Gradient Indices Research Articles

A semi-analytical methodology for predicting the vibroacoustic response of functionally graded nanoplates under thermal loads

In this investigation, the analysis of the nonlinear vibroacoustic and sound transmission loss behaviors of nanoplates made of functionally graded materials considering the nonlocal strain gradient theory is presented. It is presumed that the properties of the functionally graded nanoplate are in the form of the simple power law scheme and continuous along the thickness, under nonlinear temperature rise and incident oblique acoustic wave as well as the first-order shear deformation theory. For this purpose, applying Hamilton’s principle, the nonlinear partial differential equations of motion are derived by the displacement field function approach and by considering the von Kármán nonlinear strain-displacement relations. To solve the equations, using the Galerkin method, the nonlinear partial differential equations of motion lead to the Duffing equation. Then, applying the homotopy analysis method, the equation of the transverse movement of the nanoplate is solved semi-analytically to obtain the nonlinear frequencies. Lastly, the nonlinear vibration and acoustic response of functionally graded nanoplate are investigated by considering the variation of the significant factors such as material gradient indices, nonlocal parameters, length scale parameters, aspect ratio, dimensionless amplitude, nonlinear temperature changes, and sound characteristics of the functionally graded nanoplate.

Treatment plan quality for stereotactic treatment of multiple cranial metastases: Comparison of C-arm and O-ring treatment platforms

C-arm linacs have been used widely to treat multiple cranial metastases using stereotactic radiosurgery (SRS). A new generation of O-ring linacs offer several workflow advantages when compared to C-arm platforms. However, O-ring linacs are not able to employ couch rotations for noncoplanar beams used in SRS treatments. This study was conducted in order to simulate further possible developments of O-ring treatment units by assessing their geometrical efficiency. In this work we compare the plan quality for C-arm versus an O-ring platform including metrics that are relevant to SRS for multiple metastases. The comparison is conducted by incorporating tilted arcs on the O-ring platform therefore introducing noncoplanarity.Total 40 patients previously treated for SRS with 20 Gy single fraction were replanned for C-arm with a standard noncoplanar 5-arc arrangement and O-ring with both coplanar and noncoplanar beams. For the O-ring plans, we considered a default 3-arc coplanar arrangement, as well as 3- and 5-arc arrangements with arcs tipped up to 10 degrees from the axial plane. Target coverage, organ-at-risk (OAR) doses, monitor unit (MU) efficiency, conformity and gradient indices were assessed for all plans.For most metrics the O-ring geometries, even the coplanar arrangement, produced statistically comparable results to the C-arm. Small but significant differences were found for the 3 arc O-ring for PTV: D90%, D2% and MU/Gy and for the 5 arc O-ring at D2% when both were compared to the C-arm. Cumulative dose volume histograms (DVHs) for normal brain showed a cross-over between the C-arm and coplanar O-ring geometry at a low dose (2.3 ± 1.8 Gy), with O-ring associated with higher volumes above this cross-over dose. However, no statistical difference was seen in the brainstem, optic pathway and volumes of normal brain receiving 12 Gy or 20 Gy.This study has found that O-ring geometry linacs can produce SRS plans of comparable quality to those from a C-arm for multiple cranial metastases.

The novel Vogel's approximation method integrated with a random forest algorithm in the vibration analysis of a two-directional functionally graded taper porous beam: Assessment

A functionally graded material is a class of composite materials characterized by gradual variations in composition and microstructure, which further induces the respective changes in the material properties. This study focuses on evaluating the vibration behavior of two directional functionally graded taper porous beams (FGTPB). This approach adopts a rectangular cross-section in order to deal with the challenges related to fluctuating material characteristics and geometric tapering in both thickness and width dimensions. The research employs a novel approach that merges Vogel's approximation technique with the Random Forest algorithm, an approach that has not been used in analyzing structural vibrations, establish boundary conditions and solve equations of motion. Comparative results of the suggested beam theory with the existing literature on FGTPB materials such as alumina and SUS304 at various taper, porosity, gradient and width ratios verified it. The material gradation and porosity developed a uniform pattern in the first three modes of fundamental frequencies. Higher gradient indices increased the rigidity and natural frequencies of the beams whereas the porosity index decreased the rigidity, resulting in lower natural frequencies. By combining Vogel's approximation method with machine learning techniques, the study improved vibration behavior analysis in FGTPB. The disciplines of materials and structural engineering are significantly impacted by this.

