www.globaljournal.asia GJESR RESEARCH PAPER VOL. 1 [ISSUE 1] FEBRUARY, 2014
ISSN:- 2349–283X
ANALYSIS OF FINITE ELEMENT MESH SPACING INFLUENCE ON MODELING RESULTS *Rohit Rai Dept. of Civil Engineering M.M.M. Engineering College Gorakhpur, India Email: rohit.rai2609@gmail.com
ABSTRACT- In the present work the modeling of curved deck slab was done with computer program which was done with the help of finite element method .In model the mesh spacing was varied and its influenced on various properties i.e. deflection, bending moments, and torsional moments are discussed. In this only quadrilateral meshing is taken. And it was found that the mesh spacing changes the results of FE Analysis. However, it also was found out that after certain value of mesh divisions the results start to converge. Keywords: Deflection, Bending Moment, Transverse Moment and Torsional Moment.
OVERVIEW OF FINITE ELEMENT ANALYSIS The finite element is a technique for analyzing complicated structures by notionally cutting up the continuum of the prototype into a number of small elements which are connected at discrete joints called nodes. For each element approximate stiffness equations are derived relating displacements of the nodes to node forces between elements and in the same way the slope –deflection equation can be solved for joints in a continuous beam, an electronic computer is used to solve the very large number of simultaneous equations that relate node force and displacements. Since the basic principle of subdivision of structure into simple elements can be applied to structures of all forms and complexity, there is no logical limit to the type of structure that can be analyzed if the computer program is written in the appropriate form. Consequently finite elements provide the more versatile method of analysis at present, and for some structures only practical method .However the quantity of computation can be enormous and expensive so that the cost cannot be justified for run of mill structures. Furthermore, the numerous different theoretical formulations of element stiffness characteristics all require approximations in different ways affect the accuracy and applicability of the method .Further research and development is required before the method will have the ease of use and reliability of the simple methods of bridge deck analysis. The technique was pioneered for two dimensional elastic structures by Turner et al and Clough during the1950s.The whole structure is divided into component elements, such as straight beams, curved beams, triangular or rectangular
plate elements, which are joined at the nodes. When this method is applied to a slab, the slab is divided into triangular, rectangular or quadrilateral elements. Thus, the corners of the elements become nodes usually; the vertical deflections of the plate element are expressed in a polynomial of the coordinates of the vertices of the element. This polynomial satisfies the conditions at the corners but may violate the continuity condition along the sides of the element. During recent years, several research workers have attempted to analyze curved bridge decks by the finite element method. Jenkins and Siddall used a stiffness matrix approach and represented the deck slab with finite elements in the form of annular segments, while Cheung adopted the triangular elements. In addition, a horizontal curved box-beam highway bridge was investigated in a three dimensional sense by Aneja and Roll. MODELING OF SLABS USING FINITE ELEMENTS If the finite element method is to be a useful tool in the design of reinforced concrete flat plate structures, accurate modeling is a prerequisite. Accurate modeling involves understanding the important relationships between the physical world and the analytical simulation. As Clough states, “Depending on the validity of the assumptions made in reducing the physical problem to a numerical algorithm, the computer output may provide a detailed picture of the true physical behavior or it may not even remotely resemble it”. The following sections attempt to expose the gap between physical and analytical behavior.
42 © Virtu and Foi