Mesh Independence Analysis Research Articles

Tunable bandgap characteristic of various hexagon-type elastic metamaterials for broadband vibration attenuation

Inspired by the advantages of the hexagon lattices and auxetic metamaterials, the typical two-dimensional (2D) hexagon-type elastic metamaterials (EMs), that is, the concave, the convex, and the rectangular hexagon-type EMs, are presented for investigating the dynamic behavior systematically. Firstly, the lumped mass-spring models are used to construct the band structures, and the eigenmodes are obtained by solving the eigenvalue problem of motion equations to unveil the formation mechanisms of bandgap (BG). Note that the specific dispersion branches are characterized by eigenfrequencies with the eigenmodes presenting similar vibrational forms, rather than just ranking the eigenfrequencies from low to high. Furthermore, the dependence on the main structural parameters of the lumped mass-spring models is investigated to achieve tunability of the bandgap characteristics. Then, the continuum models are also established to study the formation of bandgaps as well as the propagation of waves based on eigenmodes and transmission. The comprehensive study of the physical mechanics of the unit cells is carried out, encompassing the analysis of iso-frequency contours, deformation fields, and mesh-independent analysis. Finally, both the numerical analysis and experimental validation demonstrate the effect of vibration attenuation on in-plane elastic waves, which has the ideal great agreement with the prediction of the band structures (the values of the frequency response functions are much less than -20 dB within the ranges of BGs). This research is expected to provide valuable insight into the design of vibration isolators, beams, plates, and other devices that are being renewed.

THERMAL ANALYSIS OF A PLATE HEAT EXCHANGER (PHE) FITTED WITH CARDING TOOL PATTERNS USING CFD MODELING

Inspired by the wool carding tools, a new plate heat exchanger (PHE) design was developed, tested, and analyzed numerically. The present research work used computational fluid dynamics (CFD) simulations to examine the impact of various parameters, such as the rib type (continuous and discrete), the arrangement type (rectangular, square, and triangular), and the geometrical parameters (transversal and longitudinal pitches) on the PHE hydraulic and thermal performances. A three-dimensional (3D) evaluation of turbulent flow over a plate fitted with carding tool patterns was conducted using the<i> k-ε </i>turbulence model within the Reynolds number range from 400 to 1800. The numerical results were compared to previous experimental research to validate the dependability of the technique, and a mesh independence analysis was performed to confirm the precision and the accuracy of the CFD method. The results show that CFD ANSYS software can effectively predict the pressure drop across the carding tools and provide valuable insights into the fluid flow behavior within the system in terms of calculating the thermal hydraulic performance parameter (THPP) and the thermal effectiveness <i>ε </i>. The ultimate goal of this research work was to identify the ideal arrangement with the highest heat transfer rate and the lowest pressure losses in terms of determining the best THPP. Compared to the conventional chevron-type PHE, the thermal performance of the novel PHE design was enhanced by 25.63% and 47% in terms of nondimensional parameters e and THPP, respectively.

Enhanced external counterpulsation treatment regulates blood flow and wall shear stress metrics in femoral artery: An in vivo study in healthy subjects

As a non-invasive assisted circulation therapy, enhanced external counterpulsation (EECP) has demonstrated potential in treatment of lower-extremity arterial disease (LEAD). However, the underlying hemodynamic mechanism remains unclear. This study aimed to conduct the first prospective investigation of the EECP-induced responses of blood flow behavior and wall shear stress (WSS) metrics in the femoral artery. Twelve healthy male volunteers were enrolled. A Doppler ultrasound-basedapproach was introduced for the in vivo determination of blood flow in the common femoral artery (CFA) and superficial femoral artery (SFA) during EECP intervention, with incremental treatment pressures ranging from 10 to 40 kPa. Three-dimensional subject-specific numerical models were developed in 6 subjects to quantitatively assess variations in WSS-derived hemodynamic metrics in the femoral bifurcation. A mesh-independence analysis was performed. Our results indicated that, compared to the pre-EECP condition, both the antegrade and retrograde blood flow volumes in the CFA and SFA were significantly augmented during EECP intervention, while the heart rate remained constant. The time average shear stress (TAWSS) over the entire femoral bifurcation increased by 32.41%, 121.30%, 178.24%, and 214.81% during EECP with treatment pressures of 10 kPa, 20 kPa, 30 kPa, and 40 kPa, respectively. The mean relative resident time (RRT) decreased by 24.53%, 61.01%, 69.81%, and 77.99%, respectively. The percentage of area with low TAWSS in the femoral artery dropped to nearly zero during EECP with a treatment pressure greater than or equal to 30 kPa. We suggest that EECP is an effective and non-invasive approach for regulating blood flow and WSS in lower extremity arteries.

