Despite the well-recognized importance of caries risk assessment, practical models remain to be established. This study was designed to develop biopsychosocial models for caries risk assessment in ...various settings. With a questionnaire, an oral examination, and biological (salivary, microbiological, and plaque pH) tests, a prospective study was conducted among 1782 children aged 3-6 years, with 1576 (88.4%) participants followed in 12 months. Multiple risk factors, indicators, and protective factors were identified. Various risk assessment models were constructed by the random selection of 50% of the cases and further validated in the remaining cases. For the prediction of a “one-year caries increment”, screening models without biological tests achieved a sensitivity/specificity of 82%/73%; with biological tests, full-blown models achieved the sensitivity/specificity of 90%/90%. For identification of a quarter of the children with high caries burden (baseline dmft > 2), a community-screening model requiring only a questionnaire reached a sensitivity/specificity of 82%/81%. These models are promising tools for cost-effective caries control and evidence-based treatment planning. Abbreviations: decayed, missing, filled teeth in primary dentition (dmft); receiver operation characteristics (ROC); relative risk (RR); confidence interval (CI); National Institutes of Health (NIH); World Health Organization (WHO); US Department of Health and Human Services (US/DHHS); American Academy of Pediatric Dentistry (AAPD).
Abstract
We report the discovery of a new unidentified extended
γ
-ray source in the Galactic plane named LHAASO J0341+5258 with a pretrial significance of 8.2 standard deviations above 25 TeV. The ...best-fit position is R.A. = 55.°34 ± 0.°11 and decl. = 52.°97 ± 0.°07. The angular size of LHAASO J0341+5258 is 0.°29 ± 0.°06
stat
± 0.°02
sys
. The flux above 25 TeV is about 20% of the flux of the Crab Nebula. Although a power-law fit of the spectrum from 10 to 200 TeV with the photon index
α
= 2.98 ± 0.19
stat
± 0.02
sys
is not excluded, the LHAASO data together with the flux upper limit at 10 GeV set by the Fermi-LAT observation, indicate a noticeable steepening of an initially hard power-law spectrum with a cutoff at ≈50 TeV. We briefly discuss the origin of ultra-high-energy gamma rays. The lack of an energetic pulsar and a young supernova remnant inside or in the vicinity of LHAASO J0341+5258 challenge, but do not exclude, both the leptonic and hadronic scenarios of gamma-ray production.
A new non-classical Kirchhoff plate model is developed using a modified couple stress theory, a surface elasticity theory and a two-parameter elastic foundation model. A variational formulation based ...on Hamilton’s principle is employed, which leads to the simultaneous determination of the equations of motion and the complete boundary conditions and provides a unified treatment of the microstructure, surface energy and foundation effects. The new plate model contains a material length scale parameter to account for the microstructure effect, three surface elastic constants to describe the surface energy effect, and two foundation moduli to represent the foundation effect. The current non-classical plate model reduces to its classical elasticity-based counterpart when the microstructure, surface energy and foundation effects are all suppressed. In addition, the newly developed plate model includes the models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases and recovers the Bernoulli–Euler beam model incorporating the microstructure, surface energy and foundation effects. To illustrate the new model, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that the deflection of the simply supported plate with or without the elastic foundation predicted by the current model is smaller than that predicted by the classical model. Also, it is observed that the difference in the deflection predicted by the new and classical plate models is very large when the plate thickness is sufficiently small, but it is diminishing with the increase of the plate thickness. For the free vibration problem, it is found that the natural frequency predicted by the new plate model with or without the elastic foundation is higher than that predicted by the classical plate model, and the difference is significant for very thin plates. These predicted trends of the size effect at the micron scale agree with those observed experimentally. In addition, it is shown both analytically and numerically that the presence of the elastic foundation reduces the plate deflection and increases the plate natural frequency, as expected.
A non-classical third-order shear deformation plate model is developed using a modified couple stress theory and Hamilton’s principle. The equations of motion and boundary conditions are ...simultaneously obtained through a variational formulation. This newly developed plate model contains one material length scale parameter and can capture both the size effect and the quadratic variation of shear strains and shear stresses along the plate thickness direction. It is shown that the new third-order shear deformation plate model recovers the non-classical Reddy-Levinson beam model and Mindlin plate model based on the modified couple stress theory as special cases. Also, the current non-classical plate model reduces to the classical elasticity-based third-order shear deformation plate model when the material length scale parameter is taken to be zero. To illustrate the new model, analytical solutions for the static bending and free vibration problems of a simply supported plate are obtained by directly applying the general forms of the governing equations and boundary conditions of the model. The numerical results show that the deflection and rotations predicted by the new plate model are smaller than those predicted by its classical elasticity-based counterpart, while the natural frequency of the plate predicted by the former is higher than that by the latter. It is further seen that the differences between the two sets of predicted values are significant when the plate thickness is small, but they are diminishing with increasing plate thickness.
