, respectively. Cell migration, proliferation, morphology, gene expressions and reactive oxygen species (ROS) activity were evaluated in-vitro. Laminin and collagen 4 expressions that are important for extracellular matrix (ECM) formation, and PDGF (Platelet-derived growth factor) and VEGF (Vascular endothelial growth factor) expressions that are important for vascularization significantly increased in the presence of both PRP and light. Besides, PRP and light improved cell migration in 3D core-and shell model synergistically. Hydrogen peroxide content decreased in both PRP and light, indicating inhibition of ROS production. It was concluded that the stimulation of platelets with light in the NIR has a great potential to use for both platelets activation and stimulation of fibroblasts. As a result, an effective therapy can be developed for chronic wounds by using scaffold-based 3D systems together with PRP and photostimulation.

3D hygro-elastic shell model for the analysis of composite and sandwich structures

The present work proposes the study of the hygrometric loading effects in the static analysis of multilayered composite and sandwich plates and shells. The employed model is based on a general exact 3D shell theory valid for one-layered and multilayered sandwich and composite plates, cylinders and cylindrical/spherical shell panels. The employed 3D equilibrium equations are developed in an orthogonal mixed curvilinear coordinate system for spherical shells in order to obtain the other simpler geometries as particular cases. A layer-wise approach is employed and equilibrium equations are solved in the thickness direction via the exponential matrix method. The partial derivatives in the in-plane directions are exactly calculated by assuming simply-supported edges and harmonic forms for the variables. The presented 3D shell model is extended to hygro-elastic cases by considering moisture content amplitudes imposed at the external surfaces of the structures in steady-state conditions. The moisture content profile through the thickness of the structures can be included in the 3D shell model using three different methodologies: it can be calculated by solving the steady-state 3D or 1D version of the Fick diffusion law, or it can be “a priori” assumed as linear through the thickness. Therefore, the developed system includes three non-homogeneous second order differential equilibrium equations that are solved after the introduction of opportune mathematical layers to consider the curvature effects through the thickness. The reduction to a first order differential equation system is obtained by redoubling the number of variables. The exponential matrix method is employed to accurately define both general and particular solutions. The implemented 3D hygro-elastic shell model is firstly validated and then it is employed with confidence for new benchmarks where the effects of thickness ratio, geometry, lamination scheme, material, thickness layer and imposed moisture content values at the external surfaces are investigated for composite and sandwich plates and shells. Showed results demonstrate the importance of an accurate developing of the elastic part of the 3D shell model combined with an appropriate evaluation of the moisture content profile through the thickness. Assumed linear moisture content profiles are correct only for thin one-layered isotropic structures, the use of the 1D Fick diffusion law allows only the correct definition of the material layer effect, the use of its 3D version allows the correct definition of both material and thickness layer effects.

Numerical Simulation for the Honeycomb Core Sandwich Panels in Bending by Homogenization Method

Nowadays, with the continuous development of science and technology, computer software has been widely applied and is increasingly popular in many fields such as the automobile, aviation, space, and shipbuilding industries. Numerical simulation is an important step in finite element analysis and product design optimization. However, it is facing challenges of reducing CAD model building time and reducing computation time. In this study, we have developed a homogenization model for the honeycomb core sandwich plate to reduce the preparation of the CAD model as well as the computational times. The homogenization consists of representing an equivalent homogenized 3D-solid obtained from the analysis calculation in-plane properties of honeycomb 3D-shell core sandwich plate. This model was implemented in the finite element software Abaqus. The simulations of tensile, in-plane shear, pure bending, and flexion tests for the case of the 3D-shell and 3D-solid models of the honeycomb core sandwich will be studied in this paper. Comparing the results obtained from the two models shows that the 3D-solid model has close results as the 3D-shell model, but the computation time is much faster. Thereby the proposed model is validated.

Combinatorial patterns of graded RhoA activation and uniform F-actin depletion promote tissue curvature.

During development, gene expression regulates cell mechanics and shape to sculpt tissues. Epithelial folding proceeds through distinct cell shape changes that occur simultaneously in different regions of a tissue. Here, using quantitative imaging in Drosophila melanogaster, we investigate how patterned cell shape changes promote tissue bending during early embryogenesis. We find that the transcription factors Twist and Snail combinatorially regulate a multicellular pattern of lateral F-actin density that differs from the previously described Myosin-2 gradient. This F-actin pattern correlates with whether cells apically constrict, stretch or maintain their shape. We show that the Myosin-2 gradient and F-actin depletion do not depend on force transmission, suggesting that transcriptional activity is required to create these patterns. The Myosin-2 gradient width results from a gradient in RhoA activation that is refined through the balance between RhoGEF2 and the RhoGAP C-GAP. Our experimental results and simulations of a 3D elastic shell model show that tuning gradient width regulates tissue curvature.

