Finite Element Method A Tool For Learning Highway Design

A computer program was developed by idealizing flexible pavement into a finite element continuum. A layered pavement was idealized as an axisymmetric solid with finite boundaries in both radial and axial directions. The axisymmetric body was then divided into a set of ring elements, rectangular in section and connected along their nodal circles. Because of symmetry, the three-dimensional problem reduces to a two dimensional case. The program is capable of handling changes of material properties such as Resilient Modulus and Poisson’s Ratio in both vertical and horizontal directions. Several other elastic multilayered computer programs are available for the structural analysis of a pavement such as ELSYM, BISAR, and ILLIPAVE. However this program is suitable for eliminating tensile stresses in granular layers by stress transfer method. Moreover this program is tailor made for analyzing runway pavements making it user friendly. Thus the demand for time and energy for learning initialization process of other advanced software is eliminated. Students have successfully used this program for not only designing the runways but also optimizing their design by simulation. The power of simulation of the program enhanced the students’ learning of runway design by providing them a feel for the large ranges of weather, load and material conditions that exist in the country. Statistical tests were conducted and results were documented on the power of simulation. Development of Finite Element Analysis A computer program was developed by idealizing the flexible pavement into a finite element continuum. In this investigation a layered pavement system was idealized as an axisymmetric solid with finite boundaries in both radial and axial directions, as shown in Fig 1. The axisymmetric body was then divided into a set of ring elements, rectangular in section and connected along their nodal circles. The finite elements are actually complete rings in the circumferential direction, and the nodal points at which they are connected are circular lines in plan view. Because of axisymmetry, the three-dimensional problem reduces to a two-dimensional case similar to a plane strain problem. Tensile stresses and strains were taken to be positive, and compressive stresses and strains negative. For each element the four nodal points were numbered in the clockwise direction. Each node has two degrees of freedom. Displacement Functions The two displacement components in a solid continuum varied as complicated functions of position. A number of approaches, including power series and Fourier series expansions, have been proposed by several researchers to represent the behavior of displacement components inside each element. Because of the assumptions made about these functions, the accuracy of the answer increases as the element size decreases. For this investigation, the displacement functions inside each element were approximated by the following: u(r,z) = b1 + b2r’ + b3z’ + b4r’z’ v(r,z) = b5 + b6r’ + b7z’ + b8r’z’ where for each element the local coordinate system r’, z’ was used, which has its origin at the center of each element.