In the present work, a new Kirchhoff plate model is developed using a modified couple-stress theory to study the bending behavior of nano-sized plates, including surface energy and microstructure ...effects. The surface elasticity theory of Gurtin and Murdoch is used to model the surface energy effects, into the framework of the modified couple-stress theory of elasticity. Newtonian continuum mechanics approach is used to derive the differential form of the equilibrium equations for the modified Kirchhoff plate theory.
The modified plate rigidity is derived to express the size effects in nanoplates. Presence of a length scale parameter, in the context of the modified couple-stress theory, enables us to express the size effect in nano-scale structures. In addition, an intrinsic length scale parameter is determined as a result of taking surface energy effects into account.
In order to illustrate the model, an analytical solution of the static bending of a simply supported nano-plate has been derived. For ultra-thin plates it is noticed that the microstructure effects on bending rigidity and deflection, through the application of the modified-couple stress theory, is highly significant than that caused by the surface energy effect.
•A new Kirchhoff nanoplate model is developed using a modified couple-stress theory, including surface energy and microstructure effects.•The surface elasticity theory is used to model the surface effects, into the framework of the modified couple-stress theory.•Newtonian continuum mechanics approach is used to derive the differential governing equations for the modified Kirchhoff plate theory.•Length scale parameters, in the context of the couple-stress and surface elasticity, are derived expressing size effects in structures.•An analytical solution of the static bending of a simply supported nanoplate has been derived.
A new Bernoulli–Euler beam model is developed using a modified couple stress theory and a surface elasticity theory. A variational formulation based on the principle of minimum total potential energy ...is employed, which leads to the simultaneous determination of the equilibrium equation and complete boundary conditions for a Bernoulli–Euler beam. The new model contains a material length scale parameter accounting for the microstructure effect in the bulk of the beam and three surface elasticity constants describing the mechanical behavior of the beam surface layer. The inclusion of these additional material constants enables the new model to capture the microstructure- and surface energy-dependent size effect. In addition, Poisson’s effect is incorporated in the current model, unlike existing beam models. The new beam model includes the models considering only the microstructure dependence or the surface energy effect as special cases. The current model reduces to the classical Bernoulli–Euler beam model when the microstructure dependence, surface energy, and Poisson’s effect are all suppressed. To demonstrate the new model, a cantilever beam problem is solved by directly applying the general formulas derived. Numerical results reveal that the beam deflection predicted by the new model is smaller than that by the classical beam model. Also, it is found that the difference between the deflections predicted by the two models is very significant when the beam thickness is small but is diminishing with the increase of the beam thickness.
A new non-classical Kirchhoff rod model is developed using the modified couple stress theory, which contains one material length scale parameter and can account for microstructure-dependent size ...effects. The governing equations and boundary conditions are determined simultaneously by a variational formulation based on the principle of minimum total potential energy. The newly developed model recovers its classical elasticity-based counterpart as a special case when the microstructure effect is not considered. To illustrate the new non-classical Kirchhoff rod model, two sample problems are analytically solved by directly applying the general formulas derived. One problem is the equilibrium analysis of a helical rod of circular cross section deformed from a straight rod, and the other is the buckling of a straight rod of circular cross section induced by an axial compressive force. In the former, the rod undergoes a twisting-dominated deformation, while in the latter the rod deformation is bending dominated. Two closed-form expressions are obtained for the force and couple needed in deforming the helical rod, and an analytical formula is derived for the critical buckling load required to perturb the axially compressed straight rod, with the microstructure effect incorporated in each case. These formulas reduce to those based on classical elasticity when the microstructure effect is suppressed. For the helical rod problem, the numerical results show that the couple predicted by the current non-classical rod model is significantly larger than that predicted by the classical model when the rod radius is very small, but the difference is diminishing with the increase in the rod radius. For the buckling problem, it is found that the critical buckling load based on the new non-classical Kirchhoff rod model is always higher than that given by the classical elasticity-based model, with the difference being significant for a very thin rod.
A new model for determining band gaps for elastic wave propagation in three-dimensional (3-D) periodic two-phase composites is developed using a modified couple stress theory that accounts for ...microstructure effects. Three types of composites, each containing a different kind of inclusion – spherical, cubic, and cube with square-rod connections, are considered, with the third one representing a co-continuous composite. The plane wave expansion method and the Bloch theorem for periodic media are employed to solve the elastic wave equations in each case, which are converted to an eigenvalue problem. The band gaps are determined from solving the characteristic equation and plotting the resulting eigen-frequencies. The new non-classical model reduces to the classical elasticity-based model when microstructure effects are suppressed. To quantitatively illustrate the newly developed model, a parametric study is conducted for 3-D periodic composites with the three kinds of inclusions. The numerical results reveal that the first band gap values predicted by the current non-classical model are smaller than those predicted by the classical elasticity-based model, and the difference between the two sets of band gap values is large when the unit cell size is very small. Also, it is seen that the volume fraction and inclusion shape have significant effects on the band gap size. These indicate that large band gaps can be attained by tailoring microstructural parameters including the unit cell size, volume fraction and inclusion shape.
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