NED University Journal of Research
ISSN 2304-716X
E-ISSN 2706-5758




NATURAL FINITE ELEMENT METHOD: A NEW PROPOSAL FOR STIFFNESS CALCULATION USING NATURAL DERIVATIVES

Author(s): Abdolrasoul Ranjbaran1, Mohammad Ranjbaran2, Shahab Ayatollahi3, Vahid Taghikhani3, Saeed Shad3
1 Associate Professor, Department of Civil and Environmental Engineering, Shiraz University, Iran, Ph. +98 917 314 5501, Fax: +98 713 6473161, Email: ranjbarn@shirazu.ac.ir.
2 PhD student, Department of Chemical and Petroleum Engineering, Shiraz University, Iran, Email: ranjbaran@che.sharif.ir.
3 Professor, Department of Chemical and Petroleum Engineering at Sharif University of Technology, Iran, Ph. +98 917 118 4379, Fax: +98 2166166421-2, Email: dr.ayatollahi@gmail.com.
4 Professor, Department of Chemical and Petroleum Engineering at Sharif University of Technology, Iran, Ph. +98 2166166417, Fax: +98 2166166421-2, Email: vahid.taghikhani@rice.edu.
5 Assistant Professor, Department of Chemical and Petroleum Engineering at Sharif University of Technology, Iran, +98 9128468677, Fax: +98 2166166421-2, Email: Saeed.shad@gmail.com.

Volume: XIII

No. 3

Pages: 61 - 68

Date: July 2016

Abstract:
The cross stiffness in the standard form of the stiffness matrix is conventionally defined as the product of the core derivatives of the shape functions which are integrated over the domain of the element. This paper proposes a new method of analysis of cracked structures in which the stiffness is simply defined as a natural derivative of the shape function. As a result, the proposed method takes less time to solve the problem as compared to the finite element method. The proposed method can be equally applied to both the uncracked and cracked structures. The derivation, implementation and verification of the proposed method have been presented and discussed in this paper.