Static Analysis of Functionally Graded Laminates According to Power-Law Variation of Elastic Modulus Under Bidirectional Bending

Three-dimensional static response of all-around simply supported functionally graded square/rectangular laminates is presented here based on higher order shear-normal (HOSNT) deformation theory and semi-analytical approach. Modulus of elasticity is assumed to be varied according to power law through the thickness of laminate and other material properties are assumed to be constant over the domain. Semi-analytical approach consists of defining two-point boundary value problem (BVP) in the thickness direction. It involves displacements and transverse stresses as primary degrees of freedoms (DOFs) and therefore, general stress boundary conditions can be applied on both top and bottom surface of laminate during the numerical solution. Whereas, in HOSNT, only displacements are considered as primary DOFs and Taylor's series are used to expand primary DOFs through thickness direction which helps to take into account of transverse cross-sectional deformation modes. Minimum potential energy is used in HOSNT to derive equilibrium and boundary equation and Navier's solutions techniques is used to obtain closed form solution. The efficiency of the developed formulation in terms of accuracy and simplicity is examined by various numerical examples and compared with available results based on shear deformation theories.