Static analysis of functionally graded and laminated composite beams using various higher-order shear deformation theories: A study with mixed finite element models

Technological advancements continuously increase the demand for advanced materials. Laminated composites and Functionally Graded Materials (FGMs) are preferred for their high strength and lightweight properties. This study examines the static behavior of laminated composite and functionally graded beams. The field equations are formulated using the principle of virtual displacements. A functional is derived using a generalized higher- order shear deformation theory that incorporates several existing beam theories as special cases. A mixed finite element model of this theory is developed, treating displacement, force, and moment as nodal degrees of freedom. Various beam problems with different thickness functions and boundary conditions are analyzed. A comparison of the present model's numerical results with those in the literature shows that the present solutions for both laminated composite and functionally graded beams are accurate. Additionally, a detailed study of the stiffness coefficients of functionally graded beams is conducted.