Based on the nonlocal elasticity theory, a unified nonlocal, nonlinear, higher-order shear deformable nanoplate model is developed to investigate the size-dependent, large-amplitude, nonlinear ...vibration of multiferroic composite rectangular nanoplates with different boundary conditions resting on an elastic foundation. By considering a unified displacement vector and using von Kármán’s strain tensor, the strain–displacement components are obtained. Using coupled nonlocal constitutive relations, the coupled ferroelastic, ferroelectric, ferromagnetic, and thermal properties of multiferroic composite materials and small-scale effect are taken into account. The electric and magnetic potential distributions in the nanoplate are calculated via Maxwell’s electromagnetic equations. Furthermore, Hamilton’s principle is utilized to obtain the mathematical formulation associated with the coupled governing equations of motions and boundary conditions. The developed model enables us to consider the effects of rotary inertia and transverse shear deformation without using any shear correction factor. Also, it can be degenerated to the models based on the Kirchhoff and existing shear deformation plate theories. To solve the large-amplitude vibration problem, an efficient multistep numerical solution approach is utilized. Effects of various important parameters such as the type of the plate theory, and parameters of nonlocality and coupled fields on the nonlinear frequency response are investigated.
Free vibration of single-layered graphene sheets (SLGSs) subjected to compressive in-plane loads and embedded in a Winkler–Pasternak elastic medium in the pre- and post-buckled configurations is ...examined herein. To consider both geometric and material nonlinearities and include the size-dependent mechanical behavior of small-scale structures without taking any additional phenomenological parameters into account, the high-order Cauchy-Born (HCB) method, hyperelastic membrane and second gradient elasticity theory are used for providing mathematical formulation. Also, the variational differential quadrature (VDQ) method and Hamilton’s principles are applied to provide a set of discretized governing equations of motion. To evaluate the free vibration of SLGSs in post-buckling domain, first, the post-buckling problem corresponding to the considered system is solved. Then, by assuming a small disturbance about the equilibrium condition, the frequency response of SLGSs is obtained as a function of the applied in-plane load. In numerical results, the effects of various parameters such as geometry, elastic foundation and boundary conditions are highlighted and discussed in detail.
A numerical approach is used herein to study the primary resonant dynamics of functionally graded (FG) cylindrical nanoscale panels taking the strain gradient effects into consideration. The basic ...relations of the paper are written based upon Mindlin’s strain gradient theory (SGT) and three-dimensional (3D) elasticity. Since the formulation is developed using Mindlin’s SGT, it is possible to reduce it to simpler size-dependent theories including modified forms of couple stress and strain gradient theories (MCST & MSGT). The governing equations is derived and directly discretized via the variational differential quadrature technique. Then, a numerical solution technique is employed to study the nonlinear resonance response of nanopanels with various edge conditions under a harmonic load. The impacts of length scale parameter, material and geometrical parameters on the frequency–response curves of nanopanels are investigated. In addition, comparisons are provided between the predictions of MSGT, MCST and the classical elasticity theory.
We investigate the effects of an increase in the production of secondary electrons when a β− source commonly used in internal radionuclide therapy, 67Cu, is radiolabelled to a super-paramagnetic iron ...oxide nanoparticle (SPION), with specific emphasis on the role of SPION cluster size and geometry. A positive relationship is found between the degree to which the nanoparticles are clustered and the associated radio-enhancement effects, with cluster population size playing a major role, as well as SPION separation within a cluster and the distance between clusters. Our simulation results indicate that SPIONs labelled with 67Cu can induce a nonlinear amplification in the number of secondary electrons produced of up to 4% in bulk, with localised regions of nearer inter-SPION separation producing an increase of over 400% for a 20 nm average SPION separation. Such variation in enhancement due to local concentration effects may help identify clinical strategies that enhance efficacy for a given radiation dosage, or achieve equal efficacy with reduced radiation dosage.
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In this article, the nonlinear bending behavior of rectangular nanoplates made of functionally graded materials (FGMs) is studied in the context of a variational formulation. To capture size ...effects, the most general form of strain gradient theory is employed. The three-dimensional (3D) elasticity theory is used for modeling the nanoplate. The governing equations are also derived in the discretized weak form using the variational differential quadrature (VDQ) method. Finally, the solution of the nonlinear bending problem is obtained by the pseudo arc-length continuation algorithm. In the numerical results, the effects of thickness-to-length scale ratio, side length-to-thickness ratio and material gradient index on the nonlinear bending response of nanoplates subject to different types of boundary conditions are analyzed. Moreover, a comparison is provided between the predictions of various strain gradient-based theories.
Based on the higher-order Cauchy–Born (HCB) rule, an atomistic-continuum multiscale model is proposed to address the large-amplitude vibration problem of graphene sheets (GSs) embedded in an elastic ...medium under various kinds of boundary conditions. By HCB, a linkage is established between the deformation of the atomic structure and macroscopical deformation gradients without any parameter fitting. The elastic foundation is formulated according to the Winkler–Pasternak model which considers both normal pressure and transverse shear stress effects. The weak form of nonlinear governing equations is derived via a variational approach, namely based on the variational differential quadrature (VDQ) method and Hamilton’s principle. In order to solve the obtained equations, a numerical scheme is adopted in which the generalized differential quadrature (GDQ) method together with a numerical Galerkin technique is utilized for discretization in the space domain, and the time-periodic discretization method is used to discretize in the time domain. The effects of the arrangement of atoms, the Winkler and Pasternak coefficients of the elastic foundation, and boundary conditions on the frequency–response curves of GSs are illustrated. It is revealed that the nonlinear effects on the response of GSs with larger size in armchair direction are less important.
