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Microgrid Modeling for Stability Analysis

Here this document is a summary of a report prepared by the IEEE PES Task Force (TF) on Microgrid (MG) Dynamic Modeling, IEEE Power and Energy Society, Tech. Rep. PES-TR106, 2023. In this paper, the major issues and challenges in microgrid modeling for stability analysis are discussed, and a review of state-of-the-art modeling approaches and trends is presented. In the context of the IEEE 1547 standard, the document covers issues associated with component models for MG dynamic studies and simulations, including generator and grid modeling, full and average converter models, unbalanced and balanced system conditions, dynamic and static loads, protection requirements, and detailed and simplified controls considering communications delays, packet losses, and security issues. Considering the future integration of grids and MGs to form broad integrated networks, a discussion is presented of the use of phasor vis-à-vis electromagnetic transient simulation tools for MG dynamic stability studies, as well as modeling scale-up issues and MG equivalent models. Specifically white-, grey-, and black-box models, are presented. This TF paper and companion report constitute a modeling guide for R&D groups working on developments and standards of MGs with a focus on stability issues.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A High Resolution Simulation of a Single Shock-Accelerated Particle

We report particle drag models, which capture macroviscous and pressure effects, have been developed over the years for various flow regimes to enable cost effective simulations of particle-laden flows. The relatively recent derivation by Maxey and Riley has provided an exact equation of motion for spherical particles in a flow field based on the continuum assumption. Many models that have been simplified from these equations have provided reasonable approximations; however, the sensitivity of particle-laden flows to particle drag requires a very accurate model to simulate. To develop such a model, a two-dimensional axisymmetric Navier–Stokes direct numerical simulation of a single particle in a transient, shock-driven flow field was conducted using the hydrocode FLAG. FLAGs capability to run arbitrary Lagrangian-Eulerian hydrodynamics coupled with solid mechanic models makes it an ideal code to capture the physics of the flow field around and in the particle as it is shock-accelerated—a challenging regime to study. The goal of this work is twofold: to provide a validation for FLAGs Navier–Stokes and heat diffusion solutions and to provide a rationale for recent experimental particle drag measurements.

42 ENGINEERING↗

A Numerical Simulation of a Single Shock-Accelerated Particle

Particle drag models, which capture macro viscous and pressure effects, have been developed over the years for various flow regimes to enable cost effective simulations of particle-laden flows. The relatively recent derivation by Maxey and Riley has provided an exact equation of motion for spherical particles in a flow field based on the continuum assumption. Many models that have been simplified from these equations have provided reasonable approximations; however, the sensitivity of particle-laden flows to particle drag requires a very accurate model to simulate. To develop such a model, a 2D axisymmetric Navier-Stokes direct numerical simulation of a single particle in a transient, shock-driven flow field was conducted in the hydrocode FLAG. FLAG’s capability to run arbitrary Lagrangian-Eulerian hydrodynamics coupled with solid mechanic models makes it an ideal code to capture the physics of the flow field around and in the particle as it is shock-accelerated – a challenging regime to study. The goal of this work is twofold: to provide a validation for FLAG’s Navier-Stokes and heat diffusion solutions, and to provide a rationale for recent experimental particle drag measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Spacecraft nonlinear control

The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.