Combined Micro-Structural Effects of Linearly Increasing Reynolds Number and Mean Inflow Velocity on Flow Fields with Mesh Independence Analysis in Non-Classical Framework

The monolithic Eulerian formulation has widely been employed for solving numerically fluid–structure interaction (FSI) problems of finite structural displacement using the same mathematical variational formulation for fluid and structural dynamics. Recently, different physical features of fluid flow have been analyzed using this approach to such coupling problems by computing the classical benchmark solutions in a non-classical framework. Despite producing decent results, the analysis of micro-structural characteristics of fluid flow by applying the classical benchmark solutions still needs to be enhanced and extended further for such coupling problems. In this paper, the classical benchmark solutions have been enhanced and extended further for analyzing the combined micro-structural effects of linearly increasing Reynolds number Re and mean inflow velocity U¯ on flow fields with mesh independence analysis by employing a monolithic Eulerian formulation in a non-classical framework. To this aim, the Cosserat fluids theory is taken into account for the present coupling problem by considering three micro-rotational degrees of freedom (dof) of fluid particles. The model equations of the proposed Cosserat fluid–structure interaction (CFSI) problem are derived using underlying laws of continuum mechanics. A numerical section presents the implementation of the benchmark problem with test examples followed by a detailed evaluation of the obtained results. The results obtained indicate that a uniform linear increase in Reynolds number Re and mean inflow velocity U¯ produce the significant combined micro-structural effects on the micro-rotation velocity field ω, and this effect is found increasing on the increase of both parameters. This combined effect of increasing Re and U¯ on the velocity field u is also observed to be very significant in a sense that horizontal and vertical flow velocity profiles experience great variation by maintaining the same pattern on each increasing value of Re and U¯ at any particular location in the computational domain. Further, the mesh independence analysis is employed to verify the convergence of obtained results. The study concludes that the linear increase in Reynolds number and mean inflow velocity affect micro-rotational velocity field significantly at the micro-structural level with mesh independence analysis. Finally, some future recommendations to enhance and extend the study with some of its limitations are presented.

Heating performance of a large-scale line heater by adding synthesized carbon- nanodots to the heater bath fluid: CFD simulation and experimental study

Numerous researchers have recently become interested in nanofluids because of their potential applications in thermal systems. Herein, various concentrations of nanofluid of synthesized carbon nanodots (C-dots) were used to survey the thermal performance of a line heater as a heater bath fluid, and a numerical model was proposed to simulate all of the line heater's components for the first time. C-dots nanoparticles were manufactured with the aid of the hydrothermal method and characterized using FTIR and XRD analysis. In addition, a two-stage approach was used to prepare the nanofluid with a varying concentration of C-dot nanoparticles, ranging from 0.5 to 5 wt%. Nanofluids were also measured and compared to the base fluid in terms of thermophysical properties. Additionally, a numerical model based on the finite element method (FEM) was proposed to simulate fluid flow and heat transfer in the line heater, and validation of the numerical results revealed good agreement with earlier studies. The mesh independence analysis shows that the results are much better and more consistent when mesh number 98,946 is used instead of the others. The results illustrate that temperatures were raised from roughly 300 K near the gas tubes to around 370 K near the fire tubes. In comparison to the situation of employing water as the bath fluid, the maximum heater power consumptions derived from the experiments and numerical findings were 9.7 % and 10.3 %, respectively.

Numerical simulation on the thermal dynamic behavior of liquid hydrogen in a storage tank for trailers

In the present study, a numerical model was established to investigate the thermal dynamic behavior of liquid hydrogen in a 40-foot ISO tank. The volume of fluids (VOF) method was applied to capture the liquid surface, and a phase change model was used to describe the evaporation phenomenon of hydrogen. The mesh independence analysis and the experimental validation have been made. Under different filling levels, motion statuses, and heat leakage conditions, the variations in pressure and temperature of the tank were investigated. The pressure of 90% filling level case was reduced by 12.09%, compared to the 50% case. Besides, the pressure of the sloshing condition has increased twofold, contrasted with the stationary one, and thermal stratification disappeared. Additionally, 16.67 min were taken for the ullage pressure to reach around 1 MPa in emergencies of being extremely heated. Some valuable conclusions and suggestions for the transportation of liquid hydrogen arrived. Those could be the references to predict the release time of boil-off hydrogen, and primarily support for gas-releasing control strategies.

