Effect of Hydrostatic Pressure on Nonlinear Vibrating of Annular Circular Plate Coupled with Bounded Fluid

The present study aims to evaluate the nonlinear vibration of an annular circular plate in contact with the fluid. Analysis of plate is based on first-order Shear Deformation Theory (FSDT) by considering of rotational inertial effects and transverse shear stresses. The governing equation of the oscillatory behavior of the fluid is determined by solving the Laplace equation and satisfying its boundary conditions. The nonlinear differential equations are solved based on the differential quadrature method and obtaining nonlinear natural frequency. In addition, the numerical results are presented for a sample plate, and the effect of some parameters such as aspect ratio, boundary conditions, fluid density, and fluid height are investigated. Finally, the results are compared with those of similar studies in the literature.

A simple higher-order beam model that is represented by two kinematic variables and three section constants

This article presents a new higher-order beam model. The present beam model is governed by differential equations that are similar to those present in some existing higher-order beam models; however, the present beam model makes use of a novel method of calculating the transverse shear stiffness, which facilitates the calculation of a shear-warping stiffness without the need for an assumed warping displacement field, and without introducing any additional kinematic variables. The present beam model also facilitates the recovery of the distributions of longitudinal normal stresses and transverse shear stresses. The authors postulate that the bending and shear terms in first-order shear deformation theory represent the first two terms in an infinite series that would constitute an ideal one-dimensional beam model, and it is suggested that the present beam model constitutes the first four terms in this hypothetical infinite series. The present beam model is solved for several example beams, and the results are compared with those of existing classical and higher-order beam models, as well as computational results from finite element analyses. It is shown that the present beam model is able to accurately represent deformed shapes and stress distributions pertaining to beams that exhibit non-trivial shear compliance as well as non-trivial shear-warping stiffness. In the case of laminated composite beams comprising a large number of laminae, the present beam model offers a level of analytical fidelity that is comparable to that of existing zigzag beam models; however, unlike zigzag beam models, the present beam model is equally well suited for the analyses of beams comprising any number of laminae.

Transient analysis of smart composite laminate

In the present study, the transient analysis of smart laminated composite plates is presented analytically using inverse hyperbolic zigzag theory. This theory is displacement based with five unknown primary mid-plane variables in conjunction with the zigzag parameters resembling the membrane and the bending components. The inter-laminar continuity conditions of transverse shear stresses at the interfaces of the smart composite plate are artificially enforced. The dynamic version of principle of virtual work is used to derive the basic equations and solved subsequently with the Navier’s solution technique. Newmark’s time integration scheme is adopted to obtain the solutions of the coupled ordinary differential equations in the time frame. The equilibrium equations of elasticity are employed in order to obtain accurate estimation of transverse shear stresses. Numerical problems on diaphragm supported smart composite plate are solved by evaluating the static responses and comparing them with elasticity solutions in the existing literature. Then the transient responses are derived for a number of time-dependent electro-mechanical loads such as triangular, sine, ramp, and staircase variation. Results show excellent accuracy with the elasticity solutions available in the literature. Further, the dynamic controlling capacity of the piezoelectric layer is studied by evaluating the electrical loads that diminish the mechanical vibrations from the system.

Accurate stress analysis of laminated composite and sandwich plates

This article is devoted to derive the analytical solution for flexural behavior of general symmetric and anti-symmetric cross-ply laminated composite and sandwich plates subjected to transverse mechanical load using the recently developed trigonometric zigzag theory. The inter-laminar continuity conditions of transverse shear stresses at the layer interfaces of the plate are enforced which is an essential condition for any zigzag model. The governing equations of equilibrium of the boundary value problem derived from the principle of minimum potential energy is reduced to a system of five partial differential equations whose solutions are obtained by Navier’s method. Attempt is made to demonstrate number of numerical problems to compare the results of the zigzag model with the elasticity solutions and with the results of other researchers in one common platform. Though in any solid mechanics problem, the displacement components are the primary unknowns, more attention is paid to the stress determination. Hence, the transverse shear stresses are evaluated using both the constitutive and equilibrium equations.

