• Structural Engineering and Mechanics
• /
• v.86 no.2
• /
• pp.167-180
• /
• 2023

This work applies a four-known quasi-3D shear deformation theory to investigate the bending behavior of a functionally graded plate resting on a viscoelastic foundation and subjected to hygro-thermo-mechanical loading. The theory utilizes a hyperbolic shape function to predict the transverse shear stress, and the transverse stretching effect of the plate is considered. The principle of virtual displacement is applied to obtain the governing differential equations, and the Navier method, which comprises an exponential term, is used to obtain the solution. Novel to the current study, the impact of the viscoelastic foundation model, which includes a time-dependent viscosity parameter in addition to Winkler's and Pasternak parameters, is carefully investigated. Numerical examples are presented to validate the theory. A parametric study is conducted to study the effect of the damping coefficient, the linear and nonlinear loadings, the power-law index, and the plate width-tothickness ratio on the plate bending response. The results show that the presence of the viscoelastic foundation causes an 18% decrease in the plate deflection and about a 10% increase in transverse shear stresses under both linear and nonlinear loading conditions. Additionally, nonlinear loading causes a one-and-a-half times increase in horizontal stresses and a nearly two-times increase in normal transverse stresses compared to linear loading. Based on the article's findings, it can be concluded that the viscosity effect plays a significant role in the bending response of plates in hygrothermal environments. Hence it shall be considered in the design.

• Computers and Concrete
• /
• v.26 no.1
• /
• pp.63-74
• /
• 2020

In this investigation, study of the bending response of functionally graded (FG) porous plates is presented using a cubic shear deformation theory. The properties of the FG-plate vary according to a power-law distribution which is modified to approximate material characteristics for considering the effect of porosities. The equilibrium equations are derived by using the principle of virtual work and solved by using Navier's procedure. Various numerical results are discussed to demonstrate the influence of the variation of the power index, the porosity parameter and the geometric ratios on the bending response of FG porous plates.

• Journal of the Korean Wood Science and Technology
• /
• v.26 no.4
• /
• pp.13-19
• /
• 1998

Stress relaxation tests have been performed under five different tensile strain levels and five different bending strain levels. Three different theoretical models have been developed based on four-element Burger's model, viscoelastic theory and viscous-viscoelastic theory. Experimental data were used to obtain parameters of the models and to verify accuracy of the models. Among the three theoretical models developed in this study, three-integral model (Model 3) based on viscous-viscoelastic theory showed the most exact estimations of stress relaxation under both tensile and bending strains and their correlation coefficients were greater than 0.99 for all the strain levels. Model 1 showed little initial stress relaxation. Model 2 showed excessive initial relaxation and, then, no relaxation after about 20 minute of strain application. Stress retention under strain decreased as strain increased, which means increased stress relaxation as strain increases. When the strain level was less than proportional limit, the effect of strain level on stress relaxation was not clearly shown. However, this effect was increased as strain level increased when strain level was greater than proportional limit.

• Steel and Composite Structures
• /
• v.31 no.5
• /
• pp.469-488
• /
• 2019

We in this paper study nonlinear bending of a functionally graded porous nanobeam subjected to multiple physical load based on the nonlocal strain gradient theory. For more reasonable analysis of nanobeams made of porous functionally graded magneto-thermo-electro-elastic materials (PFGMTEEMs), both constituent materials and the porosity appear gradient distribution in the present expression of effective material properties, which is much more suitable to the actual compared with the conventional expression of effective material properties. Besides the displacement function regarding physical neutral surface is introduced to analyze mechanical behaviors of beams made of FGMs. Then we derive nonlinear governing equations of PFGMTEEMs beams using the principle of Hamilton. To obtain analytical solutions, a two-step perturbation method is developed in nonuniform electric field and magnetic field, and then we use it to solve nonlinear equations. Finally, the analytical solutions are utilized to perform a parametric analysis, where the effect of various physical parameters on static bending deformation of nanobeams are studied in detail, such as the nonlocal parameter, strain gradient parameter, the ratio of nonlocal parameter to strain gradient parameter, porosity volume fraction, material volume fraction index, temperature, initial magnetic potentials and external electric potentials.

