By Zohar Yosibash

This introductory and self-contained e-book gathers as a lot particular 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 third-dimensional domain names. those are awarded in an  engineering terminology for functional utilization. the writer treats the mathematical   formulations from an engineering standpoint and provides high-order finite-element  methods for the computation of singular ideas 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 will be correlated to experimental observations.

 

The booklet is split into fourteen chapters, each one containing numerous sections.

Most of it (the first 9 Chapters) addresses two-dimensional domain names, where

only singular issues exist. the answer in a area of those issues admits an asymptotic growth composed of eigenpairs and associated generalized flux/stress depth elements (GFIFs/GSIFs), that are being computed analytically whilst attainable or by means of finite aspect equipment differently. Singular issues linked to weakly coupled thermoelasticity within the neighborhood of singularities also are addressed and thermal GSIFs are computed. The computed information is critical in engineering perform for predicting failure initiation in brittle material each day.  Several failure laws for two-dimensional domain names with V-notches are presented and their validity is tested by way of comparability to experimental observations. A adequate easy and trustworthy for predicting failure initiation (crack formation) in micron point digital units, related to singular points, remains to be an issue of lively study and curiosity, and is addressed herein.

 

Explicit singular strategies within the area of vertices and edges in 3-dimensional domain names are supplied within the last 5 chapters. New tools for the computation of generalized aspect flux/stress depth capabilities alongside  singular edges are provided and verified by way of numerous instance  difficulties from the sphere of fracture mechanics; together with anisotropic domain names and bimaterial interfaces. round edges also are offered 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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