On thermo-mechanical buckling of porous bi-directional functionally graded plates using isogeometric analysis

The combined thermal and mechanical loads usually lead to buckling failure of key structures in various engineering fields. It is found that porous functionally graded structures can be used to reduce and evenly prevent potential impact on the stability of structures from extremely high temperature loads. In this paper, we employ the isogeometric analysis (IGA) method to investigate the thermo-mechanical coupling buckling behaviors of porous bi-directional functionally graded (PB-FGM) plates with porosity. The material properties such as Young's modulus, Poisson's ratio, and thermal expansion coefficient are assumed to be linearly dependent on the x-axial and z-axial coordinates. Such a gradient property can be easily realized by changing the porosity distribution. Based on the first-order shear deformation theory (FSDT), the thermo-mechanical buckling behaviors of PB-FGM rectangular and circular plates under combined thermal and mechanical loads are numerically studied. This paper elucidates the mechanical mechanism through which gradient indexes, aspect ratios, loading types, and boundary conditions influence the critical thermo-mechanical coupling-induced buckling temperature.

Size-dependent vibration analysis of porous 3D-FG microshells in complex thermal environments using a neural network enhanced finite element model

This work aims to investigate the vibration behavior of porous three-directional functionally graded (3D-FG) microshells in thermal environments, where both mechanical and thermal material properties vary along three spatial directions following a power-law distribution, based on the modified couple stress theory (MCST). An isoparametric thermal element is employed for uncoupled heat conduction analysis, followed by dynamic analysis using a penalty solid element with three translation degrees of freedom (DOFs) and three rotation DOFs per node. However, due to the strong nonlinearity of the temperature field in 3D-FG microshells, obtaining exact temperature values at integration points in dynamic analysis requires a pretty dense mesh of the solid element. To overcome this issue, a back propagation (BP) neural network is utilized to predict the temperature field for various gradient indexes, enhancing the efficiency and precision of temperature distribution calculation. Numerical results demonstrate the effectiveness of the neural network enhanced finite element model. Furthermore, the effects of the material length scale parameter (MLSP), temperature difference, and gradient indexes on the natural frequencies are investigated. It is shown that higher structural stiffness weakens the impact of temperature difference on the frequency.

Analytical solution on magneto-electro-elasto-hygrothermal coupling in rotating functionally graded piezoelectric/piezomagnetic cylinders on Winkler elastic foundation

This study focuses on the multi-field coupling phenomena in a rotating functionally graded piezoelectric/piezomagnetic (FGPEPM) hollow cylinder under magneto-electro-elasto-hygrothermal loading. The cylinder is assumed to be infinitely long and on a Winkler elastic foundation. The hygrothermo parameter, magneto-electro-elastic properties, hygrothermal expansion, and density within the FGPEPM cylinder follow power laws with different gradient indexes along its thickness. Analytical solutions for the distributions of radial displacement, stresses, electric potential, magnetic potential, temperature, and moisture are derived by solving magneto-electro-elasto-hygrothermal coupling differential equations with appropriate boundary conditions. Validation against the existing analytical results for simplified models confirms the effectiveness of the present analytical solution. Numerical analyses further explore the effects of gradient indexes, rotational velocity, and elastic foundation stiffness on the multi-field coupling behavior of the FGPEPM cylinder. The findings provide valuable insights for designing multi-field coupling characteristics for FGPEPM materials.