Quantitative measures and 3D shell models reveal interactions between bands and their position on growing snail shells.

The nature of shell growth in gastropods is useful because it preserves the ontogeny of shape, colour, and banding patterns, making them an ideal system for understanding how inherited variation develops, is established and maintained within a population. However, qualitative scoring of inherited shell characters means there is a lack of knowledge regarding the mechanisms that control fine variation. Here, we combine empirical measures of quantitative variation and 3D modeling of shells to understand how bands are placed and interact. By comparing five‐banded Cepaea individuals to shells lacking individual bands, we show that individual band absence has minor but significant impacts upon the position of remaining bands, implying that the locus controlling band presence/absence mainly acts after position is established. Then, we show that the shell grows at a similar rate, except for the region below the lowermost band. This demonstrates that wider bands of Cepaea are not an artifact of greater shell growth on the lower shell; they begin wider and grow at the same rate as other bands. Finally, we show that 3D models of shell shape and banding pattern, inferred from 2D photos using ShellShaper software, are congruent with empirical measures. This work therefore establishes a method that may be used for comparative studies of quantitative banding variation in snail shells, extraction of growth parameters, and morphometrics. In the future, studies that link the banding phenotype to the network of shell matrix proteins involved in biomineralization and patterning may ultimately aid in understanding the diversity of shell forms found in molluscs.

An XFEM-VCCT coupled approach for modeling mode I fatigue delamination in composite laminates under high cycle loading

In this study, virtual crack closure technique (VCCT) and extended finite element method (XFEM) are coupled to each other as XFEM-VCCT approach to simulate mode I fatigue delamination growth in composites, employing the direct cyclic method in Abaqus. Both two-dimensional plane strain and three-dimensional finite element models under force and displacement control are considered. Numerical simulation results are compared with the existed experimental test data for double cantilever beam (DCB) specimens and validated. Finally, challenges ahead of VCCT and XFEM-VCCT are discussed in detail and the appropriate method for modeling fatigue delamination growth in laminated composites under high cycle loading is suggested. It is found that simulation of the DCB fatigue delamination via the displacement control loading leads to more accurate results in comparison to the force control. VCCT was found as a suitable method for simulation of fatigue delamination growth in 2D and 3D-shell models. While XFEM-VCCT shows high accuracy and low computational time in 3D-solid finite element models. The key conclusion is that the XFEM-VCCT coupled approach is independent of time increment, whereas the time increment is more effective on the results of VCCT analysis, and it affects the run-time significantly.

An advanced shell model for the analysis of geometrical and material nonlinear shells

In this paper layered shells subjected to static loading are considered. The displacements of the Reissner–Mindlin theory are enriched by a an additional part. These so-called fluctuation displacements include warping displacements and thickness changes. They lead to additional terms for the material deformation gradient and the Green–Lagrangian strain tensor. Within a nonlinear multi-field variational formulation the weak form of the boundary value problem accounts for the equilibrium of stress resultants and couple resultants, the local equilibrium of stresses, the geometrical field equations and the constitutive equations. For the independent shell strains an ansatz with quadratic shape functions is chosen. This leads to a significant improved convergence behaviour especially for distorted meshes. Elimination of a set of parameters on element level by static condensation yields an element stiffness matrix and residual vector of a quadrilateral shell element with the usual 5 or 6 nodal degrees of freedom. The developed model yields the complicated three-dimensional stress state in layered shells for elasticity and elasto-plasticity considering geometrical nonlinearity. In comparison with fully 3D solutions present 2D shell model requires only a fractional amount of computing time.

Breaking Earth\u2019s shell into a global plate network

The initiation mechanism of Earth’s plate tectonic cooling system remains uncertain. A growing consensus suggests that multi-plate tectonics was preceded by cooling through a single-plate lithosphere, but models for how this lithosphere was first broken into plates have not converged on a mechanism or a typical early plate scale. A commonality among prior efforts is the use of continuum mechanics approximations to evaluate this solid mechanics problem. Here we use 3D spherical shell models to demonstrate a self-organized fracture mechanism analogous to thermal expansion-driven lithospheric uplift, in which globe-spanning rifting occurs as a consequence of horizontal extension. Resultant fracture spacing is a function of lithospheric thickness and rheology, wherein geometrically-regular, polygonal-shaped tessellation is an energetically favored solution because it minimizes total crack length. Therefore, warming of the early lithosphere itself—as anticipated by previous studies—should lead to failure, propagating fractures, and the conditions necessary for the onset of multi-plate tectonics.

