A boundary element method is presented for the stress analysis of cracks in two-dimensional, linearly elastic anisotropic solids. The technique is an extension of that by Chang and Mear  for isotropic solids and involves the use of a special “regularization” for certain integrals associated with the crack line. The resulting integral equations consist of the conventional ordinary boundary terms as well as two additional terms that correspond to a distribution of concentrated forces and a distribution of dislocations along the crack line. In the numerical implementation of the formulation, the ordinary boundary integrals are treated with standard boundary element techniques, while a special numerical procedure is used to treat the crack line integrals. The resulting procedure is applied to several example problems to demonstrate the accuracy and efficiency of the method.
Domestic orders are delivered via United Parcel Service (UPS) or United States Postal Service (USPS). Transit times average 3 to 5 business days. Please be aware that UPS will not deliver packages to Post Office Boxes.
Domestic Rush Orders
Please Contact Us.
International Standard Shipping
International orders are delivered via courier post services which can be either a postal service, courier service, or a combination of both. Standard Service is untraceable. Please allow 4-7 weeks for delivery.
International Expedited Shipping
Please Contact Us.
Please be aware that carriers will not deliver packages to Post Office Boxes. Because of the variability of customs processes and procedures in different countries, ASTM International cannot guarantee transit times to international destinations. Customs duty and taxes are the responsibility of the consignee.
Shipping & Handling charges follow the rate schedule, below:
|Order Total||Shipping & Handling Fee|
|Up to $50.00||$8.20|
|$50.01 to $100.00||$16.22|
|$100.01 to $150.00||$23.89|
|$150.01 to $250.00||$31.91|
|$250.01 to $500.00||$46.31|
|$500.01 to $750.00||$63.21|
|$750.01 to $1000.00||$77.25|
|$1000.01 to $1500.00||$100.83|
|$1500.01 to $2500.00||$131.94|
|$2500.01 to $4999.00||$174.43|
|$5000.00 to $higher||$FREE|
Shipping and Handling charges are approximate. Additional charges may be incurred if your order requires multiple shipments. This does not apply to complete sets and sections.
IMPORTANT-READ THESE TERMS CAREFULLY BEFORE DOWNLOADING THIS DOCUMENT. By downloading the ASTM Document you are entering into a contract, and acknowledge that you have read this License Agreement, that you understand it and that you agree to be bound by its terms. If you do not agree to the terms of this License Agreement, promptly exit this page without downloading the ASTM Document.
Please click here to view License Agreement for Educational Institutions.
Ownership. This document is copyrighted by the ASTM International (ASTM), 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959 USA. All rights reserved. You (Licensee) have no ownership or other rights in the ASTM Document. This is not a sale; all right, title and interest in the ASTM Document (in both electronic file and hard copy) belong to ASTM. You may not remove or obscure the copyright notice or other notices contained in the ASTM Document.
Limited License. ASTM grants you a limited, non-transferable license as follows: The right to download an electronic file of this ASTM Document for temporary storage on one computer for purposes of viewing, and/or printing one copy of the ASTM document for individual use. Neither the electronic file nor the single hard copy print may be reproduced in any way. In addition, the electronic file may not be distributed elsewhere over computer networks or otherwise. That is, the electronic file cannot be e mailed, downloaded to disk, copied to another hard drive, or otherwise shared. The single hard copy print may only be distributed to other employees for their internal use within your organization; it may not be copied. This ASTM Document may not otherwise be sold or resold, rented, leased, lent or sub-licensed. The Subscriber will be responsible for all access control and security measures necessary to ensure that the Subscriber's IP addresses are not used to access the journals other than by authorized Users.
