Simple Beam Model Research Articles

Multiple-source models for electron beams of a medical linear accelerator using BEAMDP computer code

AimThe aim of this work was to develop multiple-source models for electron beams of the NEPTUN 10PC medical linear accelerator using the BEAMDP computer code. BackgroundOne of the most accurate techniques of radiotherapy dose calculation is the Monte Carlo (MC) simulation of radiation transport, which requires detailed information of the beam in the form of a phase-space file. The computing time required to simulate the beam data and obtain phase-space files from a clinical accelerator is significant. Calculation of dose distributions using multiple-source models is an alternative method to phase-space data as direct input to the dose calculation system. Materials and methodsMonte Carlo simulation of accelerator head was done in which a record was kept of the particle phase-space regarding the details of the particle history. Multiple-source models were built from the phase-space files of Monte Carlo simulations. These simplified beam models were used to generate Monte Carlo dose calculations and to compare those calculations with phase-space data for electron beams. ResultsComparison of the measured and calculated dose distributions using the phase-space files and multiple-source models for three electron beam energies showed that the measured and calculated values match well each other throughout the curves. ConclusionIt was found that dose distributions calculated using both the multiple-source models and the phase-space data agree within 1.3%, demonstrating that the models can be used for dosimetry research purposes and dose calculations in radiotherapy.

Two-Dimensional Orthotropic Plate Analysis for an Integral Thermal Protection System

plate theory. The two-dimensional plate deformations are used to obtain local integrated thermal protection system stresses through reverse homogenization. In addition, simple beam models are used to obtain local facesheet deformations and stress. The local stresses and deflections computed using the analytical method were compared with those from a detailed finite element analysis of the integrated thermal protection system. For the integrated thermal protection system examples considered in this paper, the maximum error in stresses and deflections is less than 5%. This was true for both mechanical and thermal loads acting on the integrated thermal protection system.

Low-force AFM nanomechanics with higher-eigenmode contact resonance spectroscopy **Publication of NIST, an agency of the US government, not subject to copyright.

Atomic force microscopy (AFM) methods for quantitative measurements of elastic modulus on stiff (>10 GPa) materials typically require tip–sample contact forces in the range from hundreds of nanonewtons to a few micronewtons. Such large forces can cause sample damage and preclude direct measurement of ultrathin films or nanofeatures. Here, we present a contact resonance spectroscopy AFM technique that utilizes a cantilever’s higher flexural eigenmodes to enable modulus measurements with contact forces as low as 10 nN, even on stiff materials. Analysis with a simple analytical beam model of spectra for a compliant cantilever’s fourth and fifth flexural eigenmodes in contact yielded good agreement with bulk measurements of modulus on glass samples in the 50–75 GPa range. In contrast, corresponding analysis of the conventionally used first and second eigenmode spectra gave poor agreement under the experimental conditions. We used finite element analysis to understand the dynamic contact response of a cantilever with a physically realistic geometry. Compared to lower eigenmodes, the results from higher modes are less affected by model parameters such as lateral stiffness that are either unknown or not considered in the analytical model. Overall, the technique enables local mechanical characterization of materials previously inaccessible to AFM-based nanomechanics methods.

Diversity between shell-like and beam-like regions for a cantilever cylindrical shell under follower forces

The effect of length and thickness on dynamic stability analysis of cantilever cylindrical shells under follower forces is addressed. Beck's, Leipholz's, and Hauger's problems were solved for cylindrical shells with different length-to-radius and thicknesses-to-radius ratios using the Galerkin method. First-order shear theory was used, and rotary inertias were considered in deriving the differential equations. Critical circumferential and longitudinal mode numbers and loads were evaluated for each case. Diagrams containing nondimensional load parameters vs. length and thickness parameters were plotted for each problem. For some shells with small length-to-radius ratios, flutter occurred in high longitudinal mode numbers where the first-order shear theory may not suffice to accurately evaluate the deformations. However, for long and moderately thick shells, there are ranges in which the shell can be analyzed using the simplified equivalent beam model.