Nonlinear free vibration analysis of multi-directional functionally graded porous sandwich plates

Multi-directional functionally graded materials (MFGMs) have attracted significant research attention due to their advantages over one-directional FGMs. In MFGM structures, material properties can be tailored to grade in the required direction, overcoming practical problems like excessive temperature gradients or extreme deflections. This paper aims to investigate the nonlinear free vibration of MFG porous sandwich plates to improve their application in sandwich structures. The two outer layers of the plates are composed of three-directional functionally graded material (3D-FGM), with a bi-directional functionally graded material (2D-FGM) core layer. Additionally, the porosity distribution within the material matrix is assumed to be either even or uneven across the plate thickness. A higher-order finite element model based on Shi's plate theory and the von Kármán assumption is developed. The nonlinear free vibration frequencies are determined through the maximum vibrational amplitude using an iterative algorithm with a displacement control strategy. The accuracy and effectiveness of the proposed model are demonstrated through a comparison with published data. The results show that the vibration response is significantly influenced by various parameters. Specifically, increasing the material gradient indexes in the thickness direction enhances the frequency ratio, while increasing the gradient indexes in the length and width directions reduces it. Higher porosity coefficients in the core layer decrease the frequency ratio, whereas higher pore coefficients in the outer layers increase it. The additional knowledge gained from this study can help with future analysis and design procedures related to the nonlinear responses of these complex structures.

Dosimetric comparison of HyperArc and InCise MLC-based CyberKnife plans in treating single and multiple brain metastases.

This study aimed to compare the dosimetric attributes of two multi-leaf collimator based techniques, HyperArc and Incise CyberKnife, in the treatment of brain metastases. 17 cases of brain metastases were selected including 6 patients of single lesion and 11 patients of multiple lesions. Treatment plans of HyperArc and CyberKnife were designed in Eclipse 15.5 and Precision 1.0, respectively, and transferred to Velocity 3.2 for comparison. HyperArc plans provided superior Conformity Index (0.91±0.06vs. 0.77±0.07, p<0.01) with reduced dose distribution in organs at risk (Dmax, p<0.05) and lower normal tissue exposure (V4Gy-V20Gy, p<0.05) in contrast to CyberKnife plans, although the Gradient Indexes were similar. CyberKnife plans showed higher Homogeneity Index (1.54±0.17vs. 1.39±0.09, p<0.05) and increased D2% and D50% in the target (p<0.05). Additionally, HyperArc plans had significantly fewer Monitor Units (MUs) and beam-on time (p<0.01). HyperArc plans demonstrated superior performance compared with MLC-based CyberKnife plans in terms of conformity and the sparing of critical organs and normal tissues, although no significant difference in GI outcomes was noted. Conversely, CyberKnife plans achieved a higher target dose and HI. The study suggests that HyperArc is more efficient and particularly suitable for treating larger lesions in brain metastases.

Correlations between intravascular pressure gradients and cerebral blood flow in patients with symptomatic, medically refractory, anterior circulation artery stenosis: an exploratory study

BackgroundFractional flow reserve is widely used in coronary disease management, with a threshold of 0.80. However, similar thresholds are unclear in functional assessment of intracranial atherosclerotic stenosis (ICAS).ObjectiveTo investigate the...

Feasibility of a Single-Fraction Stereotactic Dose of 30 Gy to Solitary Lung Lesions on Halcyon.