The addition of gold nanoparticles within target tissue (i.e. a tumour) to enhance the delivered radiation dose is a well studied radiotherapy treatment strategy, despite not yet having been ...translated into standard clinical practice. While several studies have used Monte Carlo simulations to investigate radiation dose enhancement by Auger electrons emitted from irradiated gold nanoparticles, none have yet considered the effects due to escaping fluorescence photons. Geant4 was used to simulate a water phantom containing 10 mg ml−1 uniformly dispersed gold (1% by mass) at 5 cm depth. Incident monoenergetic photons with energies either side of the gold K-edge at 73 keV and 139.5 keV were chosen to give the same attenuation contrast against water, where water is used as a surrogate for biological tissue. For 73 keV incident photons, adding 1% gold into the water phantom enhances the energy deposited in the phantom by a factor of 1.9 while 139.5 keV incident photons give a lower enhancement ratio of 1.5. This difference in enhancement ratio, despite the equivalent attenuation ratios, can be attributed to energy carried from the target into the surrounding volume by fluorescence photons for the higher incident photon energy. The energy de-localisation is maximal just above the K-edge with 36% of the initial energy deposit in the phantom lost to escaping fluorescence photons. Conversely we find that the absorption of more photons by gold in the phantom reduces the number of scattered photons and hence energy deposited in the surrounding volume by up to 6% for incident photons below the K-edge. For incident photons above the K-edge this is somewhat offset by fluorescence. Our results give new insight into the previously unstudied centimetre scale energy deposition outside a target, which will be valuable for the future development of treatment plans using gold nanoparticles. From these results, we can conclude that gold nanoparticles delivered to a target tumour are capable of increasing dose to the tumour whilst simultaneously decreasing scatter dose to surrounding healthy tissue.
Based on the ideas of variational differential quadrature (VDQ) method and position transformation, an efficient numerical variational strategy is proposed in this paper to analyze the large ...deformations of hyperelastic structures in the context of three-dimensional (3D) compressible and incompressible nonlinear elasticity theories. Based on the minimum total potential energy principle together with the Neo-Hookean model, the governing equations are derived. The relations of paper are presented in novel vector–matrix format. Replacing the tensor form of formulations with matricized ones is a novelty of present work since the matricized formulations can be readily employed for the programming in numerical approaches. Discretizing is also carried out via VDQ operators. For applying the VDQ technique, the irregular domain of elements is transformed into a regular one by the method of mapping of position field based on the finite element shape functions. This feature enables the proposed VDQ-transformed approach to solve problems with irregular domains. Moreover, the developed formulation is simple, compact and easy to implement. Considering structures with various shapes, several illustrative convergence and comparative investigations are given to assess the performance of the approach in both compressible and incompressible regimes. Good accuracy and computational efficiency can be reported as the features of developed VDQ-based approach.
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In the present article, an atomistic-continuum multiscale model is developed to study the free-vibration response of single-layered graphene sheets (SLGSs) embedded in an elastic medium based upon ...the higher-order Cauchy-Born (HCB) rule. In order to take both transverse shear stress and normal pressure into account, the elastic foundation is considered to be of Winkler-Pasternak type. The governing equations are derived within a variational formulation using a newly proposed method called Variational Differential Quadrature (VDQ). Using the VDQ approach together with the Generalized Differential Quadrature (GDQ) technique, the variational form of the governing equation is discretized in a computationally efficient manner. Finally, a generalized eigenvalue problem is solved to calculate the frequencies of SLGSs. The convergence and correctness of the presented numerical solutions are examined firstly. Then, a number of numerical examples are given to study the effects of boundary conditions, elastic medium and arrangement of atoms on the vibrational response of SLGSs. The present model does not involve any additional phenomenological input, and it considers size effect and material nonlinearity due to atomic interactions.
Background
SPECT-derived dose estimates in tissues of diameter less than 3× system resolution are subject to significant losses due to the limited spatial resolution of the gamma camera. ...Incorporating resolution modelling (RM) into the SPECT reconstruction has been proposed as a possible solution; however, the images produced are prone to noise amplification and Gibbs artefacts. We propose a novel approach to SPECT reconstruction in a theranostic setting, which we term SPECTRE (single photon emission computed theranostic reconstruction); using a diagnostic PET image, with its superior resolution, to guide the SPECT reconstruction of the therapeutic equivalent. This report demonstrates a proof in principle of this approach.
Methods
We have employed the hybrid kernelised expectation maximisation (HKEM) algorithm implemented in STIR, with the aim of producing SPECT images with PET-equivalent resolution. We demonstrate its application in both a dual
68
Ga/
177
Lu IEC phantom study and a clinical example using
64
Cu/
67
Cu.
Results
SPECTRE is shown to produce images comparable in accuracy and recovery to PET with minimal introduction of artefacts and amplification of noise.
Conclusion
The SPECTRE approach to image reconstruction shows improved quantitative accuracy with a reduction in noise amplification. SPECTRE shows great promise as a method of improving SPECT radioactivity concentrations, directly leading to more accurate dosimetry estimates in small structures and target lesions. Further investigation and optimisation of the algorithm parameters is needed before this reconstruction method can be utilised in a clinical setting.
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