Mechanical Buckling Analysis of Functionally Graded Plates Using an Accurate Shear Deformation Theory

In this present study, we are interested in the use of a precise theory of shear deformation for the buckling analysis of plates with functional gradation simply supported such as the refined theory of plates with four variables, several parameters of comparison have been used, dimensional and non-dimensional, the displacement field is compatible with this study, the non-use of shear correction factors is satisfied, the choice of material is very precise in such a way are variable according to the thickness of the plate and on the other hand to make comparison with other researcher and confirms that this study gives precise results and converges, the transverse shear stresses vary through the thickness, the results found is also studied and discussed.

Determination of the transverse shear stress in layered composites

An engineering approach to estimation of the transverse shear stresses in layered composites is developed. The technique is based on the well-known D. I. Zhuravsky equation for shear stresses in an isotropic beam upon transverse bending. In general, application of this equation to a composite beam is incorrect due to the heterogeneity of the composite structure. According to the proposed method, at the first stage of its implementation, a transition to the equivalent model of a homogeneous beam is made, for which the Zhuravsky formula is valid. The transition is carried out by changing the shape of the cross section of the beam, provided that the bending stiffness and generalized elastic modulus remain the same. The calculated shear stresses in the equivalent beam are then converted to the stress values in the original composite beam from the equilibrium condition. The main equations and definitions of the method as well as the analytical equation for estimation of the transverse shear stress in a composite beam are presented. The method is verified by comparing the analytical solution and the results of the numerical solution of the problem by finite element method (FEM). It is shown that laminate stacking sequence has a significant impact both on the character and on the value of the transverse shear stress distribution. The limits of the applicability of the developed technique attributed to the conditions of the validity of the hypothesis of straight normal are considered. It is noted that under this hypothesis the shear stresses do not depend on the layer shear modulus, which explains the absence of this parameter in the obtained equation. The classical theory of laminate composites is based on the similar assumptions, which gives ground to use this equation for an approximate estimation of the transverse shear stresses in in a layered composite package.

An accurate zigzag theory for bending and buckling analysis of thick laminated sandwich plates with soft core

An accurate and computationally attractive zigzag theory is developed for bending and buckling analysis of thick laminated soft core sandwich plates. The kinematic assumptions of the proposed zigzag theory are obtained by superimposing a nonlinear zigzag function on the first-order shear deformation theory. In order to obtain the accurate transverse shear stresses, a preprocessing approach based on the three-dimensional equilibrium equations and the Reissner mixed variational theorem is used. It is significant that the second-order derivatives of in-plane displacement variables have been removed from the transverse shear stresses, such that the finite element implementation is greatly simplified. Thus, based on the proposed zigzag model, a computationally efficient four-node C0 quadrilateral plate element with linear interpolation function is proposed for bending and buckling analysis of soft core sandwich plates. The advantage of the present formulation is that no post-processing approach is needed to calculate the transverse shear stresses while maintaining the computational accuracy of a linear plate element. Moreover, the accurate transverse shear stresses can be involved in the strain energy which can actively improve the accuracy of critical loads. Performance of the proposed model is assessed by comparing with several benchmark solutions. Agreement between the present results and the reference solutions is very good, and the proposed model only includes the seven displacement variables which can demonstrate the accuracy and effectiveness of the proposed model.

An Efficient Beam Element Based on Quasi-3D Theory for Static Bending Analysis of Functionally Graded Beams

In this paper, a 2-node beam element is developed based on Quasi-3D beam theory and mixed formulation for static bending of functionally graded (FG) beams. The transverse shear strains and stresses of the proposed beam element are parabolic distributions through the thickness of the beam and the transverse shear stresses on the top and bottom surfaces of the beam vanish. The proposed beam element is free of shear-looking without selective or reduced integration. The material properties of the functionally graded beam are assumed to vary according to the power-law index of the volume fraction of the constituents through the thickness of the beam. The numerical results of this study are compared with published results to illustrate the accuracy and convenience rate of the new beam element. The influence of some parametrics on the bending behavior of FGM beams is investigated.