• Structural Engineering and Mechanics
• /
• v.48 no.4
• /
• pp.547-567
• /
• 2013

Nonlinear behavior of functionally graded material (FGM) plates under thermal loads is investigated here using an efficient sinusoidal shear deformation theory. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the sinusoidal distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed efficient sinusoidal shear deformation theory contains only four unknowns. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the sinusoidal shear deformation theory based on exact neutral surface position is employed here. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The non-linear strain-displacement relations are also taken into consideration. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.

• Steel and Composite Structures
• /
• v.16 no.6
• /
• pp.611-637
• /
• 2014

A single plate shear connection, or shear tab, is a very popular shear connection due to its merit in ease of construction and material economy. However, problems in understanding the connection behavior, both in terms of strength and ductility, have been well-documented. Suggestions or design model for single plate connections in AISC Design Manual have been altered several times, with the latest edition settling down to giving designers pre-calculated design strength tables if the connection details agree with given configurations. Results from many full-scale tests and finite element models in the past suggest that shear strength of a bolt group in single plate shear connections might be affected by yield strength of plate material; therefore, this research was aimed to investigate and clarify effects of plate yield strength and thickness on shear strength of the bolt group in the connections, including the validity of using a plate thickness/bolt diameter ratio ($t_p/d_b$) in design, by using finite element models. More than 20 models have been created by using ABAQUS program with 19.0- and 22.2-mm A325N bolts and A36 and Gr.50 plates with various thicknesses. Results demonstrated that increase of plate thickness or plate yield strength, with the $t_p/d_b$ ratio remained intact, could significantly reduce shear strength of the bolt group in the connection as much as 15 percent. Results also confirmed that the $t_p/d_b$ ratio is a valid indicator to be used for guaranteeing strength sufficiency. Because the actual ratio recommended by AISC Design Manual is $t_p/d_b$ + 1.6 (mm) for connections with a number of bolts less than six and plate yield strength in construction is normally higher than the nominal value used in design, it is proposed that shear strength of a bolt group in single plate connections with a number of bolts equal or greater than seven be reduced by 15 percent and the $t_p/d_b$ ratio be limited to 0.500.

• Smart Structures and Systems
• /
• v.15 no.6
• /
• pp.1569-1582
• /
• 2015

Two hyperbolic displacement models are used for the bending response of simply-supported orthotropic laminated composite plates resting on two-parameter elastic foundations under mechanical loading. The models contain hyperbolic expressions to account for the parabolic distributions of transverse shear stresses and to satisfy the zero shear-stress conditions at the top and bottom surfaces of the plates. The present theory takes into account not only the transverse shear strains, but also their parabolic variation across the plate thickness and requires no shear correction coefficients in computing the shear stresses. The governing equations are derived and their closed-form solutions are obtained. The accuracy of the models presented is demonstrated by comparing the results obtained with solutions of other theories models given in the literature. It is found that the theories proposed can predict the bending analysis of cross-ply laminated composite plates resting on elastic foundations rather accurately. The effects of Winkler and Pasternak foundation parameters, transverse shear deformations, plate aspect ratio, and side-to-thickness ratio on deflections and stresses are investigated.

• Proceedings of the Korean Society For Composite Materials Conference
• /
• 1999.11a
• /
• pp.215-218
• /
• 1999

A general structural model, which is an extension of the Vlassov theory, is developed for the analysis of composite rotor blades with elastic couplings. A comprehensive analysis applicable to both thick-and thin-walled composite beams, which can have either open- or closed profile is formulated. The theory accounts for the effects of elastic couplings, shell wall thickness, and transverse shear deformations. A semi-complementary energy functional is used to account for the shear stress distribution in the shell wall. The bending and torsion related warpings and the shear correction factors are obtained in closed form as part of the analysis. The resulting first order shear deformation theory describes the beam kinematics in terms of the axial, flap and lag bending, flap and lag shear, torsion and torsion-warping deformations. The theory is validated against experimental results for various cross-section beams with elastic couplings.

• Smart Structures and Systems
• /
• v.1 no.3
• /
• pp.309-324
• /
• 2005

This paper presents an efficient and accurate coupled beam model for piezoelectric bimorphs based on improved first-order shear deformation theory (FSDT). The model combines the equivalent single layer approach for the mechanical displacements and a layerwise modeling for the electric potential. General electric field function is proposed to reasonably approximate the through-the-thickness distribution of the applied and induced electric potentials. Layerwise defined shear correction factor (k) accounting for nonlinear shear strain distribution is introduced into both the shear stress resultant and the electric displacement integration. Analytical solutions for free vibrations and forced response under electromechanical loads are obtained for the simply supported piezoelectric bimorphs with series or parallel arrangement, and the numerical results for various length-to-thickness ratios are compared with the exact two-dimensional piezoelasticity solution. Excellent predictions with low error estimates of local and global responses as well as the modal frequencies are observed.