Optimal Real-Time Control of Flexible Rack Feeders Using the Method of Integrodifferential Relations

AbstractRack feeders are of high practical importance as automated conveying systems. In this paper, control-oriented models are derived for an experimental setup representing the structure of a typical high bay rack feeder. On the basis of these models, feedforward control strategies are designed. The rack feeder is a viscoelastic structure consisting of two identical flexible beams which are attached to a horizontally movable carriage. The beams are rigidly connected at their tip by a pulley block which is necessary for the vertical positioning of a payload. To develop a real-time applicable control algorithm, a frequency analysis is performed for the original double-beam structure. As a consequence, a simplified Bernoulli beam model is derived with specific boundary conditions. The control objective under consideration is the positioning of the flexible beam structure at a desired position in such a way that the terminal mechanical energy stored in the beam is minimized. A modification of the Galerkin method which is based on an integrodifferential approach and a suitable finite element technique are employed to describe the viscoelastic structural vibrations and to design optimal control strategies. Results of numerical simulations are presented and compared with measured data.

Response of Long Sculpted Wire Bonds to Vibrational Excitation

The pitch of wire bond connections is decreasing to meet the need for higher interconnect densities, while at the same time, the ratio of wire length to diameter is increasing, which lowers the mechanical resonant frequency of the wire. In many applications in which MEMS sensors are coupled with ASIC front end electronics, the bonded wires can be subjected to a wide frequency spectrum of mechanical vibrations. One potential consequence is that the parasitic capacitances of the sensor could vary dynamically at a magnitude comparable to that of the sensor signal. In extreme cases, intermittent shorts or fatigue failures of the wire bonds could occur. A recent paper by Barber et. al, showed that wire bonds carrying alternating currents in a strong magnetic field could suffer fatigue failure.[1] Their analysis and experiments focused on simple loop geometries. In many applications, more complex wire bond geometries are used to minimize loop height and obtain dense wiring in stacked chip configurations. These geometries give rise to many more vibration modes with unique resonant frequencies and displaced shapes. We have used simple analytical beam models in conjunction with finite element models (FEM) to study various wire bond configurations subject to mechanical vibratory excitation. We focused on the effects of overall wire length and geometric shape on resonant modes. The finite element models were also used to calculate the capacitance between adjacent wires subject to mechanical excitation at one or more of their resonant frequencies. We show that there is an apparent shift in the time averaged capacitive coupling that increases with increasing vibration amplitude.

J-integral for delaminated beam and plate models

In this work the J-integral is applied to calculate the energy release rate in simple beam and plate models. Four examples are considered: the mode-I double-cantilever beam, the mode-II end-notched flexure, the mixed-mode I/II single-leg bending specimens and a delaminated plate with simply-supported edges, respectively. In each example the details of calculation are given, in the latter case the distribution of the energy release rate along the crack front is calculated. While for delaminated beams the literature presents the energy release rates in numerous studies, the J-integral calculation is not trivial in theses cases. Moreover for delaminated bent plates the application of the J-integral is not documented. It is shown that considering the classical plate theory there are serious limitations to calculate representative energy release rates.

Simple Beam Model to Estimate Leakage in Longitudinally Cracked Pressurized Pipes

Losses from water distribution systems are reaching alarming levels in many cities throughout the world. Leakage is often the principal cause of water loss because of aging and deterioration of these systems, and pressure has been verified to assume a key-role in water-loss management. This paper presents a simple analytical model based on a beam with elastic constraints to estimate the leak area (from which the leakage is then estimated) in longitudinally cracked pressurized pipes and to evaluate the effect of pressure on the opening area of the crack. The model is calibrated on the results of a three-dimensional finite-element analysis and then validated by experimental results. The validation has been carried out for a wide range of pipes made of different materials (PVC, cast iron, asbestos-cement, and steel) with radii ranging from 27.5 to 110 mm, thicknesses from 1.5 to 12 mm, and crack lengths from 50 to 200 mm. The beam model, notwithstanding its simplicity, provides reliable leakage evaluations in longitudinally cracked pressurized pipes.

Aeroelastic Analysis of a Hingeless Rotor Using a Dynamic Wake Model

Aeroelastic Analysis of a Hingeless Rotor Using a Dynamic Wake Model

Response Modification Approach for Safe Extension of Bridge Life

A large portion of highway bridges in the United States are reaching or have reached their intended design lives. To avoid replacing a large number of bridges simultaneously, methodologies to safely extend their lives are important to help avoid high replacement costs and to schedule bridge replacement over a longer time window. This paper proposes an approach to extend the fatigue life of vulnerable steel bridges through a response modification apparatus, consisting of a mechanical amplifier and a response modification device, which provides supplemental stiffness and damping to the bridge. Because of the relatively small deflections encountered under typical service loads, the use of a mechanical amplifier allows for a smaller apparatus and enables a more efficient device to provide adequate response modification forces to the bridge. Herein, the use of a scissor jack as the mechanical amplifier is proposed for use in bridge applications, and its utility in concert with a passive stiffness device is demonstrated by application to a simple beam structure. Reductions in moment ranges of 37% and safe life extensions of 300% are achieved on a simple beam model with the proposed response modification apparatus.

