| Abstract: | This paper presents a new element based method through a treatment of a one dimensional model problem. The case solved in this work is of a rod with variable cross-sectional area, supported along its length by variable stiffness elastic foundation, and loaded with variable axial load. The variations of all the quantities are taken as general polynomials. Using this method the exact terms in the stiffness matrix are found using the solution for the differential equation (up to any desired accuracy). The exact solution is obtained using one element for each segment with continuously varying properties, and the displacements and stresses are exact all along the rod. |