Purpose We sought to explore the feasibility of using the current co-planar Halcyon ring delivery system (RDS) with a novel multileaf collimator (MLC) aperture shape controller in delivering a single high dose of 30 Gy to solitary lung lesions via stereotactic body radiotherapy (SBRT). Materials and methods Thirteen non-small-cell lung cancer (NSCLC) patients previously treated with a single dose of 30 Gy to lung lesions via SBRT on the TrueBeam (6MV-FFF) using non-coplanar volumetric modulated arc therapy (VMAT) arcs were anonymized and replanned onto the Halcyon RDS (6MV-FFF) following RTOG-0915 single-fraction criteria. The Halcyon plans utilized a novel dynamic conformal arc (DCA)-based MLC-fitting approach before VMAT optimization with a user-defined aperture shape controller option. The clinical TrueBeam and Halcyon plans were compared via their protocol compliance, target conformity, gradient index, and dose to organs-at-risk (OAR). Treatment delivery efficacy and accuracy were assessed through end-to-end quality assurance (QA) tests on Halcyon and independent dose verification via in-house Monte Carlo (MC) second-check validation. Results All Halcyon lung SBRT plans met RTOG-0915 protocol's requirements for target coverage, conformity, and gradient indices, and maximum dose 2 cm away from the target (D2cm) while being statistically insignificant (p > 0.05) when compared to clinical TrueBeam plans. Additionally, Halcyon provided a similar dose to OAR except for the ribs, where Halcyon demonstrated a lower maximum dose (15.22 Gy vs 17.01 Gy, p < 0.001). However, Halcyon plans required a higher total monitor unit (8892 MU vs 7413 MU, p < 0.001), resulting in a higher beam modulation factor (2.96 MU/cGy vs 2.47 MU/cGy, p < 0.001) and an increase in beam-on time by a factor of 2.1 (11.11 min vs 5.3 min, p < 0.005). End-to-end QA measurements demonstrate that Halcyon plans were clinically acceptable with an average gamma passing rate of 99.8% for 2%/2mm criteria and independent MC 2nd checks within ±2.86%. Conclusion Our end-to-end testing and validation study demonstrates that by utilizing a DCA-based MLC aperture shape controller before VMAT optimization, Halcyon can be used for delivering a single dose of lung SBRT treatment. However, future improvements of Halcyon RDS are recommended to allow higher output rates, rotational couch corrections, and an integrated intrafraction motion management system that will further enhance Halcyon's capability for site-specific single dosage of SBRT.

Knowledge-based planning for Gamma Knife.

Current methods for Gamma Knife (GK) treatment planning utilizes either manual forward planning, where planners manually place shots in a tumor to achieve a desired dose distribution, or inverse planning, whereby the dose delivered to a tumor is optimized for multiple objectives based on established metrics. For other treatment modalities like IMRT and VMAT, there has been a recent push to develop knowledge-based planning (KBP) pipelines to address the limitations presented by forward and inverse planning. However, no complete KBP pipeline has been created forGK. To develop a novel (KBP) pipeline, using inverse optimization (IO) with 3D dose predictions for GK. Data were obtained for 349 patients from Sunnybrook Health Sciences Centre. A 3D dose prediction model was trained using 322 patients, based on a previously published deep learning methodology, and dose predictions were generated for the remaining 27 out-of-sample patients. A generalized IO model was developed to learn objective function weights from dose predictions. These weights were then used in an inverse planning model to generate deliverable treatment plans. A dose mimicking (DM) model was also implemented for comparison. The quality of the resulting plans was compared to their clinical counterparts using standard GK quality metrics. The performance of the models was also characterized with respect to the dosepredictions. Across all quality metrics, plans generated using the IO pipeline performed at least as well as or better than the respective clinical plans. The average conformity and gradient indices of IO plans was 0.737 0.158 and 3.356 1.030 respectively, compared to 0.713 0.124 and 3.452 1.123 for the clinical plans. IO plans also performed better than DM plans for five of the six quality metrics. Plans generated using IO also have average treatment times comparable to that of clinical plans. With regards to the dose predictions, predictions with higher conformity tend to result in higher quality KBP plans. Plans resulting from an IO KBP pipeline are, on average, of equal or superior quality compared to those obtained through manual planning. The results demonstrate the potential for the use of KBP to generate GK treatment with minimal humanintervention.

Emotion recognition based on ResNet and transfer learning

In the fields of psychology and artificial intelligence, emotion recognition is a crucial area of research. As an expression of body language, emotion recognition has a profound impact on our life and interpersonal relationships while existing models have the phenomenon of exploding or disappearing gradient indices due to the lack of information. To alleviate the aforementioned limitations, this paper further introduces the idea of residual jumping and transfer learning to conduct further research and exploration for the emotion recognition. Specifically, based on the RAF-DB dataset, the self-created model Awei and the pre-trained VGG model are combined. Numerous tests show that the suggested approach is effective. By reducing the amount of information lost during the convolution process, the residual idea can help with the issue of an exploding or vanishing gradient index brought on by an excessively long backpropagation. This will increase the correctness of the model. The pre-trained VGG model's addition improves the Awei model's parameter modification's efficacy and accuracy.