Sheen, Jyh-Jong↗

VISUAL CONTROL OF RENDEZVOUS

Space rendezvous involving human occupants will be required in many phases of space flight. In order that rendezvous capability be concurrent with other phases of manned space flight to insure that such tasks as the rotation and addition of crews for manned space station, supply of stations and launching complexes for deep-space probes, and the emergency rescue of personnel may be carried out, it is desirable to determine the ability of a human pilot to control the rendezvous maneuver. The National Aeronautics and Space Administration has conducted a study program to determine vehicle requirements and control techniques for a number of proposed methods for performing piloted space rendezvous. The final step in each phase of the rendezvous study program has been a simulation of the man-machine combination to test its feasibility. Initially, an analytical study was conducted to determine a range of conditions that would exist at the beginning of the terminal phase of rendezvous (ref. 1). Piloted systems were investigated for rendezvous control using these initial conditions. One such study of piloted rendezvous in which all the required control information was displayed to the simulator pilot on instruments is presented in reference 2. While the control of the rendezvous maneuver by use of the instrument display was shown to be feasible, the sufficiently accurate measurement of the necessary information to operate the instrument was realized to be a difficult problem. Consideration was therefore given to the possibility of maneuvering range and range rate required for the control of the rendezvous from visual sightings made during the initial control application. To provide this capability, an analytical study was made. This analytical study, presented in reference 3, derived three techniques for obtaining range and range rate visually and conducted a simplified preliminary situation to test the three analytical techniques. The study reported herein is a continuation of the simulation work begun in reference 3, and is aimed at determining the ability of a pilot to use visual information to reduce or eliminate the need for some or all of the data that would normally be displayed on instruments.

Rendezvous↗

Using Pilot Jobs and CernVM File System for Simplified Use of Containers and Software Distribution

High Energy Physics (HEP) experiments entail an abundance of computing resources, i.e. sites, to run simulations and analyses by processing data. This requirement is fulfilled by local batch farms, grid sites, private/commercial clouds, and supercomputing centers via High Throughput Computing (HTC). The growing needs of such experiments and resources being prone to trends of heterogeneity make it difficult for physicists to handle these resources directly. Additionally, HEP collaborations heavily rely on data and software releases, typically in the order of tens of gigabytes, while conducting simulations and analyses. Hence, aspects of scalability, reliability, and maintenance become crucial with regards to the distribution of the necessary data and software stack. The GlideinWMS [4] framework helps with the resource management problem by using pilot jobs, aka Glideins, to provision reliable elastic virtual clusters. Glideins are submitted to unreliable heterogeneous resources which are validated and customized by the Glideins to make the worker nodes available for end-user job execution. On the other hand, the CernVM File System (CernVM-FS or CVMFS) [1] helps with data distribution. It is a write-once, read-everywhere filesystem used to deploy scientific software to thousands of nodes on a worldwide distributed computing infrastructure. CVMFS is based on the Hyper Text Transfer Protocol and has been widely used within the particle physics community for (1) distributing experiment software and data such as calibrations, and (2) facilitating containerization by efficiently hosting container images along with providing containerization software, especially Singularity [3] GlideinWMS relies on CVMFS installed locally on the computing resources to satisfy the experiments' software needs. This requires system administrators' effort to install and maintain CVMFS at the sites and limits the use of sites, especially HPC resources, that do not have CVMFS installed. This poster presents a solution, taking advantage of Glideins to provide CVMFS at most sites without the need for a local installation. Doing so expands the pool of resources available for HEP experiments and reduces the effort of system administrators for current resources. Additionally, the proposed solution allows GlideinWMS to also start Singularity [3], a containerization software that can run unprivileged, on sites where neither CVMFS nor Singularity are available, including HPC sites. The benefits provided by this solution are: (1) lower overhead for site administrators in that they have less software to install, (2) an expanded pool of resources that run user jobs with easy access to software and data provided by CVMFS, thus making life easier for the scientists, and (3) improved flexibility to use HPC resources by enabling GlideinWMS pilot jobs to support HPC sites.

Urs, Namratha↗

Modification of a Macromechanical Finite-Element Based Model for Impact Analysis of Triaxially-Braided Composites

A macro level finite element-based model has been developed to simulate the mechanical and impact response of triaxially-braided polymer matrix composites. In the analytical model, the triaxial braid architecture is simulated by using four parallel shell elements, each of which is modeled as a laminated composite. For the current analytical approach, each shell element is considered to be a smeared homogeneous material. The commercial transient dynamic finite element code LS-DYNA is used to conduct the simulations, and a continuum damage mechanics model internal to LS-DYNA is used as the material constitutive model. The constitutive model requires stiffness and strength properties of an equivalent unidirectional composite. Simplified micromechanics methods are used to determine the equivalent stiffness properties, and results from coupon level tests on the braided composite are utilized to back out the required strength properties. Simulations of quasi-static coupon tests of several representative braided composites are conducted to demonstrate the correlation of the model. Impact simulations of a represented braided composites are conducted to demonstrate the capability of the model to predict the penetration velocity and damage patterns obtained experimentally.

