Static analysis of composite circular and straight axis beam systems by complementary functions method

In this study, the behavior of frame systems with layered composite material consisting of straight and/or circular axis uniform and variable cross-section rods under the static in-plane point/uniformly distributed loads are examined by the Complementary Functions Method (CFM). Equations governing the static behavior of the straight and circular axis rods with variable cross-section are obtained by using the Timoshenko beam theory. The axial and shear deformation effects are considered in the formulations. The fifth-order Runge- Kutta (RK5) algorithm has been employed in the solution process of initial value problems by the CFM. The rigidity matrices and load vectors of these structural elements have been obtained by the CFM and for this purpose, a computer program is coded in FORTRAN. With the help of prepared program the effects of layer sticking angle, on the nodal displacement and element end forces of frames with variable cross-section and geometry features are investigated. The effects of the E1/E2 ratio on the element end forces and nodal displacement values of the system are investigated considering different layer sticking angles.The problems are solved in the program coded in FORTRAN for several E1/E2 ratios separately. Verification of the computer program is performed with the comparison of the presented results and those of the finite element method and it is shown that they are effective and in a good agreement with ANSYS and the literature. Keywords: Complementary Functions Method, Layered Composite Frames, Variable Cross-Sectioned Rods, Static Analysis, Two Point Boundary Value Problems.