Combining Integrated Force Method and Basic Displacement Functions to Solve Nonprismatic Beams

Almost all engineering problems are indeterminate, so equilibrium equations are not sufficient to solve them and additional conditions called compatibility conditions should be satisfied. Aim of solving a problem is gaining internal forces and stresses, but because of need for compatibility conditions, direct methods of analyzing structure are abandoned. Thus indirect methods such as FEM have been developed. In such methods internal forces are back-calculated from displacements. In integrated force method (IFM) which is developed by Patnaik, compatibility conditions are formulated, so obstacle of direct method’s developing is passed. IFM does not use the idea of shape functions to calculate internal forces in domain of problem, and results are obtained at nodes. It has been shown that IFM’s results are more accurate than FEM’s, especially when stresses are needed, but since there was no flexibility based shape functions, using of this method is not so popular. Through introducing the concept of basic displacement functions (BDF) developed by R.Attarnejad, it is shown that exact shape functions are derived in terms of BDFs. They are obtained via application of flexibility method. The flexibility basis of the method ensures the true satisfaction of equilibrium equations at any interior point of element. Analysis of nonprismatic members has received a great deal attention from designers due to their wide use in practice. In this study basic displacement functions (BDF) and IFM are combined to solve nonprismatic beams. Using BDF’s shape functions help to gain stresses in all domain of problem. To show applicability of this method and exact problem is solved by combined method, FEM and analytical method. Stresses and deflection are calculated and compared. Results show that combined method is competitive especially for forces

Keywords:

Structural analysis , Nonprismatic beams , IFM , FEM