Applications of FEM and BEM in two-dimensional fracture mechanics problems

A comparison of the finite element method (FEM) and boundary element method (BEM) for the solution of two-dimensional plane strain problems in fracture mechanics is presented in this paper. Stress intensity factors (SIF's) were calculated using both methods for elastic plates with either a single-edge crack or an inclined-edge crack. In particular, two currently available programs, ANSYS for finite element analysis and BEASY for boundary element analysis, were used

Lowest order Virtual Element approximation of magnetostatic problems

We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general decompositions of the computational domain (as is natural for Virtual Element Methods) and uses as unknowns the (constant) tangential component of the magnetic field $\mathbf{H}$ on each edge, and the vertex values of the Lagrange multiplier $p$ (used to enforce the solenoidality of the magnetic induction $\mathbf{B}=\mu\mathbf{H}$). In this respect the method can be seen as the natural generalization of the lowest order Edge Finite Element Method (the so-called "first kind N\'ed\'elec" elements) to polyhedra of almost arbitrary shape, and as we show on some numerical examples it exhibits very good accuracy (for being a lowest order element) and excellent robustness with respect to distortions

Topological phases of topological insulator thin films

We study the properties of a thin film of topological insulator material. We treat the coupling between helical states at opposite surfaces of the film in the properly-adapted tunneling approximation, and show that the tunneling matrix element oscillates as function of both the film thickness and the momentum in the plane of the film for Bi$_2$Se$_3$ and Bi$_2$Te$_3$. As a result, while the magnitude of the matrix element at the center of the surface Brillouin Zone gives the gap in the energy spectrum, the sign of the matrix element uniquely determines the topological properties of the film, as demonstrated by explicitly computing the pseudospin textures and the Chern number. We find a sequence of transitions between topological and non-topological phases, separated by semimetallic states, as the film thickness varies. In the topological phase the edge states of the film always exist but only carry a spin current if the edge potentials break particle-hole symmetry. The edge states decay very slowly away from the boundary in Bi$_2$Se$_3$, making Bi$_{2}$Te$_{3}$, where this scale is shorter, a more promising candidate for the observation of these states. Our results hold for free-standing films as well as heterostructures with large-gap insulators

Free edge strain concentrations in real composite laminates: Experimental-theoretical correlation

The magnitude of the maximum shear strain at the free edge of axially loaded theta (2)/-theta(2)(s) and (+ or - theta(2) (s) composite laminates was investigated experimentally and numerically to ascertain the actual value of strain concentration in resin matrix laminates and to determine the accuracy of finite element results. Experimental results using moire interferometry show large, but finite, shear strain concentrations at the free edge of graphite-epoxy and graphite-polyimide laminates. Comparison of the experimental results with those obtained using several different finite element representations showed that a four node isoparametric finite element provided the best and most trouble free numerical results. The results indicate that the ratio of maxium shear strain at the free edge to applied axial strain varies with fiber orientation and does not exceed nine for the most critical angle which is 15 deg

Local delamination in laminates with angle ply matrix cracks. Part 1: Tension tests and stress analysis

Quasi-static tension tests were conducted on AS4/3501-6 graphite epoxy laminates. Dye penetrant enhanced x-radiography was used to document the onset of matrix cracking and the onset of local delaminations at the intersection of the matrix cracks and the free edge. Edge micrographs taken after the onset of damage were used to verify the location of the matrix cracks and local delamination through the laminate thickness. A quasi-3D finite element analysis was conducted to calculate the stresses responsible for matrix cracking in the off-axis plies. Laminated plate theory indicated that the transverse normal stresses were compressive. However, the finite element analysis yielded tensile transverse normal stresses near the free edge. Matrix cracks formed in the off-axis plies near the free edge where in-plane transverse stresses were tensile and had their greatest magnitude. The influence of the matrix crack on interlaminar stresses is also discussed

A comparison of experimental and calculated thin-shell leading-edge buckling due to thermal stresses

High-temperature thin-shell leading-edge buckling test data are analyzed using NASA structural analysis (NASTRAN) as a finite element tool for predicting thermal buckling characteristics. Buckling points are predicted for several combinations of edge boundary conditions. The problem of relating the appropriate plate area to the edge stress distribution and the stress gradient is addressed in terms of analysis assumptions. Local plasticity was found to occur on the specimen analyzed, and this tended to simplify the basic problem since it effectively equalized the stress gradient from loaded edge to loaded edge. The initial loading was found to be difficult to select for the buckling analysis because of the transient nature of thermal stress. Multiple initial model loadings are likely required for complicated thermal stress time histories before a pertinent finite element buckling analysis can be achieved. The basic mode shapes determined from experimentation were correctly identified from computation