Immersed boundary Mindlin-Reissner 3D shell element for modeling isotropic and laminated composite shells

An immersed boundary 3D shell element is presented here that is based on Mindlin-Reissner shell theory assumptions and uses quadratic B-spline approximation for the solution. It enables mesh independent analysis wherein the surface representing the shell geometry is defined independently and not by the mesh. The shell geometry is immersed in a uniform background mesh whose elements are 3D B-spline shell elements. By making the geometric model independent of the mesh, the typical difficulties associated with mesh generation can be avoided. The quadratic 3D B-spline shell elements in the mesh can represent the displacement field as a tangent continuous piece-wise polynomial approximation. The nodes of the element have three translational and no rotational degrees of freedom. The element is formulated under small-deformation and plane stress assumptions. Constructing the element based on shell theory enables the use of effective properties to model thin fiber reinforced laminated composite shell-like structures. The element formulation and the mesh independent approach are validated against a series of common shell element benchmark problems. • Immersed boundary 3D B-spline element based on Mindlin-Reissner shell theory assumptions. • Mesh independent analysis where geometry is embedded in a uniform background mesh. • The iso-parametric quadratic B-spline shell elements are used for C 1 continuous approximation. • Step boundary method (SBM) is used for applying boundary conditions. • Immersed boundary FEM for shells is validated for isotropic and composite shells.

A novel strain-based finite element family for mesh-independent analysis of the tensile failure of reinforced concrete bars

The paper presents a novel family of strain-based beam finite elements (FE) for analysis of tensile failure of a reinforced concrete bar (RC bar), with results of the analysis being independent of the applied FE mesh. The composite bar consists of a continuous longitudinal ductile reinforcing bar(s) surrounded by brittle concrete cover, which are considered separately in the model. Longitudinal slip at the contact between the concrete cover and reinforcing bars is allowed, while their relative displacements perpendicular to the axis of the RC bar are prevented. Cracks in concrete cover occur when tensile stress in concrete exceeds its tensile strength. Propagation of partially connected crack, that is, softening of the material at the crack, is described through constitutive law in form of nonlinear relationship between stresses in concrete at the crack and the width of the crack. Each separate crack is considered discretely as a discontinuity in geometry of the element. In the analysis of cracking of concrete, it is commonly assumed that the discrete crack can occur at the nodes of FE only. However, this assumption leads to dependence of the analysis results on the employed FE mesh. The presented family of FE enables occurrence of the crack anywhere along the FE. In order to achieve this, the discrete crack is excluded from equations of FE and additional boundary conditions are introduced at the discontinuity. This approach ensures that the location of the cracks, their number and their propagation are independent of the applied FE mesh. Advantages of the novel family of FE are thoroughly presented in a parametric study which investigates influence of number of FE as well as influence of degrees of interpolation and integration on the cracking of RC bar under tensile loading. Experimental results of tensile tests on the analysed bar are available in literature. It can be concluded that the results obtained with the minimal possible number of novel FE and sufficiently high degree of numerical integration scheme, applied for solving integrals in equations of FE, are considerably more accurate than the results of previous analyses with model of discrete crack at the nodes of FE only.

Dynamic increase factor (DIF) for concrete in compression and tension in FE modelling with a local concrete model

The dynamic increase factor (DIF) in the strength of concrete-like materials has been a subject of extensive investigation and debate for many years. It now tends to be generally accepted that the compression DIF as observed from standard sample tests is mainly attributable to the dynamic structural effect, whereas for concrete under tension the DIF is deemed to be governed by different mechanisms, probably more from the material and micro-fracture level. This paper presents a numerical study on the uniaxial compression and tension DIF, with a particular focus on how the DIF, irrespective of its cause, should be included in an appropriate manner in the finite element (FE) modelling with a local concrete model. The inevitable mesh-dependency issue due to numerical localisation and its implications on rate effects are examined in detail. A mesh-objective modification on the standard sample tested tension DIF is proposed with the aim to achieve relatively mesh independent analysis in the FE models where high strain-rate tension is involved. The results demonstrate that the proposed approach is effective, and reliable modelling results can be achieved with the proposed DIF modelling scheme for the local concrete model.