Goldberg, Robert K.↗

Realistic fuel spray modeling for gasoline direct injection engine applications

Fuel spray modeling plays a critical role during modern gasoline direct injection (GDI) engine development due to fuel injection’s dominant impact on engine performance and emissions as well as the complex physical processes involved. In engineering three-dimensional (3D) computational fluid dynamics (CFD) simulations, the liquid-phase fuel atomization, evaporation, and mixing are usually modeled with the discrete droplet model (DDM) adopting a Lagrangian approach for multiphase CFD simulations. To this end, general practices heavily depend on the reduced order characterization of the injector nozzle flow. However, such simplified injector modeling may lead to insufficient representations of the complex spray dynamics. To tackle this problem, this study proposes a novel workflow to numerically evaluate GDI sub-cooled and flash-boiling sprays under engine-relevant conditions using a side-mounted GDI injector together with real gasoline fuel properties. The workflow introduces a one-way coupling (OWC) method leveraging high-fidelity nozzle flow simulations to provide realistic boundary conditions to the Lagrangian injector model. The proposed workflow was first verified in a constant volume chamber (CVC) environment and then implemented in a practical GDI engine setup to study spray morphology, fuel-air mixing, and wall-wetting propensity. In addition, detailed comparison was performed between the OWC method and the conventional rate of injection (ROI) routine. In conclusion, quantitative analysis of spray characteristics was conducted to highlight possible source of discrepancies of the conventional ROI method.

33 ADVANCED PROPULSION SYSTEMS↗

A Study of Coaxial Rotor Performance and Flow Field Characteristics

As a precursor to studying the acoustics of a coaxial rotor system, the aerodynamics and flow field of a coaxial rotor were simulated to better understand the interaction between the two rotors. RotUNS, an unsteady Navier-Stokes solver that uses a simplified blade aerodynamics model, was used to predict coaxial rotor performance in hover and forward flight. RotUNS steady hover calculations showed improved performance compared to blade element momentum theory. Prior to examining the complex 3D flow field of a coaxial rotor in detail, two airfoils traveling in opposite directions with a vertical separation distance equivalent to the separation between the upper and lower rotor of the coaxial system were simulated. The pressure field generated by the two airfoils aided our interpretation of the more complex coaxial rotor system flow field. The pressure fields above, between, and below the coaxial rotor system were then examined for different azimuth positions of the upper and lower rotor blades.

Barbely, Natasha L.↗

thevenin: An Equivalent Circuit Modeling Package [SWR-24-132]

This package is a wrapper for the well-known Thevenin equivalent circuit model for simulating battery behavior with a focus on ease of use. The model is comprised of a single series resistor followed by any number of parallel RC pairs. The package includes an intuitive "experiment" interface, which simplifies the programming of constant or dynamic current, voltage, and/or power-driven loads, making it ideal for a wide range of applications, from basic tests to complex simulations. It also supports state-of-charge (SOC) and temperature-dependent properties, allowing the model to be more easily calibrated against real cells.

Randall, Corey↗

Subsurface Characterization and Machine Learning Predictions at Brady Hot Springs: Preprint

Subsurface data analysis, reservoir modeling, and machine learning (ML) techniques have been applied to the Brady Hot Springs (BHS) geothermal field in Nevada, USA to further characterize the subsurface and assist with optimizing reservoir management. Hundreds of reservoir simulations have been conducted in TETRAD-G and CMG STARS to explore different injection and production fluid flow rates and allocations and to develop a training data set for ML. This process included simulating the historical injection and production since 1979 and prediction of future performance through 2040. ML networks were created and trained using TensorFlow based on multilayer perceptron (MLP), long short-term memory (LSTM), and convolutional neural network (CNN) architectures. These networks took as input selected flow rates, injection temperatures, and historical field operation data and produced estimates of future production temperatures. This approach was first successfully tested on a simplified single fracture doublet system, followed by the application to the BHS reservoir. Using an initial BHS dataset with 37 simulated scenarios, the trained and validated network predicted the production temperature for 6 production wells with the mean absolute percentage error of less than 8%. In a complementary analysis effort, the principal component analysis applied to 13 BHS geological parameters revealed that vertical fracture permeability shows the strongest correlation with fault density and fault intersection density. A new BHS reservoir model was developed considering the fault intersection density as proxy for permeability. This new reservoir model helps to explore under-exploited zones in the reservoir. A data gathering plan to obtain additional subsurface data was developed; it includes temperature surveying for three idle injection wells, at which the reservoir simulations indicate high bottom-hole temperatures. The collected data assist with calibrating the reservoir model and may lead to converting these wells to producers to access under-exploited zones in the reservoir. Data gathering activities are planned for the first quarter of 2021.

