Modeling elastic wave propagation in fluid-filled boreholes drilled in nonhomogeneous media: BEM – MLPG versus BEM-FEM coupling

The efficiency of two coupling formulations, the boundary element method (BEM)-meshless local Petrov–Galerkin (MLPG) versus the BEM-finite element method (FEM), used to simulate the elastic wave propagation in fluid-filled boreholes generated by a blast load, is compared. The longitudinal geometry is assumed to be invariant in the axial direction (2.5D formulation). The material properties in the vicinity of the borehole are assumed to be nonhomogeneous as a result of the construction process and the ageing of the material. In both models, the BEM is used to tackle the propagation within the fluid domain inside the borehole and the unbounded homogeneous domain. The MLPG and the FEM are used to simulate the confined, damaged, nonhomogeneous, surrounding borehole, thus utilizing the advantages of these methods in modeling nonhomogeneous bounded media. In both numerical techniques the coupling is accomplished directly at the nodal points located at the common interfaces. Continuity of stresses and displacements is imposed at the solid–solid interface, while continuity of normal stresses and displacements and null shear stress are prescribed at the fluid–solid interface. The performance of each coupled BEM-MLPG and BEM-FEM approach is determined using referenced results provided by an analytical solution developed for a circular multi-layered subdomain. The comparison of the coupled techniques is evaluated for different excitation frequencies, axial wavenumbers and degrees of freedom (nodal points).Ministerio de Economía y Competitividad BIA2013-43085-PCentro Informático Científico de Andalucía (CICA

Bending analyses of 1D orthorhombic quasicrystal plates

AbstractThe meshless Petrov–Galerkin method (MLPG) is applied to plate bending analysis in 1D orthorhombic quasicrystals (QCs) under static and transient dynamic loads. The Bak and elasto-hydrodynamic models are applied for phason governing equation in the elastodynamic case. The phason displacement for the orthorhombic QC in the first-order shear deformation plate theory depends only on the in-plane coordinates on the mean plate surface. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the center of a circle surrounding this node. The coupled governing partial differential equations are satisfied in a weak-form on small fictitious subdomains. The spatial variations of the phonon and phason displacements are approximated by the moving least-squares (MLS) scheme. After performing the spatial MLS approximation, a system of ordinary differential equations (ODEs) for nodal unknowns is obtained. The system of the ODEs of the second order is solved by the Houbolt finite-difference scheme. Our numerical examples demonstrate clearly the effect of the coupling parameter on both static and dynamic phonon/phason deflections

Fracture analysis in continuously nonhomogeneous magneto-electro-elastic solids under a thermal load by the MLPG

AbstractA meshless method based on the local Petrov–Galerkin approach is proposed, to solve initial-boundary value problems of magneto-electro-elastic solids with continuously varying material properties. Stationary and transient thermal problems are considered in this paper. The mechanical 2-D fields are described by the equations of motion with an inertial term. Nodal points are spread on the analyzed domain, and each node is surrounded by a small circle for simplicity. The spatial variation of displacements, electric and magnetic potentials is approximated by the moving least-squares (MLS) scheme. After performing the spatial integrations, one obtains a system of ordinary differential equations for certain nodal unknowns. That system is solved numerically by the Houbolt finite-difference scheme as a time stepping method

Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element

The modulus of elasticity of some materials changes under tensile and compressive states is simulated by constructing a typical material nonlinearity in a numerical analysis in this paper. The meshless Finite Block Method (FBM) has been developed to deal with 3D semi-infinite structures in the bimodular materials in this paper. The Lagrange polynomial interpolation is utilized to construct the meshless shape function with the mapping technique to transform the irregular finite domain or semi-infinite physical solids into a normalized domain. A shear modulus strategy is developed to present the nonlinear characteristics of bimodular material. In order to verify the efficiency and accuracy of FBM, the numerical results are compared with both analytical and numerical solutions provided by Finite Element Method (FEM) in four examples

