Ambar K. Mitra

An algorithm for the solution of inverse Laplace problems and its application in flaw identification in materials

Abstract An algorithm for solving an inverse problem in steady state heat conduction is developed. In this problem, the location and shape of the inner boundary of a doubly connected domain is unknown. Instead, additional experimental data are provided at several points on the outer boundary. Through an iterative process, the unknown boundary is determined by minimizing a functional. Convergence properties of the algorithm are examined, and the stopping criterion for the iterative process is developed from numerical experiments in a simple case. The scheme is shown to perform well for the complex case of an L-shaped crack in a square domain.

Grid redistribution based on measurable error indicators for the direct boundary element method

Abstract The quality of solution obtained by using the boundary element method is dependent on how the boundary is discretized. This particularly true when the geometry is complex or the field variables are singular at certain points on the boundary. In regions along the boundary where the field variable or its normal derivative has large gradients, a finer discretization is necessary in order to improve the quality of the solution. Most rules of grid optimization for the boundary element method are related to minimizing error in an appropriate boundary error norm. The error norm should be measurable, reliable, and easy to compute. In this paper, a suitable error norm is defined, and the procedure for its computation is presented. Further, a strategy for grid redistribution is examined. In this scheme, the number of nodal points remain constant, but these points are repositioned, reducing the size of the elements in regions of large error.

A comparison of the semidiscontinuous element and multiple node with auxiliary boundary collocation approaches for the boundary element method

Several approaches have been considered to resolve boundary element formulation problems associated with geometric corners and edges as well as discontinuous boundary conditions. The semidiscontinuous element and multiple node approaches are perhaps the two most widely used methods. In the semidiscontinuous element approach, functional and collocation nodes are moved off geometric corners, edges, and lines of discontinuous boundary conditions. In the multiple node approach, multiple nodes are placed at corners, and double nodes are placed along edges and along lines of discontinuous boundary conditions. The purpose of this paper is to elucidate the differences between these two approaches and perform a direct comparison of the approaches by considering several numerical example problems.

The evaluation of the normal derivative along the boundary in the direct boundary element method

Abstract An integral representation for the normal derivative of a harmonic function at a field point along the boundary is derived for the direct boundary element method. The representation is written in terms of strongly singular integrals. Methods for evaluating these strongly singular integrals analytically are presented.

Non-uniqueness in the integral equation formulation of the biharmonic equation in multiply connected domains

Abstract In the boundary integral equation method, the biharmonic equation is converted to a pair of integral equations by using Greens third identity. In multiply connected domains, for a particular exceptional geometry the integral equations do not have a unique solution. Additional constraint equations are derived to enforce uniqueness in such situations. Two example problems are solved to demonstrate the effectiveness of the constraints.

Prediction of elastic properties of fiber-reinforced unidirectional composites

Abstract The purpose of this work is the evaluation of the global stiffness of a unidirectional fiber-reinforced composite. The effect of crenulations and debonding is also studied. The interfacial stresses for crenulated and debonded fibres are calculated. It is found that the crenulations of fibers affect the stress distribution more than the global stiffness. The boundary element method is employed in all calculations. In the use of the boundary element method for a multiple zone problem, certain difficulties arise at the corners that are present at the fiber-matrix interfaces. ‘shear modification’ scheme is developed for resolving such difficulties.

Numerical and Analytical Modeling of Free-Jet Melt Spinning for Fe75−Si10−B15 (at. %) Metallic Glasses

Amorphous fiber, ribbon, or film is produced through melt spinning. In this manufacturing process, a continuous delivery of amorphous material is simultaneously dependent on the wheel spinning rate, metallic liquid viscosity, surface tension force, heat transfer inside the melt pool and along the substrate, and other parameters. An analysis of a free-jet melt spinning for fiber manufacture has been performed to relate the process control parameters with amorphous formation. We present a numerical simulation of transient impingement of a free melt jet with a rapidly rotating wheel, along with theoretical estimates of melt ribbon thickness, to investigate dynamical characteristics of the flow in melt pool. The nucleation temperature and the critical cooling rate are predicted in the paper for alloy Fe75–Si10–B15 (at. %). Thermal conduction is found to dominate undercooling in melt spinning by comparing the temperature and velocity measurements with our numerical simulation and the analytical solutions.

Use of eigenfunctions in the optimization of the grid for the boundary element method

Abstract A scheme for grid optimization for the boundary element method is developed. The scheme utilizes the functional behavior of unknowns along the boundary. The functional behavior of these unknowns is estimated by a local eigenfunction analysis performed at certain critical points on the boundary. Based on this eigenfunction analysis, the user can construct an optimal grid with certain tolerance, in a preprocessor, before the integral equations are solved. The relationships between this tolerance and two error norms are established through numerical experiments. It is shown that the tolerance provides excellent upper bounds for the error norms. As a result, the user gets an idea about the quality of the solution even before the integral equations are solved.