Beam theory reformulation to implement various boundary conditions for generalized differential quadrature method: Fid-Bau Portal

Beam theory reformulation to implement various boundary conditions for generalized differential quadrature method

Keleshteri, M.M. / Jelovica, J.

Highlights • Reddy and Euler–Bernoulli beam theories are reformulated by using a new function. • Based on the presented approach, the order of the governing equation is reduced. • The original GDQ method can be used for any boundary condition with no extra steps. • Buckling and vibration behavior of isotropic, FG and porous beams are considered. • The proposed approach is accurate and easy to implement.

Abstract Generalized differential quadrature (GDQ) method is often used for static and dynamic analysis of structures due to its simplicity and low computational cost. The difficulty arises in the implementation of boundary conditions for higher-order differential equations. A few approaches exist to overcome this issue, but all are more complicated than the original GDQ, increasing the computational cost or having other limitations. In this paper, a novel approach is proposed where the order of the governing differential equations of Euler-Bernoulli and Reddy-Bickford beams is reduced from four to two by introducing a new dependent function. The generality and accuracy of the new approach are demonstrated through its application to the buckling and vibration analysis of different kind of composites, specifically beams made of functionally graded material (FGM), and porous material, considering various combinations of boundary conditions. High accuracy is achieved in comparison to literature.