Crack-face displacements for embedded elliptic and semi-elliptical surface cracks

Analytical expressions for the crack-face displacements of an embedded elliptic crack in infinite solid subjected to arbitrary tractions are obtained. The tractions on the crack faces are assumed to be expressed in a polynomial form. These displacements expressions complete the exact solution of Vijayakumar and Atluri, and Nishioki and Atluri. For the special case of an embedded crack in an infinite solid subjected to uniform pressure loading, the present displacements agree with those by Green and Sneddon. The displacement equations derived were used with the finite-element alternating method (FEAM) for the analysis of a semi-elliptic surface crack in a finite solid subjected to remote tensile loading. The maximum opening displacements obtained with FEAM are compared to those with the finite-element method with singularity elements. The maximum crack opening displacements by the two methods showed good agreement

Meshless Local Petrov-Galerkin (MLPG) Method with Orthogonal Polynomials for Euler-Bernoulli Beam Problems

In this paper, the feasibility of orthogonal polynomials in the meshless local Petrov Galerkin method (MLPG) method is studied. The orthogonal polynomials, Chebyshev and Legendre polynomials, are used in this MLPG method as trial functions. The test functions used were power functions with smooth derivatives at their ends. The performance of these methods is studied by applying these methods to Euler-Bernoulli beam problems. The MLPG-Galerkin and Legendre methods passed all the patch tests for simple beam problems. Next the formulations are tested on complex beam problems such as beams with partial loadings and continuous beam problems. Problems with load discontinuities and additional supports require special attention. Near discontinuities, judicious choice of number of nodes and nodal placements are needed to obtain accurate deflections, slopes, moments and shear forces. As polynomial functions are used, the large number of nodes can create a transformation matrix that is ill-conditioned, resulting in problems with the inversion of the matrix. The conditioning worsens as the number of nodes are increased beyond 20. Quadruple precision was needed for models to obtain accurate solutions. Even with quadruple precision the accuracy of the method suffers as the number of nodes is increased beyond 20. This appears to be a drawback of the MLPG-Chebyshev and MLPG-Legendre methods

Finite-Size Effects on Nucleation in a First-Order Phase Transition

We discuss finite-size effects on homogeneous nucleation in first-order phase transitions. We study their implications for cosmological phase transitions and to the hadronization of a quark-gluon plasma generated in high-energy heavy ion collisions. Very general arguments allow us to show that the finite size of the early universe has virtually no relevance in the process of nucleation and in the growth of cosmological bubbles during the primordial quark-hadron and the electroweak phase transitions. In the case of high-energy heavy ion collisions, finite-size effects play an important role in the late-stage growth of hadronic bubbles.Comment: 6 pages, no figures, 1 reference adde

Tree Species Composition and Forest Stratification along the Gradients in the Dry Deciduous Forests of Godavari Valley, Telangana, India

It is important to understand the tree species composition, abundance, species diversity and stratification in tropical dry deciduous forests that are under threat. A quadrat study was attempted in the dry deciduous forests along the ecological gradients in the Godavari Valley of northern Telangana, India. The study records the presence of 110 flowering plant taxa belonging to 82 genera and 37 families in 120 sampled plots, and there was enumeration of 15,192 individuals of ≥10 cm girth at breast height. Tectona grandis (teak) is the principal forest cover component in the region, which often formed pure stands in Adilabad and, to some extent, in Nizamabad districts. Further down to the Warangal district, teak was gradually replaced by Terminalia alata. Twenty tree species were found dominant at one place to the other, and the top 10 dominant taxa have shared nearly 41% of the total density of the forest cover. The tree relative density ranged from 0.007% to 20.84%. The values of Importance Value Index were between 0.245 (12 spp. including some exotics) and 32.6 (teak). These baseline data help to know the change detection along the gradients in the tropical forest ecosystem of a major river valley in the region and the drivers of change

A boundary element alternating method for two-dimensional mixed-mode fracture problems

A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort