Analysis of Cracks in Solids
Published in November 1999
Book
Hardback
408 pages
978-1-85312-625-3 (ISBN)
Description
The need for progress in modelling and analysis of crack problems in solids has resulted in renewed attempts at using modern approaches to boundary value problems. By taking a different viewpoint on the traditional treatment of many problems, such as crack theory, the range that can be resolved through mathematical tools is enlarged. This book provides a fresh outlook on crack problems, displaying new methods of studying these and proposing new models for cracks in elastic and nonelastic bodies satisfying physically suitable nonpenetration conditions between crack faces. Two- and three-dimensional bodies, plates and shells with cracks are considered. Properties of solutions such as existence of solutions, regularity up to the crack faces, and convergence of solutions as parameters of a system are varying are established, while different constitutive laws such as elastic, thermoelastic and elastoplastic are also analysed. The new approach presented by the authors is intriguing because it fails to lead to violation of physical properties. In addition, the boundary conditions analysed are given in the form of inequalities, and are properly nonpenetration conditions of crack faces.
This implies that similar problems may be considered from the contact mechanics standpoint. The contents are divided under the following headings: Introduction; Cracks in Plates and Shells; Cracks in Complicated Plates; Variation of Cracks in Solids; and Cracks in Elastoplastic Bodies.
This implies that similar problems may be considered from the contact mechanics standpoint. The contents are divided under the following headings: Introduction; Cracks in Plates and Shells; Cracks in Complicated Plates; Variation of Cracks in Solids; and Cracks in Elastoplastic Bodies.
More details
Series
Language
English
Place of publication
Southampton
United Kingdom
Target group
College/higher education
Professional and scholarly
Illustrations
illustrations
Dimensions
Height: 242 mm
Width: 165 mm
ISBN-13
978-1-85312-625-3 (9781853126253)
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Schweitzer Classification
Content
Introduction: Modelling of solids with cracks - Elements of convex analysis; Approximation methods; Problems with singular boundaries. Cracks in plates and shells: Viscoelastic contact problem for a plate; A plate under creep conditions; A plate with vertical and horizontal displacements; Contact problem for a plate having a crack; Cracks of minimal opening in plates; Solving methods for plates with cracks; Contact problem for a shell with a crack; Signorini problem for cracks in shells; Simplified nonpenetration conditions in contact problems; Solving methods for the simplified models. Cracks in complicated plates: Plate with a crack under the creep condition; Contact of two plates one of which has a crack; Thermoelastic plates with cracks; Cracks of minimal opening in thermoelastic plates; Inclined cracks in plates; Friction problem for plates with cracks. Variation of cracks in solids: Variation of a crack length; A plate with a crack; A crack moving to the external boundary; A case of a shallow shell; A crack near the boundary; Asymptotics of the energy functional for the Poisson equation; Asymptotics of the energy functional for the Lam? equations; Three-dimensional case; Extreme crack shapes in a shallow shell. Cracks in elastoplastic bodies: Elastoplastic problems for the Hencky model; Elastoplastic problems for the Prandtl-Reuss model; Elastoplastic problems for plates with cracks; The Prandtl-Reuss elastoplastic plates; Contact elastoplastic problem for the curvilinear Kirchhoff rod; Contact elastoplastic problem for the curvilinear Timoshenko rod; Viscoelastoplastic curvilinear Timoshenko rod; Curvilinear rod under creep conditions; Conclusion.