Showing papers by "M. Ganapathi published in 2020"

Dynamic buckling of classical/non-classical curved beams by nonlocal nonlinear finite element accounting for size dependent effect and using higher-order shear flexible model

Abstract: This paper investigates the dynamic snap-through buckling of classical and non-classical curved beams subjected to a suddenly applied step load The small scale effect prevalent in non-classical beams, viz, micro and nanobeam, is modeled using the nonlocal elasticity approach The formulation accounts for moderately large deflection and rotation The governing equilibrium equations are derived using the dynamic version of the principle of virtual work and are subsequently simplified in terms of the generalized displacements for the development of a nonlocal nonlinear finite element model The spatial domain comprises of 3-noded higher-order curved beam elements based on shear flexible theory associated with sine function The nonlinear governing equations are solved using the incremental stiffness matrices and by adopting direct time integration method The critical dynamic buckling load is identified by the smallest load at which there is a sudden rise in the amplitude of vibration The efficacy of model here is compared against the available analytical studies for the local and nonlocal beams A detailed study is made to highlight the effects of the geometric parameter, initial condition, nonlocal parameter, load duration, and boundary conditions on the dynamic stability of both classical and non-classical curved beams The nature and degree of participation of various eigen modes accountable for the dynamic snap-through behavior are examined a posteriori using the modal expansion approach Some interesting observations made here are valuable for the optimal design of such structural members against fatigue and instability

Nonlinear bending of porous curved beams reinforced by functionally graded nanocomposite graphene platelets applying an efficient shear flexible finite element approach

Abstract: In the present study, the nonlinear flexural bending of thick and thin porous curved composite beams reinforced and functionally graded by graphene platelets is carried out using a three-noded C1 continuous curved beam finite element developed introducing an efficient shear deformation theory based on trigonometric function. The nonlinearity through the strain–displacement relationship by introducing von Karman’s assumptions is considered. The nonlinear equilibrium equations resulting from minimum potential energy principle are numerically solved based on the direct iteration technique. The bending nonlinear features through the load–deflection relationship are presented by selecting various design parameters like long and short beams, shallow and deep curved cases, support conditions, the variation of graphene platelets in the metal foam and the existence of porosity. This investigation reveals that the level of nonlinearity gets noticeably affected by the depth coupled with the curved beam slenderness ratio.

Nonlinear supersonic flutter study of porous 2D curved panels including graphene platelets reinforcement effect using trigonometric shear deformable finite element

Abstract: The nonlinear panel flutter behaviour of two-dimensional porous curved panel reinforced by graphene platelets exposed to a supersonic flow is investigated A curved beam element developed based on the trigonometric shear deformation theory is employed The formulation integrates the geometric nonlinearity with von Karman’s approximation The effort to model the fluid–structure interaction is reduced by implementing the first-order form of piston theory aerodynamics to describe the flow and accounting for the influence of static aerodynamic load due to the inherent geometric curvature of the panel The nonlinear governing equations are formulated adopting the Lagrangian formulation The panel deflection under the static aerodynamic load is evaluated using the Newton–Raphson iteration method The flutter behaviour is analysed with reference to the large deflection equilibrium state through an eigenvalue analysis and by tracing the complex eigenvalues and identifying the first coalescence of any two vibratory modes The flutter dynamic pressure is also predicted iteratively using the eigenvalue approach for the selected range of limit cycle amplitudes The influence of static aerodynamic load and vibration amplitude on the flutter characteristics is brought out for both isotropic and graphene reinforced composite panels with different boundary conditions The pre-flutter static deflection shape of the panel is also examined The material parameters such as porosity level in the metal foam and the graphene platelet content are assessed on the nonlinear flutter features of 2D panels

Nonlocal strain gradient finite element analysis of nanobeams using two-variable trigonometric shear deformation theory

Abstract: In the present paper, a new trigonometric two-variable shear deformation beam nonlocal strain gradient theory is developed and applied to investigate the combined effects of nonlocal stress and strain gradient on the bending, buckling and free vibration analysis of nanobeams. The model introduces a nonlocal stress field parameter and a length scale parameter to capture the size effect. The governing equations derived are solved employing finite element method using a 3-nodes beam element, developed for this purpose. The predictive capability of the proposed model is shown through illustrative examples for bending, buckling and free vibration of nanobeams. Comparisons with other higher-order shear deformation beam theory are also performed to validate its numerical implementation and assess its accuracy within the nonlocal context.