Analysis of composite bridges with intermediate diaphragms & assessment of design guidelines

In this research effort, the generalized warping and distortional problem of straight or horizontally curved composite beams of arbitrary cross section, loading and boundary conditions is presented. An inclined plane of curvature is also considered (with respect to the horizontal plane) in order to account for a slope in the cross-section plane. Additionally, a finite stiffness of diaphragmatic plates has been introduced in the formulation in order to compare with the beam models where rigid diaphragms are considered, as usually is assumed in practice. The numerical method employed for the 1D beam formulation is based on Isogeometric tools (NURBS) while the 3D shell or solid models are developed in Finite Element commercial software for composite cross sections with diaphragms. The influence of friction on the contact interaction between the concrete and steel parts is also considered. The number of intermediate diaphragms is determined according to commonly used bridge design guidelines and the results are compared to the developed arrangements in order to assess the overall structural behavior of bridge decks. Straight or curved beam models with open or closed composite cross sections of full (1D proposed beam) or partial material-bonding (3D solid/shell models) and various arrangements of intermediate diaphragms and materials have been studied.

Beam & Shell Models for Composite Straight or Curved Bridge Decks with Intermediate Diaphragms & Assessment of Design Specifications

In this research effort, the generalized warping and distortional problem of straight or horizontally curved composite beams of arbitrary cross section, loading and boundary conditions is presented. An inclined plane of curvature is considered. Additionally, the stiffness of diaphragmatic plates has been introduced in the formulation in order to compare with the case where rigid diaphragms are assumed. Isogeometric tools (NURBS) are employed in order to obtain the results for the 1D formulation and 3D shell models are developed in FEM commercial software for composite cross sections with diaphragms. The number of intermediate diaphragms according to bridges design specifications is compared to the analyzed diaphragmatic arrangements in order to assess the overall structural behavior of bridges decks. For this purpose, examples of curved beam models with open or closed cross sections and various arrangements of diaphragms have been studied.

Mechanical assessment of hollow-circular FRP beams

The present work represents an analysis on the mechanical characterization of fiber reinforced hollow circular beams. This research is based on an analytical background along with some extensions. Since exact solution is available for structures in plane strain, such reference is considered as an initial comparison for a new approach for studying fiber- reinforced beams based on a homogenization method. The implemented method, introduce an easy application for designers who want to employ fiber reinforced beams for designing frame structures. The present approach is based on a 3D beam-frame element equivalent to a 3D shell model used as a reference for the actual composite configuration. This simple approach helps to consider the anisotropy inherited in such profiles. Sample frame structures are shown in order to demonstrate the advantages and disadvantages of the present methodology alongside the positive and negative aspects of employing fiber reinforced beams in place of the more common steel beams in civil applications.

Development of a computational fluid dynamics model for mucociliary clearance in the nasal cavity

Intranasal drug delivery has attracted significant attention because of the opportunity to deliver systemic drugs directly to the blood stream. However, the mucociliary clearance poses a challenge in gaining high efficacy of intranasal drug delivery because cilia continuously carry the mucus blanket towards the laryngeal region. To better understand mucus flow behaviour on the human nasal cavity wall, we present computational model development, and evaluation of mucus motion on a realistic nasal cavity model reconstructed from CT-scans. The model development involved two approaches based on the actual nasal cavity geometry namely: (i) unwrapped-surface model in 2D domain and (ii) 3D-shell model. Conservation equations of fluid motion were applied to the domains, where a mucus production source term was used to initiate the mucus motion. The analysis included mucus flow patterns, virtual saccharin tests and quantitative velocity magnitude analysis, which demonstrated that the 3D-shell model results provided better agreement with experimental data. The unwrapped-surface model also suffered from mesh-deformations during the unwrapping stage and this led to higher mucus velocity compared to experimental data. Therefore, the 3D-shell model was recommended for future mucus flow simulations. As a first step towards mucus motion modelling this study provides important information that accurately simulates a mucus velocity field on a human nasal cavity wall, for assessment of toxicology and efficacy of intranasal drug delivery.

GBT post-buckling analysis based on the Implicit Corotational Method

In this work, the post-buckling analysis of thin-walled beams by using the Generalized Beam Theory (GBT) is presented. To this purpose, a geometrically nonlinear GBT finite element is developed by exploiting the features of mixed-stress GBT finite element formulation in the framework of the Implicit Corotational Method (ICM). The application of the ICM to GBT is briefly discussed and the details necessary to successfully transform the linear GBT finite element in its nonlinear counterpart are illustrated. The numerical results show how the proposed finite element can deal with global and distortional geometrically nonlinear phenomena, in good accordance with respect to 3D shell models.