A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains

We consider fourth‐order singularly perturbed problems posed on smooth domains and the approximation of their solution by a mixed Finite Element Method on the so‐called Spectral Boundary Layer Mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at an exponential rate when the error is measured in the energy norm. Numerical examples illustrate our theoretical findings.     

The local ultraconvergence of high‐order finite element method for second‐order elliptic problems with constant coefficients over a rectangular partition

In this article, we will discuss the local ultraconvergence of high‐degree finite element method based on a rectangular partition for the second‐degree elliptic problem with constant coefficients in Ω ? ?² , u( y ) = 0 on ?Ω . Based on suitable regularity, ultraconvergence of the displacement of the extrapolated kth (k ≥ 3) degree finite element solution has been obtained by an extrapolation technique. Finally, numerical experiments are applied to demonstrate our theoretical findings.     

Evaluation of RBFs for volume data interpolation in CFD

A greedy method for choosing an optimum reduced set of control points is integrated with RBF interpolation and evaluated for the purpose of interpolating large‐volume data sets in CFD. Given a function defined at a set of points, the greedy method selects a small subset of these points that is sufficient to keep the interpolation error at all the remaining points below a chosen bound. This is equivalent to a type of data compression and would have useful storage, post‐processing, and computational applications in CFD. To test the method in terms of both the point selection scheme and the suitability of reduced control point volume interpolation, a trial application of the interpolation to velocity fields in CFD volume meshes is considered. To optimise the point selection process, and attempt to be able to capture multiple length scales, a variable support radius formulation has also been included. Structured and unstructured mesh cases are considered for aerofoils, a wing case and a wing‐body case. For smooth volume functions, the method is shown to work well, producing accurate velocity interpolations using a very small number of the cells in the mesh. For general complex fields including large gradients, the method is still shown to be effective, although large gradients require more interpolation points to be used.Copyright © 2013 John Wiley & Sons, Ltd.     

Exact pressure integrations on submerged bodies in waves using a quadtree adaptive mesh algorithm

The development of an adaptive free surface, mesh cutting, methodology, in order to analytically integrate pressures on varying wet parts of partially submerged surfaces in the presence of waves, is presented. Given a function of free‐surface elevation, the algorithm checks for the intersection of the body with the free surface and, based on user‐defined parameters, modifies the initial mesh, by subdividing the elements where necessary and eliminating others, via a quadtree approach. Redundant sub‐divisions, generated in the quad‐division process, are partially eliminated, but the quadrilateral nature of the elements is always kept. The free‐surface function must be single‐valued and its definition domain simply connected. Hydrostatic and Froude–Krylov forces are computed exactly on each panel by means of analytical formulations, which are derived and presented, based on the theory of linear gravity waves and from applying Green's theorem. Copyright © 2014 John Wiley & Sons, Ltd.     

A high‐order element based adaptive mesh refinement strategy for three‐dimensional unstructured grid

Adaptive mesh refinement (AMR) shows attractive properties in automatically refining the flow region of interest, and with AMR, better prediction can be obtained with much less labor work and cost compared to manually remeshing or the global mesh refinement. Cartesian AMR is well established; however, AMR on hybrid unstructured mesh, which is heavily used in the high‐Reynolds number flow simulation, is less matured and existing methods may result in degraded mesh quality, which mostly happens in the boundary layer or near the sharp geometric features. User intervention or additional constraints, such as freezing all boundary layer elements or refining the whole boundary layer, are required to assist the refinement process. In this work, a novel AMR strategy is developed to handle existing difficulties. In the new method, high‐order unstructured elements are first generated based on the baseline mesh; then the refinement is conducted in the parametric space; at last, the mesh suitable for the solver is output. Generating refined elements in the parametric space with high‐order elements is the key of this method and this helps to guarantee both the accuracy and robustness. With the current method, 3‐dimensional hybrid unstructured mesh of huge size and complex geometry can be automatically refined, without user intervention nor additional constraints. With test cases including the 2‐dimensional airfoil and 3‐dimensional full aircraft, the current AMR method proves to be accurate, simple, and robust.     

Search for a Steric Penultimate Effect: Copolymerization of 2,3,4-Trimethyl-3-pentyl Methacrylate with Styrene

The hindered monomer, 2,3,4-trimethyl-3-pentyl methacrylate (I), was synthesized for penultimate effect studies. Since it readily homopoiymerized (km¹¹¹≠ 0) and readily copolymerized with styrene, copolymerizations of I with styrene were carried out at 60°C in benzene with AIBN as initiator. The conversion to copolymer and the copolymer composition were determined by using GLC techniques. Composition-conversion data was analyzed by performing a computerized nonlinear least-squares fitting to the integrated form of the penultimate model equation. The experimental design included the use of optimized M¹°/M²° ratios. The penultimate reactivity ratios calculated from these data were r¹′ = 0.23, r¹′= 0.59, r² = 0.59, r²′ = 1.34. Thus, when I is the penultimate unit, a terminal styryl radical prefers to add styrene, whereas when styrene is the penultimate unit, terminal styryl radicals prefer to add I. These results constitute the best evidence for a steric penultimate effect yet available in the literature from composition-conversion studies. However, the case is not yet proved. Further studies to strengthen this conclusion are proposed.     