40 EE - Geothermal Technologies Office (EE-4G)↗

Atomistic insights into the synergistic effects of tensile strain and hydroxyl group on increasing the thermal conductivity of monohydric alcohols as latent heat storage materials

The low thermal conductivity of linear monohydric alcohols significantly limits their performance when used as latent heat storage materials. It was found that imposing certain mechanical strains on nanomaterials with highly ordered structures can lead to appreciable thermal conductivity enhancement. To explore the potential of enhancing the intrinsic thermal conductivity of monohydric alcohols, a simplified ideal crystal model was employed for molecular arrangement in this work. The variation of atomistic heat transfer as a function of tensile strains was exploited by non-equilibrium molecular dynamics simulations. Furthermore, the influence of stretching on the vibration density of states and the corresponding molecular morphology were revealed. The results suggested that the thermal conductivity of monohydric alcohols with such simplified ideal crystalline structures can increase by about 170 % at the strain of 0.1. The distance between neighboring interfaces was found to determine the energy of inter-molecular interactions at the crystal grain boundaries. The hydrogen bonds energy has not reached the critical value when increasing tensile strains from 0 to 0.1. In contrast, the strongest van der Walls interactions for alkanes were obtained at the strain of 0.06 where the interfacial distances of alkanes have achieved their equilibrium distances. In addition, the interfacial heat transfer coefficient of ideal crystal monohydric alcohols at hydroxyl interfaces was found to be threefold than that between methyl interfaces, in consistent with the strength of inter-molecular interactions between functional groups at the interfaces.

36 MATERIALS SCIENCE↗

Investigation of North American Vegetation Variability under Recent Climate: A Study Using the SSiB4/TRIFFID Biophysical/Dynamic Vegetation Model

Recent studies have shown that current dynamic vegetation models have serious weaknesses in reproducing the observed vegetation dynamics and contribute to bias in climate simulations. This study intends to identify the major factors that underlie the connections between vegetation dynamics and climate variability and investigates vegetation spatial distribution and temporal variability at seasonal to decadal scales over North America (NA) to assess a 2-D biophysical model/dynamic vegetation model's (Simplified Simple Biosphere Model version 4, coupled with the Top-down Representation of Interactive Foliage and Flora Including Dynamics Model (SSiB4/TRIFFID)) ability to simulate these characteristics for the past 60 years (1948 through 2008). Satellite data are employed as constraints for the study and to compare the relationships between vegetation and climate from the observational and the simulation data sets. Trends in NA vegetation over this period are examined. The optimum temperature for photosynthesis, leaf drop threshold temperatures, and competition coefficients in the Lotka-Volterra equation, which describes the population dynamics of species competing for some common resource, have been identified as having major impacts on vegetation spatial distribution and obtaining proper initial vegetation conditions in SSiB4/TRIFFID. The finding that vegetation competition coefficients significantly affect vegetation distribution suggests the importance of including biotic effects in dynamical vegetation modeling. The improved SSiB4/TRIFFID can reproduce the main features of the NA distributions of dominant vegetation types, the vegetation fraction, and leaf area index (LAI), including its seasonal, interannual, and decadal variabilities. The simulated NA LAI also shows a general increasing trend after the 1970s in responding to warming. Both simulation and satellite observations reveal that LAI increased substantially in the southeastern U.S. starting from the 1980s. The effects of the severe drought during 1987-1992 and the last decade in the southwestern U.S. on vegetation are also evident from decreases in the simulated and satellite-derived LAIs. Both simulated and satellite-derived LAIs have the strongest correlations with air temperature at northern middle to high latitudes in spring reflecting the effect of these climatic variables on photosynthesis and phenological processes. Meanwhile, in southwestern dry lands, negative correlations appear due to the heat and moisture stress there during the summer. Furthermore, there are also positive correlations between soil wetness and LAI, which increases from spring to summer. The present study shows both the current improvements and remaining weaknesses in dynamical vegetation models. It also highlights large continental-scale variations that have occurred in NA vegetation over the past six decades and their potential relations to climate. With more observational data availability, more studies with differentmodels and focusing on different regions will be possible and are necessary to achieve comprehensive understanding of the vegetation dynamics and climate interactions.

