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

Vibration of thin elastic FGM plates with multi-gradation effects

In this paper we investigate the vibration response of thin elastic FGM plates with combination of transversal and/or in-plane gradation of various material parameters subjected to transient tension loading. The equations of motion and initial-boundary conditions for transient problems are derived within Kirchhoff-Love plate theory. For numerical modelling of plates with dynamic multi-gradation coupling effects, it is developed the strong formulation with using the meshless approximation of field variables by the Moving Least Square (MLS) approximation scheme. Several numerical examples are presented for illustration of the multi-gradation coupling effects in vibration response of elastic FGM plates

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

Higher Education’s Anchor Mission: Measuring Place-Based Engagement

The Anchor Dashboard project highlights university efforts to address tenacious community challenges and serves as a tool for how institutions can form more strategic economic and social relationships with local communities, especially those that are low income. One of the case studies is for Buffalo, NY