• Structural Engineering and Mechanics
• /
• v.43 no.2
• /
• pp.253-271
• /
• 2012

To analyze the bending and transverse shear effects of laminated composite plates, a thirteen nodes triangular element will be presented. The suggested formulations consider a parabolic variation of the transverse shear strains through the thickness. As a result, there is no need to use shear correction coefficients in computing the shear stresses. The proposed element can model both thin and thick plates without any problems, such as shear locking and spurious modes. Moreover, the effectiveness of $w_{,n}$, as an independent degree of freedom, is concluded by the present study. To perform the accuracy tests, several examples will be solved. Numerical results for the orthotropic materials with different boundary conditions, shapes, number of layers, thickness ratios and fiber orientations will be presented. The suggested element calculates the deflections and stresses more accurate than those available in the literature.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.2 no.4
• /
• pp.9-17
• /
• 1994

Effect of Newtonian and non-Newtonian oils on minimum ol film thickness in engine journal bearing were investigated at various oil viscosities. The influence of oil viscosity and engine operating conditions on minimum oil film thickness of main bearing and con-rod bearing was examined. Minimum oil film thickness for Newtonian oils increased uniformly with kinematic viscosity. But the correlation between kinematic viscosity and minimum oil film thickness was very poor for non-Newtonian oils. According to the straight-line regression analysis for non-Newtonian oils, high temperature high shear viscosity at 1 $1{\times}10^6Sec^{-1}$, $150^{\circ}C$ increase the coefficient of determination from 0.41 to 0.77. Con-rod bearing showed better correlation between minimum oil film thickness and engine operating conditions than main bearing.

• Structural Engineering and Mechanics
• /
• v.66 no.1
• /
• pp.61-73
• /
• 2018

In this article, a higher shear deformation theory (HSDT) is improved to consider the influence of thickness stretching in functionally graded (FG) plates. The proposed HSDT has fewer numbers of variables and equations of motion than the first-order shear deformation theory (FSDT), but considers the transverse shear deformation influences without requiring shear correction coefficients. The kinematic of the present improved HSDT is modified by considering undetermined integral terms in in-plane displacements and a parabolic distribution of the vertical displacement within the thickness, and consequently, the thickness stretching influence is taken into account. Analytical solutions of simply supported FG plates are found, and the computed results are compared with 3D solutions and those generated by other HSDTs. Verification examples demonstrate that the developed theory is not only more accurate than the refined plate theory, but also comparable with the HSDTs which use more number of variables.

• Tunnel and Underground Space
• /
• v.14 no.5
• /
• pp.318-326
• /
• 2004

In this study, a new direct shear apparatus was developed to investigate the shear characteristics of the rock joints at various conditions. Using the developed apparatus, various experiments on filled rock joints were carried out considering the asperity angle, the normal stress, the type and thickness of filling material and to investigated the basic shear characteristics of filled rock joints were analyzed. According to the experiments performed under the constant normal stress condition by varying the asperity angle, the type and thickness of filling material, it was shown that the behavior and strength of filled rock joint could be defined by the type and thickness of the filling material. The dilation angle of the filled joints was found to be smaller than that of unfilled rock joint, and thereby, the effect of roughness was also reduced due to the filling material. And critical thickness ratio varied according to stress level and roughness as well as the type of filing materials.

• Steel and Composite Structures
• /
• v.18 no.6
• /
• pp.1493-1515
• /
• 2015

A new refined hyperbolic shear deformation theory (RHSDT), which involves only four unknown functions as against five in case of other shear deformation theories, is presented for the thermoelastic bending analysis of functionally graded sandwich plates. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The sandwich plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity, Poisson's ratio of the faces, and thermal expansion coefficients are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. Several kinds of sandwich plates are used taking into account the symmetry of the plate and the thickness of each layer. The influences played by the transverse shear deformation, thermal load, plate aspect ratio and volume fraction distribution are studied. Numerical results for deflections and stresses of functionally graded metal-ceramic plates are investigated. It can be concluded that the proposed theory is accurate and simple in solving the thermoelastic bending behavior of functionally graded plates.