Nuclear quantum effect and temperature dependency on the hydrogen‐bonded structure of base pairs

The structure of Watson–Crick‐type adenine‐thymine and guanine‐cytosine pairs has been studied by hybrid Monte Carlo (HMC) and path integral hybrid Monte Carlo (PIHMC) simulations with the use of semiempirical PM6‐DH+ method in the gas phase. We elucidated the nuclear quantum effect and temperature dependency on the hydrogen‐bonded moiety of base pairs. It was shown that the contribution of nuclear quantum effect on the hydrogen‐bonded structure is significant not only at low temperature 150 K but also at temperature as high as 450 K. The relative position of hydrogen‐bonded proton between two heavy atoms and the nuclear quantum nature of the proton are also shown. Furthermore, we have applied principal component analysis to HMC and PIHMC simulations to analyze the nuclear quantum effect on intermolecular motions. We found that the ratio of Buckle mode (lowest vibrational mode from normal mode analysis) decreases due to the nuclear quantum effect, whereas that of Propeller mode (second lowest vibrational mode) increases. In addition, nonplanar structures of base pairs were found to become stable due to the nuclear quantum effect from two‐dimensional free energy landscape along Buckle and Propeller modes. © 2013 Wiley Periodicals, Inc.     

Performance of a parallel viscoelastic-viscoplastic model for a microcellular thermoplastic foam on wide temperature range

This paper is concerned with the experimental testing and the constitutive modelling of a thermoplastic microcellular polyethylene-terephthalate (MC-PET) foam on the temperature range of 21–210 °C in order to investigate the temperature-dependent performance of the applied parallel viscoelastic-viscoplastic material model. By means of carefully designed uniaxial mechanical tests in temperature chamber, the viscous, elastic and yielding behaviours of the investigated material are identified, which are then applied for selecting suitable viscoelastic-viscoplastic constitutive models. The material characterization process is conducted using finite-element-based fitting method, including also the analysis of the applied numerical optimization algorithm. The fitting results are used to analyse the parameter sensitivity and to propose closed-form analytical relations for the temperature dependency of the material parameters. Finally, the utilisation of the analytical temperature functions for speeding up the parameter-fitting process is also demonstrated.     

Effect of working temperature on the interfacial behavior of overmolded hybrid fiber reinforced polypropylene composites

In the present study, the interfacial behavior of overmolded hybrid fiber reinforced polypropylene composites (hybrid composites) in the working temperature range from 23 °C to 90 °C was studied by experimental and constitutive methods. Monotonic and cycle loading-unloading single-lap-shear tests were employed to determine the interfacial properties of hybrid composites. The experimental results show that both interfacial shear strength and shear stiffness decrease with increasing working temperature. A regression function was adopted to evaluate the decaying degree of interfacial properties with increasing working temperature. The shear stress-displacement relationship under monotonic loading exhibits nonlinear behavior after an initial elastic region. The envelope lines of shear stress-displacement of hybrid composites under cyclic loading indicate that the nonlinearity in the curve is caused by the plastic deformation of polypropylene in the interphase region. A constitutive model was built to describe the nonlinear shear stress-displacement relation of hybrid composites at different working temperatures. A full suite of temperature-dependent plastic parameters in the model was obtained from cyclic loading-unloading tensile tests. The predicted shear stress–displacement curves agreed well with experimental results from different working temperatures. In addition, the failure mode of hybrid composites varied with working temperature.     

Nonlinear free vibrations of porous composite microplates incorporating various microstructural-dependent strain gradient tensors

The main objective of the present numerical analysis is to predict the nonlinear frequency ratios associated with the nonlinear free vibration response of porous composite plates at microscale in the presence of different microstructural gradient tensors. To achieve this end, by taking cubic-type elements into account, isogeometric models of porous composite microplates are obtained with and without a central cutout and relevant to various porosity patterns of distribution along the plate thickness. The established unconventional models have the capability to capture the effects of various unconventional gradient tensors continuity on the basis of a refined shear deformable plate formulation. For the simply supported microsized uniform porous functionally graded material (U-PFGM) plate having the oscillation amplitude equal to the plate thickness, it is revealed that the rotation gradient tensor causes to reduce the frequency ratio about 0.73%, the dilatation gradient tensor causes to reduce it about 1.93%, and the deviatoric stretch gradient tensor leads to a decrease of it about 5.19%. On the other hand, for the clamped microsized U-PFGM plate having the oscillation amplitude equal to the plate thickness, these percentages are equal to 0.62%, 1.64%, and 4.40%, respectively. Accordingly, it is found that by changing the boundary conditions from clamped to simply supported, the effect of microsize on the reduction of frequency ratio decreases a bit.