ASTM International grants to the Subscriber and Authorized Users at the Subscriber's Authorized Site, online access to ASTM's journal for which the Subscriber maintains a current subscription to the print or online version. This grant extends only to the Subscriber and such Authorized Users individually and may not be transferred to, or extended to, others. For reprints of a journal article, please contact ASTM Customer Service, 100 Barr Harbor Dr., PO Box C700, West Conshohocken, PA 19428, phone: 610-832-9555; fax: 610-832-9585; e-mail: firstname.lastname@example.org
Verification: ASTM has the right to verify compliance with this License Agreement, at its expense, and at any time during the course of normal business hours. To do so, ASTM will engage an independent consultant, subject to a confidentiality agreement, to review your use of ASTM Documents. You agree to permit access to your information and computer systems for this purpose. Verification will take place upon no less than 15 days notice, during normal business hours and in a manner that does not interfere unreasonably with your operations. If verification reveals unlicensed use of ASTM Documents, you must reimburse ASTM for the costs incurred in verification and reimburse ASTM for any unlicensed uses. By invoking this procedure, ASTM does not waive any of its rights to enforce this Agreement or to protect its intellectual property by any other means permitted by law.
Passwords. You must immediately notify ASTM of any known or suspected unauthorized use(s) of your password, or any known or suspected breach of security, including the loss, theft or unauthorized disclosure of your password or any unauthorized access to or use of The ASTM Document. You are solely responsible for maintaining the confidentiality of your password and for ensuring the authorized access and use of The ASTM Document.
Definitions. For purposes of this License, an Authorized Site is a localized site (one geographical location) that is under a single administration at a single location. For a Subscriber with locations in more than one city, each city is considered to be a different site. For a Subscriber with multiple locations in the same city, each location is considered to be a different site. (If you are seeking online access for multiple sites, please contact Kathe Hooper, ASTM International, at email@example.com or phone: 610-832-9634). Authorized User means only the employees, faculty, staff, and students officially affiliated with the Subscriber at the Authorized Site, and persons with legal access to the library's collections and facilities at the Authorized Site, using an IP address within the range identified in the subscription. Authorized Users may be persons remote from the Subscriber's physical location whose access is administered from the Authorized Site, but not persons at remote sites or campuses with separate administrations. For example, an employee of the Subscriber may be considered to be an Authorized User when accessing the Subscriber's network from home or while traveling to another city; however, employees of a branch campus or facility in another city are not considered to be Authorized Users. Subscriber is the person or entity which has subscribed to the ASTM journal and agreed to the terms of this limited license.
Termination. This Agreement is effective until terminated. You may terminate this Agreement at any time by destroying all copies (hard, digital or in any media) of the ASTM Document (journal).
Governing Law, Venue, Jurisdiction. This Agreement shall be interpreted and construed in accordance with the laws of the Commonwealth of Pennsylvania. Licensee agrees to submit to jurisdiction and venue in the state and federal courts of Pennsylvania for any dispute which may arise under this Agreement. You also agree to waive any claim of immunity you may possess.
Integration. This Agreement is the entire agreement between you and ASTM relating to its subject matter. It supersedes all prior or contemporaneous oral or written communications, proposals, representations and warranties and prevails over any conflicting or additional terms of any quote, order, acknowledgment, or other communication between the parties relating to its subject matter during the term of this Agreement. No modification of this Agreement will be binding, unless in writing and signed by an authorized representative of each party.
Disclaimer of Warranty. Unless specified in this Agreement, all express or implied conditions, representations and warranties, including any implied warranty of merchantability, fitness for a particular purpose or non-infringement are disclaimed, except to the extent that these disclaimers are held to be legally invalid.
Limitation of Liability. To the extent not prohibited by law, in no event will ASTM be liable for any loss, damage, lost data or for special, indirect, consequential or punitive damages, however caused regardless of the theory of liability, arising out of or related to the use or downloading of the ASTM Document. In no event will ASTM’s liability exceed the amount paid by you under this License Agreement.
These documents are copyrighted by ASTM International, 100 Barr Harbor Drive,PO Box C700, West Conshohocken, PA 19428-2959 USA. All rights reserved.