Mechanistic modeling and numerical simulation of axial flow catalytic reactor for naphtha reforming unit.

Naphtha catalytic reforming (NCR) process has been of tremendous attention all over the world owing to the significant requirement for high-quality gasoline. Industrialized naphtha reforming unit at oil refineries applies a series of fixed bed reactors (FBRs) to improve the quality of the low-octane hydrocarbons and convert them to more valuable products. The prominent purpose of this research is to understand the catalytic reactor of naphtha reforming unit. For this aim, an appropriate mechanistic modeling and its related CFD-based computational simulation is presented to predict the behavior of the system when the reactors are of the axial flow type. Also, the triangular meshing technique (TMT) is performed in this paper due to its brilliant ability to analyze the results of model’s predictions along with improving the computational accuracy. Additionally, mesh independence analysis is done to find the optimum number of meshes needed for reaching the results convergence. Moreover, suitable kinetic and thermodynamic equations are derived based on Smith model to describe the NCR process. The results proved that the proceeding of NCR process inside the reactor significantly increased the concentration amount of aromatic materials, lighter ends and hydrogen, while deteriorated the concentration amount of naphthene and paraffin. Moreover, the pressure drop along the reactor length was achieved very low, which can be considered as one of the momentous advantages of NCR process.

Design of experiments and goodness-of-fit in comparison of velocity fields in curved open channel flow simulation

Abstract In this paper, a methodology is suggested to evaluate the goodness-of-fit between observed and numerically predicted variables in curved open channel flows. The mathematical model uses the continuity and the Reynolds averaged Navier–Stokes (RANS) equations with the RNG κ-ɛ turbulence model, numerically solved with the commercial software Ansys Inc. The concept of design of experiments (DOE) together with some criteria of goodness-of-fit was used in a new coherent suggested methodology for the calibration and validation of the numerical model. The goodness-of-fit criterion was applied to secondary flow variables like helicity, intensity of the secondary current and the vortex index instead of the primary variables like the velocity field and the free surface. This methodology guarantees that the numerical model reproduces values of the response variables very near to the observed values and it is valid for the mesh independence analysis and the setup of other numerical parameters, including those related to the boundary conditions.

Design and numerical investigation to visualize the fluid flow and thermal characteristics of non-axisymmetric convergent nozzle

In this paper, numerical simulations are conducted to visualize the fluid flow and thermal characteristics of a non-axisymmetric convergent nozzle. The novel design methodology is based on curve-fitting approach. The curves used for designing the nozzle are based on a combination of fifth and third order polynomial at upper and lower surfaces respectively. The computations are performed using commercially available computational fluid dynamics (CFD) tool ANSYS CFX®. Firstly, mesh independence analysis are carried out. Then, numerical simulation is further validated for medium and low-pressure helium by comparing it with the available experimental data. Thereafter, an exhaustive analysis is carried out to compare the fluid flow behavior inside the nozzle for two cryogenic fluids, nitrogen and helium at three different inlet pressure and temperature. The fluid flow pattern, pressure, velocity, Prandtl number, static enthalpy, Reynolds number, eddy viscosity, etc. are identified at various positions. The Mach number and temperature at the outlet of the nozzle is the key feature of this analysis which satisfies the criteria for a nozzle which is used for the high, medium and low-pressure turbine. The analysis provides a better understanding of the further improvement of the design methodology or performed an experiment. The designed nozzle has a tremendous effect on the fluid flow behavior and suitable for impulse type turbine with a small amount of reaction used in a turboexpander. The work proposes a new design methodology for designing a non-axisymmetric airfoil convergent nozzle of rectangular cross-section.

On the computational fluid dynamics of PEM fuel cells (PEMFCs): an investigation on mesh independence analysis

The results clearly show that the polarization curve is not enough to check the independency in grid in PEMFC computational fluid dynamic modeling.

