Abstract: In this paper, we have used an analytical method to analyze the vibratory behavior of plates in materials with gradient of properties, simply supported, proposing a refined non polynomial theory. The number of unknown functions involved in this theory is only four, as compared to five in the case of other higher shear deformation theories. The transverse shearing effects are studied according to the thickness of the plate. The motion equations for the FGM plates are obtained by the Hamilton principle application, the solutions are obtained using the Navier method, and then the fundamental frequencies are found, solving an eigenvalue equation system, the results of this analysis are presented and compared to those available in the literature.
Abstract: The reinforcement and repair of concrete structures by bonding composite materials have become relatively common operations. Different types of composite materials can be used: carbon fiber reinforced polymer (CFRP), glass fiber reinforced polymer (GFRP) as well as functionally graded material (FGM). The development of analytical and numerical models describing the mechanical behavior of structures in civil engineering reinforced by composite materials is necessary. These models will enable engineers to select, design, and size adequate reinforcements for the various types of damaged structures. This study focuses on the free vibration behavior of orthotropic laminated composite plates using a refined shear deformation theory. In these models, the distribution of transverse shear stresses is considered as parabolic satisfying the zero-shear stress condition on the top and bottom surfaces of the plates without using shear correction factors. In this analysis, the equation of motion for simply supported thick laminated rectangular plates is obtained by using the Hamilton’s principle. The accuracy of the developed model is demonstrated by comparing our results with solutions derived from other higher order models and with data found in the literature. Besides, a finite-element analysis is used to calculate the natural frequencies of laminated composite plates and is compared with those obtained by the analytical approach.
Abstract: In this paper geometrically nonlinear static behavior of laminated composite hollow super-elliptic beams is investigated using generalized differential quadrature method. Super-elliptic beam can have both oval and elliptic cross-sections by adjusting parameters in super-ellipse formulation (also known as Lamé curves). Equilibrium equations of super-elliptic beam are obtained using the virtual work principle. Geometric nonlinearity is taken into account using von-Kármán nonlinear strain-displacement relations. Spatial derivatives in strains are expressed with the generalized differential quadrature method. Transverse shear effect is considered through the first-order shear deformation theory. Static equilibrium equations are solved using Newton-Raphson method. Several composite super-elliptic beam problems are solved with the proposed method. Effects of layer orientations of composite material, boundary conditions, ovality and ellipticity on bending behavior are investigated.
Abstract: The end panels of a large rectangular industrial duct,
which experience significant internal pressures, also experience
considerable transverse shear due to transfer of gravity loads to the
supports. The current design practice of such thin plate panels for
shear load is based on methods used for the design of plate girder
webs. The structural arrangements, the loadings and the resulting
behavior associated with the industrial duct end panels are, however,
significantly different from those of the web of a plate girder. The
large aspect ratio of the end panels gives rise to multiple bands of
tension fields, whereas the plate girder web design is based on one
tension field. In addition to shear, the industrial end panels are
subjected to internal pressure which in turn produces significant
membrane action. This paper reports a study which was undertaken
to review the current industrial analysis and design methods and to
propose a comprehensive method of designing industrial duct end
panels for shear resistance. In this investigation, a nonlinear finite element model was
developed to simulate the behavior of industrial duct end panel, along
with the associated edge stiffeners, subjected to transverse shear and
internal pressures. The model considered the geometric imperfections
and constitutive relations for steels. Six scale independent
dimensionless parameters that govern the behavior of such end panel
were identified and were then used in a parametric study. It was
concluded that the plate slenderness dominates the shear strength of
stockier end panels, and whereas, both the plate slenderness and the
aspect ratio influence the shear strength of slender end panels. Based
on these studies, this paper proposes design aids for estimating the
shear strength of rectangular duct end panels.
Abstract: A trigonometric shear deformation theory for flexure of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick cantilever isotropic beams are considered for the numerical studies to demonstrate the efficiency of the. Results obtained are discussed critically with those of other theories.
Abstract: A trigonometric shear deformation theory for flexure of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick simply supported isotropic beams are considered for the numerical studies to demonstrate the efficiency of the results obtained is discussed critically with those of other theories.
Abstract: Two geometrically nonlinear plate theories, based either on first- or third-order transverse shear deformation theory are used for finite element modeling and simulation of the transient response of smart structures incorporating piezoelectric layers. In particular the time histories of nonlinear vibrations and sensor voltage output of a thin beam with a piezoelectric patch bonded to the surface due to an applied step force are studied.
Abstract: This article considers the positional buckling of
composite thick plates under thermal loading . For this purpose , the
complex finite strip method is used . In analysis of complex finite
strip, harmonic complex function in longitudinal direction , cubic
functions in transversal direction and parabola distribution of
transverse shear strain in thickness of thick plate based on higherorder
shear deformation theory are used . In given examples , the
effect of angles of stratification , number of layers , dimensions ratio
and length – to – thick ratio across critical temperature are
considered.
Abstract: Equilibrium and stability equations of a thin rectangular plate with length a, width b, and thickness h(x)=C1x+C2, made of functionally graded materials under thermal loads are derived based on the first order shear deformation theory. It is assumed that the material properties vary as a power form of thickness coordinate variable z. The derived equilibrium and buckling equations are then solved analytically for a plate with simply supported boundary conditions. One type of thermal loading, uniform temperature rise and gradient through the thickness are considered, and the buckling temperatures are derived. The influences of the plate aspect ratio, the relative thickness, the gradient index and the transverse shear on buckling temperature difference are all discussed.
Abstract: Structural behavior of ring stiffened thick walled
cylinders made of functionally graded materials (FGMs) is
investigated in this paper. Functionally graded materials are inhomogeneous composites which are usually made from a mixture
of metal and ceramic. The gradient compositional variation of the
constituents from one surface to the other provides an elegant solution to the problem of high transverse shear stresses that are
induced when two dissimilar materials with large differences in material properties are bonded. FGM formation of the cylinder is
modeled by power-law exponent and the variation of characteristics is supposed to be in radial direction.
A finite element formulation is derived for the analysis. According to the property variation of the constituent materials in the radial
direction of the wall, it is not convenient to use conventional elements to model and analyze the structure of the stiffened FGM
cylinders. In this paper a new cylindrical super-element is used to model the finite element formulation and analyze the static and
modal behavior of stiffened FGM thick walled cylinders. By using
this super-element the number of elements, which are needed for
modeling, will reduce significantly and the process time is less in comparison with conventional finite element formulations. Results for static and modal analysis are evaluated and verified by
comparison to finite element formulation with conventional
elements. Comparison indicates a good conformity between results.