climate variability↗

A Simplified Building Modeling Approach for Identifying Whole Building Retrofits

Building Energy Modeling (BEM) is an effective strategy for optimizing new and retrofit building design, evaluating its energy savings potential and rating its energy performance. However, because of the complexity and expense of modeling, only a small percentage of buildings are simulated. Over 80% of buildings are <25,000 ft2, and the cost associated with BEM can be a big deterrent for reaching this subsector, which usually ends up complying with energy codes and qualifying for incentives using prescriptive measures or generalized design guides. Similarly, efficiency considerations for small building retrofits are often identified through deemed measures or Technical Reference Manuals, which though a scalable and convenient approach, can limit innovation in design and optimization of measures. Simplification of the modeling process, where appropriate, can lead to increased energy savings and more informed decision making. This paper will discuss the development of a ruleset for a simplified approach based on the Performance Rating Method (PRM) contained in ASHRAE Standard 90.1. The approach aims to simplify and lower the cost of the energy modeling process in a controlled and documented manner. An anticipated outcome is an increased use of BEM and its effectiveness in the design, retrofit and operation of commercial buildings. In addition, simplification of the modeling process will result in fewer errors from misinterpretations of both program requirements and program intent in simulation software. The paper will discuss the need and advantages of a simplified modeling approach for whole building retrofits and the technical process for achieving the same.

Goel, Supriya↗

Development and Validation of SAM Multi-dimensional Flow Model for Thermal Mixing and Stratification Modeling

Thermal mixing and stratification in large pools or enclosures are very important phenomena that are critical to nuclear reactor safety. Because of the wide ranges of time and length scales associated with such phenomena, accurate modeling and simulation of thermal mixing and stratification remain as the key unresolved, challenging problems for reactor transient analyses. In traditional system analysis codes, simplified zero-dimensional (0-D) models are widely used for their high numerical efficiency, but they generally suffer from very limited prediction accuracies or range of applicability. Like traditional system analysis codes, the current version of the SAM code has implemented such simplified 0-D and one-dimensional mixing models. On the other hand, high-resolution Computational Fluid Dynamics (CFD) tools are often used to model complex thermal mixing and stratification phenomena. They are, however, generally numerically expensive, and they require large amounts of computational resources. It is therefore desirable to implement advanced and efficient thermal mixing and stratification modeling capabilities embedded in a system analysis code. This approach will improve the accuracy of reactor safety analyses when thermal mixing and stratification are involved, and also avoid using the large computational resources needed for high-resolution CFD analysis. Currently, with the support of the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation program, an effort has been launched to develop and implement a multi-dimensional flow model in the system analysis code SAM, and demonstrate its applications to model thermal mixing and stratification phenomena in large enclosures. The main outcomes of this research and development activity are summarized in this report, which presents an attempt to include a built-in advanced multi-dimensional flow model in a system analysis code with the focus on overcoming the simulation challenges of thermal mixing and stratification phenomena. In this report, we start with the introduction of existing SAM code capabilities to simulate thermal mixing and stratification phenomena, which is followed by a short summary of the multi-dimensional model implemented in the SAM code, including both the physical model and the Finite Element Method code implementation. In this study, two options were implemented in the SAM code to model turbulent flows: a relatively simple built-in turbulence model and an interface to accept externally computed turbulent viscosities (e.g., from a high- resolution CFD simulation). Code validation studies on this newly added capability were then carried out to compare SAM simulation results with experimental data from the SUPERCAVNA facility, which was designed to study the complex flow recirculation and thermal stratification phenomena relevant to sodium fast reactor designs. In this study, one transient and two steady-state test cases were used for code validation. Different approaches have been used to model the complex turbulence flow fields in the SUPERCAVNA facility. A highly simplified zero-equation turbulence model was first used, but it was determined that it is too simple to capture the complex turbulence flow fields in these test cases. Subsequently, the code validation continued with the use of turbulent viscosity data from high-resolution STAR-CCM+ CFD simulations to improve the accuracy of the results. Using this approach, the SAM simulation results showed very good agreement with both the SUPERCAVNA experimental data and STAR-CCM+ simulation results. In this report, we demonstrate the development, implementation, and successful validation of a multi-dimensional flow model in the SAM code, which aims to improve the simulation accuracy for complex thermal mixing and stratification phenomena. Lessons have also been learned, including that in cases where the flow fields are not well predicted by the zero-equation model, the iinput of turbulent viscosities from an external source can enhance the overall predictive capabilities needed to accurately capture complex thermal-hydraulic phenomena. Therefore, future research will be needed to further improve the code’s capabilities, such as by developing a more efficient and robust approach to capture the turbulence effects in the SAM code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Decoding the formation of hammerhead ion populations observed by Parker Solar Probe