• Computers and Concrete
• /
• v.33 no.1
• /
• pp.91-102
• /
• 2024

Beam-shaped components commonly rotate along a fixed axis when massive mechanical structures like rotors, jet engine blades, motor turbines, and rotating railway crossings perform their functions. For these structures to be useful in real life, their mechanical behavior is essential. Therefore, this is the first article to use the modified shear deformation theory type hyperbolic sine functions theory and the FEM to study the static bending response of rotating functionally graded GPL-reinforced composite (FG-GPLRC) beams with initial geometrical deficiencies in thermal media. Graphene platelets (GPLs) in three different configurations are woven into the beam's composition to increase its strength. By comparing the numerical results with those of previously published studies, we can assess the robustness of the theory and mechanical model employed in this study. Parameter studies are performed to determine the effect of various geometric and physical variables, such as rotation speed and temperature, on the bending reactions of structures.

• Steel and Composite Structures
• /
• v.5 no.5
• /
• pp.359-374
• /
• 2005

This paper presents the experimental and theoretical results of the viscoplastic response and collapse of 316L stainless steel tubes subjected to cyclic bending. The tube bending machine and curvature-ovalization measurement apparatus, which was designed by Pan et al. (1998), were used for conducting the cyclic curvature-controlled experiment. Three different curvature-rates were controlled to highlight the characteristic of viscoplastic response and collapse. Next, the endochronic theory and the principle of virtual work were used to simulate the viscoplastic response of 316L stainless steel tubes under cyclic bending. In addition, a proposed theoretical formulation (Lee and Pan 2001) was used to simulate the relationship between the controlled cyclic curvature and the number of cycles to produce buckling under cyclic bending at different curvature-rates (viscoplastic collapse). It has been shown that the theoretical simulations of the response and collapse correlate well with the experimental data.

• Steel and Composite Structures
• /
• v.19 no.4
• /
• pp.829-841
• /
• 2015

In this paper, a refined exponential shear deformation beam theory is developed for bending analysis of functionally graded beams. The theory account for parabolic variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Contrary to the others refined theories elaborated, where the stretching effect is neglected, in the current investigation this so-called "stretching effect" is taken into consideration. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present shear deformation beam theory, the equilibrium equations are derived from the principle of virtual displacements. Analytical solutions for static are obtained. Numerical examples are presented to verify the accuracy of the present theory.

• Steel and Composite Structures
• /
• v.17 no.3
• /
• pp.321-338
• /
• 2014

In the present study, a new simple first-order shear deformation theory is presented for laminated composite plates. Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher-order shear deformation theories. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions of simply supported antisymmetric cross-ply and angle-ply laminates are obtained and the results are compared with the exact three-dimensional (3D) solutions and those predicted by existing theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of laminated composite plates.

• Structural Engineering and Mechanics
• /
• v.8 no.2
• /
• pp.151-164
• /
• 1999

The large deflection theory of the Mindlin plate and Galerkin's method are employed to examine the static responses of a plate produced by the weight of the plate, and the dynamic responses of the plate caused by the coupling effect of these static responses with a set of moving forces. Results obtained by the large deflection theory are compared with those by the small deflection theory. The results indicate that the effect of weight of the plate increases the modal frequencies of the structure. The deviations of dynamic transverse deflection and of dynamic bending moment produced by a moving concentrated force between the two theories are significant for a thin plate with a large area. Both dynamic transverse deflection and dynamic bending moment obtained by the Mindlin plate theory are greater than those by the classical plate.

• Structural Engineering and Mechanics
• /
• v.66 no.3
• /
• pp.317-328
• /
• 2018

In this paper, a new refined quasi-three-dimensional (3D) shear deformation theory for the bending analysis of functionally graded plate is presented. The number of unknown functions involved in this theory is only four against five or more in the case of the other shear and normal deformation theories. Due to its quasi-3D nature, the stretching effect is taken into account in the formulation of governing equations. In addition, the effect of different micromechanical models on the bending response of these plates is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG plates whose properties vary continuously across the thickness according to a simple power law. The present theory accounts for both shear deformation and thickness stretching effects by a parabolic variation of displacements across the thickness, and the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The problem is solved for a plate simply supported on its edges and the Navier solution is used. The results of the present method are compared with others from the literature where a good agreement has been found. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG plates.