A numerically validated probabilistic model of a simplified total hip replacement construct

Hip replacement constructs are paradigms of uncertain systems, and as such are suited to the application of probabilistic methods to assess their structural integrity. In order to gain confidence in a probabilistic model, it would be useful to verify the findings with experimental data; however, this is difficult to achieve in practice because of the exhaustive number of parameter combinations that need to be tested. As an alternative to experimental testing, benchmarking can be carried out provided a known analytical solution is available. To this end, a simplified 2D two-beam model of the femoral part of a total hip replacement construct was utilised to analyse uncertainties and variability in the construct as it is subjected to load. The use of a simplified model enabled geometric parameters to be investigated; these are commonly not considered in probabilistic models due to the increased complexity involved. Analytical and finite element representations of the model were developed and compared. The probabilistic study used the Monte Carlo simulation technique and the first-order reliability method to look at the inducible displacement of a hip implant, a phenomenon that has been linked to the most common cause of hip implant failure, aseptic loosening. Excellent correlation was observed between the analytical and probabilistic solutions, and it was shown that probabilistic approaches could efficiently predict the response of the simplified beam model while readily identifying the parameters most likely to compromise the structural integrity of the construct.

Damage Detection Analysis of Reinforced Concrete Simple Beams Based on Three Dimensional Curvature Mode

The damage detection based on curvature mode was discussed in this paper, a three dimensional reinforced concrete simple beam model was established by finite element software, two models of before and after damage were compared also. The results showed that, before and after damage, the natural frequency, vibration modes and displacement modes had small difference, yet the curvature modes of model had great change in the location of damage.

Alzheimer's Aβ(1-40) Amyloid Fibrils Feature Size-Dependent Mechanical Properties

Amyloid fibrils are highly ordered protein aggregates that are associated with several pathological processes, including prion propagation and Alzheimer's disease. A key issue in amyloid science is the need to understand the mechanical properties of amyloid fibrils and fibers to quantify biomechanical interactions with surrounding tissues, and to identify mechanobiological mechanisms associated with changes of material properties as amyloid fibrils grow from nanoscale to microscale structures. Here we report a series of computational studies in which atomistic simulation, elastic network modeling, and finite element simulation are utilized to elucidate the mechanical properties of Alzheimer's Aβ(1-40) amyloid fibrils as a function of the length of the protein filament for both twofold and threefold symmetric amyloid fibrils. We calculate the elastic constants associated with torsional, bending, and tensile deformation as a function of the size of the amyloid fibril, covering fibril lengths ranging from nanometers to micrometers. The resulting Young's moduli are found to be consistent with available experimental measurements obtained from long amyloid fibrils, and predicted to be in the range of 20–31 GPa. Our results show that Aβ(1-40) amyloid fibrils feature a remarkable structural stability and mechanical rigidity for fibrils longer than ≈100 nm. However, local instabilities that emerge at the ends of short fibrils (on the order of tens of nanometers) reduce their stability and contribute to their disassociation under extreme mechanical or chemical conditions, suggesting that longer amyloid fibrils are more stable. Moreover, we find that amyloids with lengths shorter than the periodicity of their helical pitch, typically between 90 and 130 nm, feature significant size effects of their bending stiffness due the anisotropy in the fibril's cross section. At even smaller lengths (⪅50 nm), shear effects dominate lateral deformation of amyloid fibrils, suggesting that simple Euler-Bernoulli beam models fail to describe the mechanics of amyloid fibrils appropriately. Our studies reveal the importance of size effects in elucidating the mechanical properties of amyloid fibrils. This issue is of great importance for comparing experimental and simulation results, and gaining a general understanding of the biological mechanisms underlying the growth of ectopic amyloid materials.