Nonlinear vibrations analysis of two-directional functionally graded porous cylindrical shells resting on elastic substrates in a thermal environment based on Donnell nonlinear shell theory

The primary objective of this study is to investigate the nonlinear free vibrational characteristics of temperature-dependent two-directional functionally graded porous (TDFGP) cylindrical shells resting on elastic substrates in a thermal environment. To accomplish this, the thermomechanical equations are derived based on the Donnell nonlinear shell theory framework in conjunction with the von Kármán assumption. Two-directional functionally graded porous cylindrical shell models have mechanical properties that can change smoothly and continuously across the length and thickness of the shell. Additionally, it is assumed that the internal porosities in the matrix materials can be dispersed into two independent patterns, either even or uneven porosity distribution. The nonlinearity in free vibration assessed via the nonlinear-to-linear frequency ratio concerning the central deflection amplitude can be gained employing the Galerkin discretization approach and modified Poincare–Lindstedt (P-L) method. The accuracy and effectiveness of the present analytical model are indicated through comparison with existing solutions. Finally, some comprehensive parametric investigations are carried out to gain insight into the impacts of several factors on the nonlinear free vibration characteristics of structures under different conditions. The results of this article demonstrate that parameters such as gradient indices, volume fraction, distribution pattern of porosity, geometric parameters, and ambient temperature rise significantly influence the structure’s nonlinear frequency and free vibration response.

Effect of porosity on the nonlinear free vibrational behavior of two-directional functionally graded porous cone-shaped shells resting on elastic substrates

The present article describes an analytical approach to investigate the nonlinear free vibrational behavior of a two-directional functionally graded porous (TDFGP) cone-shaped shell resting on elastic substrates. A mixture model with the power-law distribution functions is utilized to obtain the TDFGP shell’s mechanical properties. In addition, it is assumed that the internal porosities in the matrix materials can be dispersed into two independent patterns, either even or uneven porosity distribution. The field displacement in the TDFGP shell is approximated using first-order shear deformation theory. Hamilton’s principle and von Karman’s large deformation assumptions give a dynamic model for the TDFGP shell. The Galerkin decomposition method is employed to discretize the governing partial differential equations into time-dependent ordinary differential equations. The harmonic balance method is used to analytically solve the final time-dependent equations and acquire the nonlinear frequency response of the TDFGP shell. Research has been conducted on porosity, gradient indexes, elastic substrates, boundary conditions, and geometric ratios through parametric studies to investigate the outcomes and their applicability to real-world issues.

Nonlinear free vibrational behavior of temperature-dependent two-directional functionally graded truncated cone-like shells in thermal environment

This article investigates nonlinear free vibrations of temperature-dependent two-directional functionally graded (TDTDFG) cone-like shells in thermal environment. The structure material is a combination of ceramic and metal with temperature-dependent mechanical characteristics varying continuously in the thickness and longitudinal directions. Initially, the thermomechanical dynamic equations of the system are modeled based on the first-order shear deformation theory (FSDT) and the strain-displacement relations of von Kármán. Afterward, the final governing equation for the structure’s transverse motion is obtained using the Galerkin discretization method. Finally, the governing equation is solved using improved Lindstedt-Poincaré method as an analytical technique, resulting in an equation for calculating the nonlinear frequencies of the shell. To validate the research’s results, the system frequencies are calculated under different conditions and compared with the results of previous studies. After ensuring the accuracy of the results, a parametric study is performed to evaluate the effects of various parameters on the linear and nonlinear frequencies of the TDTDFG cone-like shell in thermal environment. The results of this study have demonstrated that gradient indices, geometric ratios, and thermal environment have a significant influence on the nonlinear vibration behavior of structures.

