An extended finite element method with smooth nodal stress

The enrichment formulation of double-interpolation finite element method (DFEM) is developed in this paper. DFEM is first proposed by Zheng \emph{et al} (2011) and it requires two stages of interpolation to construct the trial function. The first stage of interpolation is the same as the standard finite element interpolation. Then the interpolation is reproduced by an additional procedure using the nodal values and nodal gradients which are derived from the first stage as interpolants. The re-constructed trial functions are now able to produce continuous nodal gradients, smooth nodal stress without post-processing and higher order basis without increasing the total degrees of freedom. Several benchmark numerical examples are performed to investigate accuracy and efficiency of DFEM and enriched DFEM. When compared with standard FEM, super-convergence rate and better accuracy are obtained by DFEM. For the numerical simulation of crack propagation, better accuracy is obtained in the evaluation of displacement norm, energy norm and the stress intensity factor

Very high energy emission from the hard spectrum sources HESS J1641-463, HESS J1741-302 and HESS J1826-130

A recent study of the diffuse $\gamma$-ray emission in the Central Molecular Zone using very high energy (VHE, E $>$ 0.1 TeV) H.E.S.S. data suggests that the Galactic Center (GC) is the most plausible supplier of Galactic ultra-relativistic cosmic-rays (CRs) up to the knee at about 10$^{15}$ eV (PeV). However, the GC might not be the only source capable to accelerate CRs up to PeV energies in the Galaxy. Here we present H.E.S.S. data analysis results and interpretation of three H.E.S.S. sources, with spectra extending beyond 10 TeV and relatively hard spectral indices compared with the average spectral index of H.E.S.S. sources, namely HESS J1641-463, HESS J1741-302 and HESS J1826-130. Although the nature of these VHE $\gamma$-ray sources is still open, their spectra suggest that the astrophysical objects producing such emission must be capable of accelerating the parental particle population up to energies of at least several hundreds of TeV. Assuming a hadronic scenario, dense gas regions can provide rich target material for accelerated particles to produce VHE $\gamma$-ray emission via proton-proton interactions followed by a subsequent $\pi^{0}$ decay. Thus, detailed investigations of the interstellar medium along the line of sight to all of these sources have been performed by using data from available atomic and molecular hydrogen surveys. The results point out the existence of dense interstellar gas structures coincident with the best fit positions of these sources. One can find possible hadronic models with CRs being accelerated close to the PeV energies to explain the $\gamma$-ray emission from all of these sources, which opens up the possibility that a population of PeV CR accelerators might be active in the Galaxy.Comment: 8 pages, 2 figures, in Proceedings of 35th ICRC, Busan (Korea) 201

HESS J1826−-130: A Very Hard γ\gamma-Ray Spectrum Source in the Galactic Plane

HESS J1826$-$130 is an unidentified hard spectrum source discovered by H.E.S.S. along the Galactic plane, the spectral index being $\Gamma$ = 1.6 with an exponential cut-off at about 12 TeV. While the source does not have a clear counterpart at longer wavelengths, the very hard spectrum emission at TeV energies implies that electrons or protons accelerated up to several hundreds of TeV are responsible for the emission. In the hadronic case, the VHE emission can be produced by runaway cosmic-rays colliding with the dense molecular clouds spatially coincident with the H.E.S.S. source.Comment: 6 pages, 3 figures, Proceedings of the 6th International Symposium on High Energy Gamma-Ray Astronomy (Gamma2016), Heidelberg, German

A volume-averaged nodal projection method for the Reissner-Mindlin plate model

We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The proposed approach uses linear maximum-entropy approximations and is built variationally on a two-field potential energy functional wherein the shear strain, written in terms of the primitive variables, is computed via a volume-averaged nodal projection operator that is constructed from the Kirchhoff constraint of the three-field mixed weak form. The stability of the method is rendered by adding bubble-like enrichment to the rotation degrees of freedom. Some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses

Identification of Critical Molecular Components in a Multiscale Cancer Model Based on the Integration of Monte Carlo, Resampling, and ANOVA

To date, parameters defining biological properties in multiscale disease models are commonly obtained from a variety of sources. It is thus important to examine the influence of parameter perturbations on system behavior, rather than to limit the model to a specific set of parameters. Such sensitivity analysis can be used to investigate how changes in input parameters affect model outputs. However, multiscale cancer models require special attention because they generally take longer to run than does a series of signaling pathway analysis tasks. In this article, we propose a global sensitivity analysis method based on the integration of Monte Carlo, resampling, and analysis of variance. This method provides solutions to (1) how to render the large number of parameter variation combinations computationally manageable, and (2) how to effectively quantify the sampling distribution of the sensitivity index to address the inherent computational intensity issue. We exemplify the feasibility of this method using a two-dimensional molecular-microscopic agent-based model previously developed for simulating non-small cell lung cancer; in this model, an epidermal growth factor (EGF)-induced, EGF receptor-mediated signaling pathway was implemented at the molecular level. Here, the cross-scale effects of molecular parameters on two tumor growth evaluation measures, i.e., tumor volume and expansion rate, at the microscopic level are assessed. Analysis finds that ERK, a downstream molecule of the EGF receptor signaling pathway, has the most important impact on regulating both measures. The potential to apply this method to therapeutic target discovery is discussed

Isogeometric analysis for functionally graded microplates based on modified couple stress theory

Analysis of static bending, free vibration and buckling behaviours of functionally graded microplates is investigated in this study. The main idea is to use the isogeometric analysis in associated with novel four-variable refined plate theory and quasi-3D theory. More importantly, the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The convergence and verification show the validity and efficiency of this proposed computational approach in comparison with those existing in the literature. It is further applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and length-to-thickness ratios on the responses of the microplates.Comment: 57 pages, 14 figures, 18 table

Natural frequencies of cracked functionally graded material plates by the extended finite element method

In this paper, the linear free flexural vibration of cracked functionally graded material plates is studied using the extended finite element method. A 4-noded quadrilateral plate bending element based on field and edge consistency requirement with 20 degrees of freedom per element is used for this study. The natural frequencies and mode shapes of simply supported and clamped square and rectangular plates are computed as a function of gradient index, crack length, crack orientation and crack location. The effect of thickness and influence of multiple cracks is also studied.Comment: 38 pages, 14 figures, 10 tables; Composite Structures, 201