Simple Higher Shear Deformation Theory Research Articles

Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory

A new simple “four-variable shear deformation” plate model is proposed in this work to demonstrate the hygro-thermal environment effects on dynamic and buckling of functionally graded material “sandwich plates” supported by “Winkler–Pasternak” elastic foundations. Equations of motion are obtained from Hamilton’s principle containing the hygro-thermal influences. This model uses only “four variables” and considers trigonometric variation of “transverse shear stress.” In addition, these stresses become zero at the upper and lower surfaces of the “sandwich plate.” The novelty of this formulation is the addition of the integral term in the field of displacement, which leads to a reduction of the number of unknowns and basic equations. Various kinds of functionally graded material “sandwich plates” are examined in this study. To verify the validity of the model, the calculated results are compared with the existing results. Comparison investigations reveal that the computed results of the proposed formulation are in excellent agreement with those of other “higher shear deformation theories.” Parametric investigation is established to demonstrate the effects of temperature rise, moisture condition, elastic foundation coefficients, and power law index on the vibration and buckling of functionally graded material “sandwich plates.”

Nonlinear bending of thin and thick unsymmetrically laminated composite beams using refined finite element model

Nonlinear bending behaviour of unsymmetrically laminated composite beams using von Karman's large deflection theory is investigated. For this purpose, a one-dimensional finite element having twelve degrees of freedom per node based on a simple higher shear deformation theory (HSDT) which satisfies the zero transverse shear stress at the top and bottom surface and avoids the use of shear correction factors is developed. The advantage of the present higher order theory is that first-order shear deformation theory (FSDT) and classical lamination theory (CLT) can be obtained easily by dropping the higher order terms associated with transverse shear deflection or all the terms associated with transverse shear deflection from the kinematic relations. To show the effect of transverse shear on the transverse deflection, the first-order shear deformation theory and classical lamination theory results are also presented. Unsymmetrically laminated composite beams, due to the existence of bending-extension coupling are shown to have direction dependent nonlinear bending stiffness, resulting in softening/hardening type of nonlinearity for one direction of transverse loading and hardening type nonlinearity for the other direction. It is shown that this softening type of nonlinearity at small loads changes to hardening type of nonlinearity for higher loads. Results are presented for various types of lay-ups, slenderness ratios and boundary conditions.