Dynamic analysis of double cracked bi-directional functionally graded nanobeam using the differential quadrature method

This study investigates the free vibration behavior of a double cracked nanobeam composed of bi-directional functionally graded material. The analysis incorporates Eringen’s nonlocal elasticity theory and the Euler–Bernoulli theory. The material properties are considered to vary in both the thickness and length directions. The cracked nanobeam is modeled as a series of interconnected sub-beams, with rotational springs placed at the cracked sections. This modeling approach accounts for the discontinuities in rotational displacement resulting from bending, which is directly related to the bending moment transmitted by the cracked section. The problem is solved using the differential quadrature method, which approximates the derivatives of the field quantities by employing a weighted linear sum of the nodal values. By doing so, the problem is transformed into a linear algebraic system. Various supporting cases are examined, and a parametric study is conducted to analyze the impact of the axial and transverse gradient indices, nonlocal parameter, and crack severity on the obtained results.

Insights into the dosimetric and geometric characteristics of stereotactic radiosurgery for multiple brain metastases: A systematic review.

GammaKnife (GK) and CyberKnife (CK) have been the mainstay stereotactic radiosurgery (SRS) solution for multiple brain metastases (MBM) for several years. Recent technological advancement has seen an increase in single-isocentre C-arm linac-based SRS. This systematic review focuses on dosimetric and geometric insights into contemporary MBM SRS and thereby establish if linac-based SRS has matured to match the mainstay SRS delivery systems. The PubMed, Web of Science and Scopus databases were interrogated which yielded 891 relevant articles that narrowed to 20 articles after removing duplicates and applying the inclusion and exclusion criteria. Primary studies which reported the use of SRS for treatment of MBM SRS and reported the technical aspects including dosimetry were included. The review was limited to English language publications from January 2015 to August 2023. Only full-length papers were included in the final analysis. Opinion papers, commentary pieces, letters to the editor, abstracts, conference proceedings and editorials were excluded. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines were followed. The reporting of conformity indices (CI) and gradient indices, V12Gy, monitor units and the impact of translational and rotational shifts were extracted and analysed. The single-isocentre technique for MBM dominated recent SRS studies and the most studied delivery platforms were Varian. The C-arm linac-based SRS plan quality and normal brain tissue sparing was comparable to GK and CK and in some cases better. The most used nominal beam energy was 6FFF, and optimised couch and collimator angles could reduce mean normal brain dose by 11.3%. Reduction in volume of the healthy brain receiving a certain dose was dependent on the number and size of the metastases and the relative geometric location. GK and CK required 4.5-8.4 times treatment time compared with linac-based SRS. Rotational shifts caused larger changes in CI in C-arm linac-based single-isocentre SRS. C-arm linac-based SRS produced comparable MBM plan quality and the delivery is notably shorter compared to GK and CK SRS.

Assessing torrentiality in catchments of the tropical Andes: A morphometric approach

