By Zohar Yosibash
This introductory and self-contained e-book gathers as a lot specific mathematical effects at the linear-elastic and heat-conduction solutions locally of singular issues in two-dimensional domain names, and singular edges and vertices in 3-dimensional domain names. those are offered in an engineering terminology for useful utilization. the writer treats the mathematical formulations from an engineering standpoint and offers high-order finite-element methods for the computation of singular options in isotropic and anisotropic fabrics, and multi-material interfaces. The right interpretation of the consequences in engineering perform is endorsed, in order that the computed info might be correlated to experimental observations.
The publication is split into fourteen chapters, every one containing a number of sections.
Most of it (the first 9 Chapters) addresses two-dimensional domain names, where
only singular issues exist. the answer in a region of those issues admits an asymptotic enlargement composed of eigenpairs and associated generalized flux/stress depth components (GFIFs/GSIFs), that are being computed analytically whilst attainable or by way of finite aspect equipment in a different way. Singular issues linked to weakly coupled thermoelasticity within the neighborhood of singularities also are addressed and thermal GSIFs are computed. The computed info is necessary in engineering perform for predicting failure initiation in brittle material every day. Several failure laws for two-dimensional domain names with V-notches are presented and their validity is tested through comparability to experimental observations. A adequate easy and trustworthy situation for predicting failure initiation (crack formation) in micron point digital units, concerning singular points, continues to be a subject of energetic study and curiosity, and is addressed herein.
Explicit singular options within the region of vertices and edges in three-d domain names are supplied within the closing 5 chapters. New equipment for the computation of generalized part flux/stress depth services alongside singular edges are awarded and validated by means of a number of instance difficulties from the sphere of fracture mechanics; together with anisotropic domain names and bimaterial interfaces. round edges also are provided and the writer concludes with a few comments on open questions.
This good illustrated ebook will attract either utilized mathematicians and engineers operating within the box of fracture mechanics and singularities.
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Additional info for Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation: 37 (Interdisciplinary Applied Mathematics)
Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation: 37 (Interdisciplinary Applied Mathematics) by Zohar Yosibash