Flapping Wing Micro Air Vehicle Wing Manufacture and Force Testing

Numerous wing manufacturing techniques have been developed by various universities for research on Flapping Wing Micro Air Vehicles. Minimal attention though is given to repeatability of wing aerodynamics and dynamic response, which is crucial to avoid asymmetric flapping. Thus the focus of this research becomes twofold. First, repeatable wing manufacturing techniques are developed to ensure flapping wings have similar aerodynamic and dynamic characteristics. For this purpose, four wing designs were selected to not only test the aerodynamics of the different designs, but to also validate manufacturing techniques. The various wing designs are assessed using two methods: dynamic and aerodynamic data. Dynamic data, specifically the wing\u27s structural dynamic response, is measured using a 3D laser vibrometer. From this vibration data, the wings natural frequency modes can be determined which should correlate strongly within the various wing designs if the manufacturing techniques are repeatable. Next, using a piezoelectric flapping actuator, the four wing designs are flapped with force data collected. This data is then used to determine the aerodynamic characteristics of each wing. From the two methods of wing evaluation, it was found that the wings manufactured using a three-layer carbon layup showed greater structural dynamic modal repeatability as compared to one-layer carbon wings. Additionally, Wing Design 3 flapped with the most efficiency with a significantly higher lift to drag ratio as compared to the other wing designs. From this research, the wing manufacturing techniques are quantitatively shown to be repeatable while an optimal wing design based on the maximum lift-to-drag ratio is found which can be used for future research

Hybrid meshless/displacement discontinuity method for FGM Reissner's plate with cracks

Growing applications of non-homogenous media in engineering structures require the application of powerful computational tools. A novel hybrid Meshless Displacement Discontinuity Method (MDDM) for cracked Reissner's plate in Functionally Graded Materials (FGMs) is presented in this paper. The fundamental solutions of slope and deflection discontinuity for an isotropic homogenous media are chosen as a part of general solutions to create the gaps between the crack surfaces. The governing equation is satisfied by using the meshless methods such as the Meshless Local Petrov-Galerkin (MLPG) and the Point Collocation Method (PCM) with Lagrange series interpolation and mapping technique. The Stress Intensity Factors (SIFs) are evaluated analytically with the Chebyshev polynomials. The accuracy is verified by comparison of numerical and analytical results

TiO2 film properties as a function of processing temperature, volume 3

Thin film TiO2 was produced at 150 C by chemical vapor deposition using hydrolysis of tetraisopropyl titanate. Films were amorphous as grown, but annealing in air caused crystallization, with anatase formed beginning at 350 C and rutile at 700 C. Density and index of refraction increased substantially with increasing anneal temperature, while etch susceptibility in HF and H2SO4 decreased. Comparison with literature data showed two groups of processes. One group yields films having properties that gradually approach those of rutile with increasing process temperature. The other group gives rutile directly at moderate temperatures. Deposition of amorphous film followed by etching and annealing is suggested as a means for pattern definition

Habitat connectivity in reef fish communities and marine reserve design in Old Providence-Santa Catalina, Colombia

On the insular platform of Old Providence/Santa Catalina, Colombia, we compared nearshore lagoonal patch reefs to those on the northern bank distant from the islands to determine the importance of habitat connectivity to fish community structure. Nearshore patch reefs had greater proximity to mangrove, seagrass and rocky shore habitats, and they had significantly more individuals. Nearshore reefs also tended to have a greater total biomass, more species, a higher proportion of predators of mobile invertebrates and small fishes, and a lower proportion of herbivores. Biomass of snappers and grunts at nearshore sites was four times greater compared to bank sites, and was correlated with the amount of seagrass and sand/rubble habitat within 500 m of each patch reef. We also compared length-frequency distributions and abundances of grunts and snappers among all sites (deep and shallow forereefs, patch reefs and deep and shallow leeside slopes). The results were consistent with ontogenetic migrations from shallow sites, primarily seagrass and mangrove habitats, to deeper sites and to those further out on the bank. The evidence suggests that species differed in both distance and direction of dispersal, which may be affected by the abundance and distribution of preferred habitats. Marine reserves near the islands should target nearshore nursery areas and patch reefs harboring species of limited dispersal capability. Reserves on the northern bank would protect spawners of those species showing the greatest dispersal capability

Numerics of boundary-domain integral and integro-differential equations for BVP with variable coefficient in 3D

This is the post-print version of the article. The official published version can be accessed from the links below - Copyright @ 2013 Springer-VerlagA numerical implementation of the direct boundary-domain integral and integro-differential equations, BDIDEs, for treatment of the Dirichlet problem for a scalar elliptic PDE with variable coefficient in a three-dimensional domain is discussed. The mesh-based discretisation of the BDIEs with tetrahedron domain elements in conjunction with collocation method leads to a system of linear algebraic equations (discretised BDIE). The involved fully populated matrices are approximated by means of the H-Matrix/adaptive cross approximation technique. Convergence of the method is investigated.This study is partially supported by the EPSRC grant EP/H020497/1:"Mathematical Analysis of Localised-Boundary-Domain Integral Equations for Variable-Coefficients Boundary Value Problems"