Development of piezoelectric actuated mechanism for flapping wing micro-aerial vehicle applications

A piezoelectric actuated two-bar two-flexure motion amplification mechanism for flapping wing micro-aerial vehicle application has been investigated. fr*A as an optimisation criterion has been introduced where fr is its fundamental resonant frequency of the system and A the vibration amplitude at the wing tip, or the free tip deflection at quasi-static operation. This criterion can be used to obtain the best piezoelectric actuation mechanism with the best energy transmission coefficient for flapping wing micro-aerial vehicle applications, and is a measurable quantity therefore can be compared with experimental results. A simplified beam model has been developed to calculate the fundamental resonant frequency for the full system consisted of piezoelectric actuator, motion amplification mechanism and the attached wing and the calculated values were compared with the measured results. A clear trend of the criteria fr*A varying with the two-flexure dimension, stiffness and setting angle have been obtained from the measured data and also the predicted results as a guideline for optimal design of the system.

INFLUENCE OF OBJECTIVE FUNCTIONS IN STRUCTURAL DAMAGE IDENTIFICATION USING REFINED AND SIMPLE MODELS

The most usual approach for solving damage identification problems is the use of the finite element (FE) model updating method. To apply the method, a minimization of an objective function measuring the fit between measured and model predicted data is performed. Then, the success of the procedure depends strongly on the accuracy of the FE model and the choice of a suitable objective function. Although detailed FE models provide an accurate means for calculating the dynamic response of the structure, their size and complexity involve a large number of parameters to be updated and a high computational cost. In order to shorten the computational time, more simplified and practical models able to model the global dynamic response of the structure accurately would be desirable. Furthermore, working with several objective functions instead of only one would increase the robustness and performance of the procedure. In this paper, a multi-objective simple beam model is proposed and compared with a more refined model based on plane elements. Furthermore, in the multi-objective framework, different combinations of objective functions are studied. The reliability and effectiveness of the proposed model has been evaluated in a damage detection problem of a reinforced concrete frame experimentally tested under different levels of damage.

Electron beam – plasma system with the return current and directivity of its X-ray emission

<i>Aims. <i/>An evolution of the electron distribution function in the beam-plasma system with the return current is computed numerically for different parameters. The X-ray bremsstrahlung corresponding to such an electron distribution is calculated and the directivity of the X-ray emission is studied.<i>Methods. <i/>For computations of the electron distribution functions we used a 3-D particle-in-cell electromagnetic code. The directivity of the X-ray emission was calculated using the angle-dependent electron-ion bremsstrahlung cross-section.<i>Results. <i/>It was found that the resulting electron distribution function depends on the magnetic field assumed along the electron beam propagation direction. For small magnetic fields the electron distribution function becomes broad in the direction perpendicular to the beam propagation due to the Weibel instability and the return current is formed by the electrons in a broad and shifted bulk of the distribution. On the other hand, for stronger magnetic fields the distribution is more extended in the beam-propagation direction and the return current is formed by the electrons in the extended distribution tail. In all cases, the anisotropy of the electron distribution decreases rapidly due to fast collisionless processes. However, the magnetic field reduces this anisotropy decrease. The X-ray directivity shows the same trend and it is always closer to the isotropic case than that in a simple beaming model.

Simulation of photon energy spectra from Varian 2100C and 2300C/D Linacs: Simplified estimates with PENELOPE Monte Carlo models

Photon energy spectra of Varian Clinac 2100C and 2300C/D treatment heads were calculated with PENELOPE-2006, using simplified Monte Carlo models. These spectra constitute the basis of beam models used for the calculation of correction factors required for the Austrian absorbed dose to water primary standard. To validate the models, simulated depth dose curves in water and calculated radiation quality factors ( TPR 20,10) were compared with ionization chamber measurements. In addition the results are discussed in context with detailed Monte Carlo studies from the literature in reference to mean spectral photon energy and degree of equivalence between simulated and calculated percentage-depth-dose curves. Mean absolute deviations between measured and simulated depth dose curves smaller than 2.0% were found. The differences between simulation and measurement of TPR 20,10 were smaller than 2.6%. This shows the usefulness of the simplified beam models in applications since their dependence on energy spectra and radiation quality is small in comparison to its energy range.