Torrential flows represent one of the most catastrophic natural hazards in the Andes, and Colombia is not an exception. We computed and analyzed ten morphometric indexes, classified by the catchment geometry and relief characteristics, for 149 torrential catchments across Colombian Andes three branches (Western, Central, and Eastern cordilleras). We divided the study area into six tectonic-stratigraphic regions, and employed statistical tests such as the Shapiro-Wilk and ANOVA One-Way Permutation tests to assess index distributions within each region. The ANOVA One-Way Permutation test results revealed significant differences in the distributions of form factor (p-value 0.048), mean gradient (p-value 0.009), relief ratio (p-value 0.003), Melton ratio (p-value 0.006), and hypsometric integral (p-value 0.000) indices among regions. Likewise, the pairwise comparison tests identified that the following regions are different between them for Melton ratio: Central Cordillera and Plateau Antioqueño (p-value 0.032), Garzón Massif and Plateau Antioqueño (p-value 0.015), Garzón Massif and Santander Massif (p-value 0.05), and Plateau Antioqueño and Western Cordillera (p-value 0.032); for relief ratio: Central Cordillera and Plateau Antioqueño (p-value 0.0219), Estern Cordillera and Plateau Antioqueño (p-value 0.0425), Garzón Massif and Plateau Antioqueño (p-value 0.0058), Plateau Antioqueño and Western Cordillera (p-value 0.053); for hypsometric integral: Central Cordillera and Western Cordillera (p-value 0.0004), Eastern Cordillera and Western Cordillera (p-value 0.0004), Garzón Massif and Western Cordillera (p-value 0.0004), Plateau Antioqueño and Western Cordillera (p-value 0.0161), and Santander Massif and Western Cordillera (p-value 0.002). Based on the findings we computed confidence intervals for the population median of the studied morphometric parameters according to the region employing a non-parametric bootstrapping method. The statistical analysis highlights the importance of the geological and geomorphological features in the morphometric indices analysis as part of the torrential flow susceptibility assessment.Applying our findings, we tested proposed thresholds in a case study of the Santander Massif (Eastern Cordillera of Colombia), focusing on the 2020 Piedecuesta Flow. In the study case, we demonstrated the relevance of identifying the feeder catchments where the morphometric indices would be calculated from, especially in areas where significant hydrologic changes occur. Volumetric concentration variations along the Piedecuesta Flow path highlight the need to prioritize the recognition of feeder catchments as an imperative part of the susceptibility assessment. Our approach enriches the knowledge base for identifying torrential-prone basins and has important implications for natural hazard management, aiming at mitigating the impact of torrential flows in the Andes.

Thermo-mechanical behavior of 2D functionally graded porous-auxetic metamaterial rotating disk with an auxetic foundation

In the present study, the thermo-mechanical behavior of two-directional functionally graded porous-auxetic metamaterial rotating disk (2D-FGPAMRD) has been analyzed. The rotating disk subjected to combination of transient thermal and steady mechanical loads and supported by an auxetic foundation. Haber-Schaim (H-S) frictionless elastic foundation model is considered to drive the structure-structure interaction. The governing equations are obtained based on the thermoelasticity theory. The response of disk to mechanical and thermal loads has been obtained by solving nonhomogeneous governing equations. To this end, the alternating direction implicit (ADI) finite difference scheme and combination of state-space and differential quadrature (DQ) methods have applied to solve the Fourier heat conduction and thermoelasticity equations, respectively. In the numerical examples, the effects of porosity and auxeticity, as well as inhomogeneity indices of the disk on its thermo-mechanical behavior have been investigated for the first time. The results reveal that, the elastic field components of rapid heating disk are significantly affected by the nature of temperature diffusion, inhomogeneity indices and the auxeticity of the disk material. Besides, the changes of thermal expansion gradient indices provide a relaxation in the normal transverse stress.

Stereotactic body radiotherapy with volumetric intensity-modulated arc therapy and flattening filter-free beams: dosimetric considerations.

The present study comparatively evaluates the impact of energy-matched flattening filter-free (FFF) photon beams with different energy levels on the physical-dosimetric quality of lung and liver stereotactic body radiotherapy (SBRT) treatment plans. For this purpose, 54different lung and liver lesions from 44patients who had already received SBRT combined with volumetric modulated arc therapy (VMAT) were included in this retrospective planning study. Planning computed tomography scans already available were used for the renewed planning with 6MV, 6MV-FFF, 10MV, and 10MV-FFF under constant planning objectives. The treatment delivery data, dosimetric distributions, and dose-volume histograms as well as parameters such as the conformity index and gradient indices were the basis for the evaluation and comparison of treatment plans. Asignificant reduction of beam-on time (BOT) was achieved due to the high dose rates of FFF beams. In addition, we showed that for FFF beams compared to flattened beams of the same energy level, smaller planning target volumes (PTV) require fewer monitor units (MU) than larger PTVs. An equal to slightly superior target volume coverage and sparing of healthy tissue as well as organs at risk in both lung and liver lesions were found. Significant differences were seen mainly in the medium to lower dose range. We found that FFF beams together with VMAT represent an excellent combination for SBRT of lung or liver lesions with shortest BOT for 10MV-FFF but significant dose savings for 6MV-FFF in lung lesions.