Based on Kirchhoff's hypothesis and relevant variational principles, this work presents an assumed hybrid-displacement finite element model to solve the bending problems of thin cracked plates subjected to static and dynamic loadings. To provide a potential method of non-destructive testing in evaluating the integrity o~ structure, natural vibrations of the thin cracked plate are also studied. Since the integrand of the associated functional contains the second-order derivatives of the lateral displacement of the plate, the compatibility requirements for the lateral displacement and its normal slope at inter-element boundaries are enforced in an integral sense through the use of a Lagrangian multiplier technique. The proper singular behaviours for the bending stresses and strains are incorporated in the singular elements around the crack-tips. The static and dynamic symmetric and anti-symmetric bending stress intensity factors can be directly computed. To avoid underestimation of dynamic bending stress intensity factors, the important role of the singular elements is also demonstrated. Good correlations between the computed results and available solutions in the literature show the accuracy and efficiency of the present work. Some new solutions for the bending thin cracked plates are then drawn.
The creation of nanostructures on polycrystalline silicon wafer surface to reduce the solar reflection can enhance the solar absorption and thus increase the solar-electricity conversion efficiency of solar cells. The self-masking reactive ion etching (RIE) was studied to directly fabricate nanostructures on silicon surface without using a masking process for antireflection purpose. Reactive gases comprising chlorine (Cl), sulfur hexafluoride (SF), and oxygen (O) were activated by radio-frequency plasma in an RIE system at a typical pressure of 120-130 mTorr to fabricate the nanoscale pyramids. Poly-Si wafers were etched directly without masking for 6-10 min to create surface nanostructures by varying the compositions of SF, Cl, and O gas mixtures in the etching process. The wafers were then treated with acid (KOH:HO = 1:1) for 1 min to remove the damage layer (100 nm) induced by dry etching. The damage layer significantly reduced the solar cell efficiencies by affecting the electrical properties of the surface layer. The light reflectivity from the surface after acid treatment could be significantly reduced to <10% for the wavelengths between 500 and 900 nm. The effects of RIE and surface treatment conditions on the surface nanostructures and the optical performance as well as the efficiencies of solar cells will be presented and discussed. The authors have successfully fabricated large-area (156 × 156 mm) subwavelength antireflection structure on poly-Si substrates, which could improve the solar cell efficiency reproducibly up to 16.27%, higher than 15.56% using wet etching.
At the nanoscale, surface effect could cause atomistic structures a pre-stressed or pre-deformed state, which would consequently have a great dependence on their bulk mechanical properties. Besides, according to molecular mechanics [1,2], the effect of the non-bonding interactions among the atoms that are separated by equal or more than two bonds, say, van der Waals (vdW) forces, should be taken into account. Thus, the underlying objective of the study attempts to explore the extent of the surface effect and the in-layer vdW interactions on the mechanical properties of single/multi-walled carbon nanotubes(S/MWCNTs) with two different types of chiralities, including zigzag and armchair. To deal with the problem, an atomistic-continuum modeling (ACM) approach is introduced. The ACM is established by molecular dynamics (MD) simulation and equivalent continuum modeling (ECM). MD simulation is adopted to derive the initial equilibrium state of CNTs due to the surface effect, and the ECM is applied to calculate the mechanical properties of CNTs. The ECM is formulated based on the finite element (FE) approximations, which are composed of three-dimensional beam elements and one-dimensional non-linear spring elements. They basically represent the bonding and non-bonding interactions, respectively. The equivalent material constants of these two types of elements are derived from classical molecular mechanics and beam theory. The present results are also compared with those obtained from other simulations and experiments.
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