Geometrically nonlinear dynamic analysis of laminated composite plate using a nonpolynomial shear deformation theory. (January 2021) - Thakur, Babu Ranjan; Verma, Surendra; Singh, B.N.; Maiti, D.K.
Abstract: A computationally efficient C 0 finite element model in conjunction with the nonpolynomial shear deformation theory (NPSDT) is extended to examine the free and forced vibration behavior of laminated composite plates. The employed NPSDT assumes the nonlinear distribution of in-plane displacements which qualify the requirement of traction free boundary conditions at the top and bottom surfaces. The present formulation utilizes both von Kármán and Green–Lagrange type of strain–displacement relations to model the geometric nonlinearity. Using Hamilton's principle, the nonlinear governing equation of motion is derived and then discretized based on the nine-noded Lagrange element. The obtained equations are solved by utilizing unconditionally stable Newmark's scheme in conjunction with Newton–Raphson method. A damping effect in the transient analysis has been introduced in the framework of the Rayleigh damping model. The steady state forced vibration analysis has also been carried out by employing harmonic force with excitation frequency around the natural frequency. The arc-length continuation method is applied to obtained the frequency response. The present model has been validated for a wide range of problems and a detailed numerical study has been carried out for several types of boundary conditions under various types of loading with different magnitude of the load. Highlights: Geometrically non-linear dynamic analysis of laminated composite plate using nonpolynomial shear deformation theory. Both von Karman and Green–Lagrange strain are considered for incorporation of geometric nonlinearity. Rayleigh-damping model employed to get the damped response. Nonlinear steady state forced vibration response obtained for the excitation frequency around the natural frequency.