Context. In situ observations by the Parker Solar Probe (PSP) have revealed new properties of the proton velocity distributions (VDs), including hammerhead features that suggest a non-isotropic broadening of the beams. Aims. The present work proposes a very plausible explanation for the formation of hammerhead proton populations through the action of a proton firehose-like instability triggered by the proton beam. Methods. We investigated a self-generated firehose-like instability driven by the relative drift of ion populations using a simplified moment-based quasi-linear (QL) theory. While simpler and faster than advanced numerical simulations, this toy model provided rapid insights and concisely highlighted the role of plasma micro-instabilities in relaxing the observed anisotropies of particle VDs in the solar wind and space plasmas. Results. The QL theory proposed here shows that the resulting transverse waves are right-hand polarized and have two consequences on the protons: (i) They reduce the relative drift between the beam and the core, but above all, (ii) they induce a strong perpendicular temperature anisotropy specific to the observed hammerhead ion beam. Moreover, the long-run QL results suggest that these hammerhead distributions are rather transitory states that are still subject to relaxation mechanisms, in which instabilities such as the one discussed here are very likely involved. This foundational work motivates future detailed studies using advanced methods.

Shaaban, Shaaban M. (ORCID:000000030465598X)↗

Peculiar velocity estimation from kinetic SZ effect using deep neural networks

ABSTRACT The Sunyaev–Zel’dolvich (SZ) effect is expected to be instrumental in measuring velocities of distant clusters in near future telescope surveys. We simplify the calculation of peculiar velocities of galaxy clusters using deep learning frameworks trained on numerical simulations to avoid the independent estimation of the optical depth. Images of distorted photon backgrounds are generated for idealized observations using one of the largest cosmological hydrodynamical simulations, the Magneticum simulations. The model is tested to determine its ability of estimating peculiar velocities from future kinetic SZ observations under different noise conditions. The deep learning algorithm displays robustness in estimating peculiar velocities from kinetic SZ effect by an improvement in accuracy of about 17 per cent compared to the analytical approach.

Wang, Yuyu (ORCID:0000000202458547)↗

The vibration of a box-type structure. II - Response to a travelling pressure wave.

A finite element method is formulated for determining the transient response of a box-type structure to a traveling, arbitrarily shaped pressure wave. The method is illustrated by considering an example of practical concern - the sonic boom. The acceleration-time histories of a closed box are compared with those obtained experimentally from a simulated boom. Satisfactory agreement is obtained with only four rectangular elements per individual face and a simplified loading of the box.

Popplewell, N.↗