Characteristic analysis on the pressure fluctuation in the impeller of a low specific speed mixed flow pump

To explore the pressure fluctuation characteristics of a low speed specific speed mixed flow pump caused by rotor-stator interaction, the unsteady flow was simulated with CFX for the whole flow passage of a mixed flow pump with a specific speed of 148.8. The structured mesh of the computation domain was generated with ICEM CFD and TurboGrid, and mesh-independent analysis was done in the design condition. Through the comparison with the experiment data, the reliability of the simulation was verified. In different locations of the impeller passage, monitoring points were set. With Fast Fourier Transform (FFT), the characteristic analysis on the pressure fluctuation in the impeller passage was done for three flow rate conditions (0.75Qd, Qd, 1.25Qd). The results show that the pressure fluctuation amplitude increases from the inlet to the outlet. And the maximum values in different flow rates exist near the hub of the outlet; The pressure fluctuation is small in the design condition, but the largest in the small flow rate condition, accompanied by the secondary dominant frequencies with large amplitudes; In the small flow rate condition and design condition, the dominant frequency varies from the inlet to the outlet because the combine action of the impeller and guide vane; while in the large flow rate condition, the pressure fluctuation in the whole impeller passage is affected significantly by the guide vane, and the domain frequency is 8 times the rotational frequency of impeller. In addition, the change of pressure fluctuation from the pressure surface to the suction surface in the off-design conditions is investigated, and the results demonstrates that the intensity of the pressure fluctuation in the impeller passage is closely related with the impeller as well as the distribution of the vorticity and the pressure.

Numerical Investigation of Rotational Speed on Pump as Turbine for Microhydro Applications

Pump as Turbine (PAT) always has been a favourable solution to generate electricity in rural areas when there is a potential microhydro site. Such systems have lower capital cost, and they are easier to maintain than commercially-available microhydro turbines. Normally, PAT is designed to run at a rated rotational speed so it can directly couple with an induction generator in order to match the synchronous speed. In an actual scenario, the PAT’s rotational speed changes and fluctuates with respect to flow rate due to the absence of a hydraulic control mechanism. It is essential to understand how the PAT behaves under different rotational speeds in order to design good microhydro systems. The aim of this study was to conduct simulation analysis of the effect of rotational speed on PAT’s performance curve over a range of flow rates. ANSYS CFX software was used as the Computational Fluid Dynamic (CFD) simulation tool in this study. Three distinct flow domains was modelled by Computer Aided Design (CAD) software and assembled as the computational fluid domains. Mesh independence analysis and convergence criteria were set to ensure the accuracy of the model. The torque generated by the impeller was collected from the simulation data and presented in the PAT performance curve. It was observed that the pressure head and torque generated increased at higher rotational speeds, thus maintaining the efficiency value. The results showed that the efficiency of the PAT was maintained around 76.5% for rotational speeds between 1350 to 1650 RPM, but the best efficiency point shifted to lower flow rate for lower rotational speed. The outcomes of this study will be useful for turbomachinery researchers, microhydro users, and project engineers for predicting the PAT performance for designing microhydro systems.

Numerical investigation on cooling performance of hot stamping tool with various channel designs

This paper investigates the cooling performance of hot stamping tool with various cooling channel designs, i.e., straight hole, longitudinal CCC (conformal cooling channel), transversal CCC, parallel CCC, serpentine CCC. The cooling channels are placed inside the hot stamping tool for dissipating heat during stamping process. Turbulent flow of a Newtonian fluid in a circular cross-sectional channel is analyzed by a three-dimensional computational fluid dynamic approach. Four Reynolds numbers and four outlet pressures are researched through full factorial design to evaluate the effect on the performance of various cooling channel designs. Disparate priority of each design at different boundaries is discussed in the light of numerical results. Evaluation indicators such as maximum temperature, average temperature, temperature uniformity, velocity and pressure drop are used to assess the cooling performance. Meanwhile, figures of merit, i.e., heat dissipated per unit pumping power, is also compared for five channel designs. Moreover, the reliability of this research method is verified by means of mesh independence analysis and single cooling pipe experiment. It is concluded that serpentine CCC is better than other designs at low Reynolds number, while longitudinal CCC is the best design at high Reynolds number. Besides, with the increase of mass flow rate, the maximum temperature and average temperature tend to decrease, but the temperature uniformity, pressure drop and maximum velocity tend to increase. The cooling performance mainly depends on mass flow rate and channel shape, but not outlet pressure. However, the pressure inside the channels is determined by the outlet pressure. It is also calculated that longitudinal CCC has the highest FoM (figure of merit) which represents the best cooling performance. Furthermore, it is proved that the relative error of simulation and experiment results can be controlled within 10% by mesh independence analysis and single cooling pipe experiment.