SU‐FF‐T‐418: Development of An Easy to Commission Electron Beam Model Using Highly Accurate Fluence Benchmarks From Full Monte Carlo Treatment Head Simulations and Measurements

Purpose: Development of an easy to commission electron beam model using highly accurate fluence benchmarks from Monte Carlo treatment head simulations and measurements. Method and Materials: A simple electron beam model consists of the key treatment head components: a circular primary source for electrons, a disk representing the secondary scattering foil and a ring representing the monitor chamber sidewall. The primary source accounts for scatter in the exit window and primary foil. The angular distribution of the primary source is chosen to match the lateral dose profiles from measurements with only the primary foil in the treatment head. The energy spectrum is derived from unfolding measured depth dose curves from large fields. The angular distribution of the primary source is broadened analytically using accurate scattering theory to account for the secondary scattering foil. The lateral extent of the beam is restricted to account for the collimation by the sidewall of the monitor chamber. Phase space data generated from the simple electron beam model is used with the EGSnrc user code BEAMnrc to simulate the secondary collimators and scattering of the electrons in air. Results: Primary foil simulations with the beam model, with no secondary scattering foil or monitor chamber in the beam line, match measured dose profiles of large fields within 1%–2%. Fluence profiles were in comparable agreement with the benchmark. Energy spectra were cleanly unfolded from measured depth dose curves from large fields. Peak energy was within 0.05 MeV of the fluence benchmark. Preliminary results for the full clinical beam with the secondary foil and chamber in place are promising. Conclusions: The influence of the different treatment head components on the beam were accurately determined with the detailed fluence benchmarks, which proved instrumental in development of this beam model. Research sponsored by NIH R01_CA104777.

SU-FF-T-629: XBeam: An Accurate, Easily Commissioned Radiotherapy X-Ray Beam Model

Purpose: To develop a simple x-ray beam model which is accurate in both fluence and dose and easy to commission, validating against recently developed gold standard Monte Carlo fluence benchmarks for Siemens and Varian clinical beams. Method and Materials: Dose distributions and relative output factors were measured in water for 6 and 18 MV clinical beams for 1–40 cm wide square fields. A compact ion chamber and photon diode was used to measure the profiles, a parallel-plate chamber for percentage depth dose (PDD). The beam model consists of three sources: a spot and a ring for photons and a ring for electrons. The free parameters were adjusted based on select measurements. The central axis energy distribution was sampled from the thin-target Schiff bremsstrahlung spectrum, and attenuated through a flattener of thickness adjusted to match the measured PDD in small fields. Particles statistical weights were adjusted at different positions to match the measured profiles. Analytical sampling procedures were developed to generate the full phase space above the jaws. Results: Spectral reconstruction resulted in a good match to the measured small field depth dose curves for the Siemens beams. The energy distribution is in good agreement with the fluence benchmark. XBeam fluence and dose along the diagonal of the largest field for the Siemens beams are in good agreement with measurements out to 25 cm. An overestimate outside of the penumbral region will be improved by adjusting the spot size. Comprehensive comparisons to fluence benchmarks for Siemens and Varian beams are in progress and will be presented. Conclusion: XBeam has a minimum number of free parameters, which are fitted to dose measurements within realistic limits. Preliminary results indicate the model will be easy to commission and accurate in both fluence and dose. The fluence benchmarks greatly facilitated development of the beam model.

Seasonal Thermal Displacements of Gravity Dams Located in Northern Regions

Seasonal temperature displacements are an important component of the total displacements recorded by pendulum measurements at gravity dams located in northern regions. A hybrid dam displacement model is presented in this paper to interpret these displacements and extrapolate the response for an extreme thermal event not yet experienced by the dam. The hybrid model uses a simplified deterministic structural dam representation with beam elements in complement to a hydrostatic seasonal time (HST) statistical displacement model. Comparisons are first established between 1D heat transfer analyses of typical gravity dam sections, and 2D finite-element (FE) analyses. Thermomechanical displacements are compared to show the validity of the proposed simplified deterministic beam model for typical dams. A case study of an actual 40 m gravity dam located in Quebec, Canada is then presented. It is shown that the deterministic model can be calibrated using the pendulum displacements and the HST model. The calibrated deterministic model is then used to extrapolate the displacement response for extreme thermal events not yet experienced by the dam. The proposed methodology represents a simple extension of the gravity method, widely used to verify gravity dam stability, as a first step to interpret recorded pendulum displacements and set appropriate warning and alarm levels on a rational basis before developing 2D and 3D thermomechanical FE deterministic dam models that require a lot of resources and expertise to be used effectively.