Use of Coupled Smooth-Particle Hydrodynamics/Lagrangian Method in the Simulation of Deformable Projectile Penetration

Mesh-dependent finite element (FE) analysis poses considerable limitations in terms of applying it in large deformation problems. As simulations such as projectile penetration are largely dependent on the material failure criterion, the artificial element erosion technique, which is usually incorporated in mesh-dependent FE techniques, may result in considerable inaccuracies. Therefore, over the last few decades, computational mechanists and engineers have focussed on implementing a mesh-independent analysis method to overcome the numerical instabilities that occur in mesh-dependent FE methods. The smooth-particle hydrodynamics (SPH) technique is one of the methods that is becoming popular among computational mechanists and engineers. The knowledge and understanding of different parameters involved in such simulation is essential prior to its application. In this study, a comprehensive numerical investigation of projectile penetration through monolithic aluminium plates using the SPH technique has been performed. While there have been studies reported in published literatures on the application of the SPH technique on projectile simulations, very limited attention has been placed on investigating the influence of different parameters on the analysis results, especially on deformation of the projectiles. One of the main objectives of this study is to investigate the contribution of different numerical parameters on the simulation of complete penetration of deformable projectiles (5.56 mm x 45 mm NATO standard) through 16 mm AA5061-H116 aluminium plates. The effects of particle density, smooth length, different particle sorting options, and scale factor for smooth length, have been parametrically studied and presented. In addition, the penetration mechanism of projectiles through a metallic target has been numerically and experimentally studied. Numerical simulations show very good agreement with the experimental results. The velocity time histories for monolithic aluminium plates show a “dip” in its velocity reduction, which is considerably difficult to observe in mesh-dependent methods. Three stages of the penetration process have been numerically identified and discussed.

Modeling of a microreactor for propylene production by the catalytic dehydrogenation of propane

A model of a microreactor was proposed to analyze the production of propylene by the propane dehydrogenation using a catalytic surface of V2O5/TiO2 doped with Rb. The reactor is a 50mm length tube of 2mm diameter whose wall is a catalytic surface, modeled using finite volume method in cylindrical coordinates over a tangential plane. Dehydrogenation kinetics is reported by Grabowski (2004). First, a mesh independence analysis was done to assure the adequate cell size. Second, a parametric analysis changing Reynolds number at different temperatures and propane-oxygen relations was done to find the Reynolds range to effectively use the reactor length (Re from 1 to 10). Then at the later Reynolds interval a parametric analysis involving temperature and composition was done to create productivity surfaces to find the highest productivity operation conditions. Finally, an analysis varying pressure at the maximum productivity conditions (Re=1, T=500K, C3H8/O2=2) was developed.

Set-Up Analysis and Optimization of CFD Simulations for Radial Turbines

This paper proposes a CFD method for simulating radial turbocharger turbine flows. A review is presented of the computational model in terms of meshing, mesh movement strategy, and computational algorithm in turbomachinery CFD simulations. A novel local mesh independence analysis is developed for this purpose. This procedure is aimed at distributing the cells more efficiently by selecting suitable cell sizes for the different regions of the domain to optimize the use of the available computational resources. Pressure- and density-based solvers are compared. The influence of the moving-mesh strategy was analyzed, and small differences were observed in the region near the maximum efficiency point, while these differences increased when off-design conditions were considered. Finally, a comparison of the results with data from an experimental test bench shows that the proposed computational methodology can be used to characterize radial turbomachinery. The objective of the analysis and the optimization of the case configuration was to establish some general guidelines for CFD turbomachinery simulations.

Mesh independent analysis of shell-like structures

Mesh independent analysis is motivated by the desire to use accurate geometric models represented as equations rather than approximated by a mesh. The trial and test functions are approximated or interpolated on a background mesh that is independent of the geometry. This background mesh is easy to generate because it does not have to conform to the geometry. Essential boundary conditions can be applied using the implicit boundary method where the trial and test functions are constructed utilizing approximate step functions such that the boundary conditions are guaranteed to be satisfied. This approach has been demonstrated for two-dimensional (2D) and three-dimensional (3D) structural analysis and is extended in this paper to model shell-like structures. The background mesh consists of 3D elements that use uniform B-spline approximations, and the shell geometry is assumed to be defined as parametric surfaces to allow arbitrarily complex shell-like structures to be modeled. Several benchmark problems are used to study the validity of these 3D B-spline shell elements. Copyright © 2012 John Wiley & Sons, Ltd.