• Steel and Composite Structures
• /
• v.25 no.6
• /
• pp.649-661
• /
• 2017

This paper is motivated by the lack of studies in the technical literature concerning to the influence of carbon nanotubes (CNTs) waviness and aspect ratio on the vibrational behavior of functionally graded nanocomposite annular sector plates resting on two-parameter elastic foundations. The carbon nanotube-reinforced (CNTR) plate has smooth variation of CNT fraction based on the power-law distribution in the thickness direction, and the material properties are also estimated by the extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. Parametric studies are carried out to highlight the influence of CNTs volume fraction, waviness and aspect ratio, boundary conditions and elastic foundation on vibrational behavior of FG-CNT thick sectorial plates. The study is carried out based on three-dimensional theory of elasticity and in contrary to two-dimensional theories, such as classical, the first- and the higher-order shear deformation plate theories, this approach does not neglect transverse normal deformations. The annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. For an overall comprehension on 3-D vibration of annular sector plates, some mode shape contour plots are reported in this research work.

• Steel and Composite Structures
• /
• v.26 no.2
• /
• pp.125-137
• /
• 2018

In this work, the bending and free vibration analysis of multilayered plates and shells is presented by utilizing a new higher order shear deformation theory (HSDT). The proposed involves only four unknowns, which is even less than the first shear deformation theory (FSDT) and without requiring the shear correction coefficient. Unlike the conventional HSDTs, the present one presents a novel displacement field which incorporates undetermined integral variables. The equations of motion are derived by using the Hamilton's principle. These equations are then solved via Navier-type, closed form solutions. Bending and vibration results are found for cylindrical and spherical shells and plates for simply supported boundary conditions. Bending and vibration problems are treated as individual cases. Panels are subjected to sinusoidal, distributed and point loads. Results are presented for thick to thin as well as shallow and deep shells. The computed results are compared with the exact 3D elasticity theory and with several other conventional HSDTs. The proposed HSDT is found to be precise compared to other several existing ones for investigating the static and dynamic response of isotropic and multilayered composite shell and plate structures.

• Journal of the Architectural Institute of Korea Structure & Construction
• /
• v.34 no.9
• /
• pp.3-10
• /
• 2018

While computer environments have been dramatically developed in recent years, as the building structures become larger, the structural analysis models are also becoming more complex. So there is still a need to model one shear wall with one finite element. From the viewpoint of the concept of FEA, if one shear wall is modeled by one finite element, the result of analysis is not likely accurate. Shear wall may be modelled with various finite elements. Among them, considering the displacement compatibility condition with the beam element connected to the shear wall, plane stress element with in-plane rotational stiffness is preferred. Therefore, in order to analyze one shear wall with one finite element accurately, it is necessary to evaluate finite elements developed for the shear wall analysis and to develop various plane stress elements with rotational stiffness continuously. According to the above mentioned need, in this study, the theory about a plane stress element using hierarchical interpolation equation is reviewed and stiffness matrix is derived. And then, a computer program using this theory is developed. Developed computer program is used for numerical experiments to evaluate the analysis results using commercial programs such as SAP2000, ETABS, PERFORM-3D and MIDAS. Finally, the deflection equation of a cantilever beam with narrow rectangular section and bent by an end load P is derived according to the elasticity theory, and it is used to for comparison with theoretical solution.

• Journal of the Korean Wood Science and Technology
• /
• v.42 no.4
• /
• pp.367-375
• /
• 2014

A simplified material model, which was efficiently implemented in a three-dimensional finite solid element (3D FE) analysis for wood was developed. The bi-linear elasto-plastic anisotropic material theory was adopted to describe constitutive relations of wood in three major directions including longitudinal, radial and tangential direction. The assumption of transverse isotropy was made to reduce the requisite 27 material constants to 6 independent constants including elastic moduli, yield stresses and Poisson's ratios in the parallel, and perpendicular to grain directions. The results of Douglas fir compression tests in the three directions were compared to the 3D FE simulation incorporated with the wood material model developed in this study. Successful agreements of the results were found in the load-deformation curves and the permanent deformations. Future works and difficulties expected in the advanced application of the model were discussed.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.16 no.3
• /
• pp.251-260
• /
• 2003

A three dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of deep, tapered rods and beams with circular cross section. Unlike conventional rod and beam theories, which are mathematically one-dimensional (1-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u/sup r/, u/sub θ/ and u/sub z/, in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in , and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the rods and beams are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the rods and beams. Novel numerical results are tabulated for nine different tapered rods and beams with linear, quadratic, and cubic variations of radial thickness in the axial direction using the 3D theory. Comparisons are also made with results for linearly tapered beams from 1-D classical Euler-Bernoulli beam theory.

• Interaction and multiscale mechanics
• /
• v.2 no.3
• /
• pp.321-332
• /
• 2009

Recent development in composites containing phase-transforming particles, such as vanadium dioxide or barium titanate, reveals the overall stiffness and viscoelastic damping of the composites may be unbounded (Lakes et al. 2001, Jaglinski et al. 2007). Negative stiffness is induced from phase transformation predicted by the Landau phase transformation theory. Although this unbounded phenomenon is theoretically supported with the composite homogenization theory, detailed stress analyses of the composites are still lacking. In this work, we analyze the stress distribution of the Hashin-Shtrikman (HS) composite and its two-dimensional variant, namely a circular inclusion in a square plate, under the assumption that the Young's modulus of the inclusion is negative. Assumption of negative stiffness is a priori in the present analysis. For stress analysis, a closed form solution for the HS model and finite element solutions for the 2D composite are presented. A static loading condition is adopted to estimate the effective modulus of the composites by the ratio of stress to average strain on the loading edges. It is found that the interfacial stresses between the circular inclusion and matrix increase dramatically when the negative stiffness is so tuned that overall stiffness is unbounded. Furthermore, it is found that stress distributions in the inclusion are not uniform, contrary to Eshelby's theorem, which states, for two-phase, infinite composites, the inclusion's stress distribution is uniform when the shape of the inclusion has higher symmetry than an ellipse. The stability of the composites is discussed from the viewpoint of deterioration of perfect interface conditions due to excessive interfacial stresses.

• Smart Structures and Systems
• /
• v.22 no.3
• /
• pp.259-276
• /
• 2018

This paper studies the energies and energy release rate (ERR) for the initially rotationally symmetric compressed (or stretched) in the inward (outward) radial direction of the PZT/Elastic/PZT sandwich circular plate with interface penny-shaped cracks. The investigations are made by utilizing the so-called three-dimensional linearized field equations and relations of electro-elasticity for piezoelectric materials. The quantities related to the initial stress state are determined within the scope of the classical linear theory of piezoelectricity. Mathematical formulation of the corresponding problem and determination of the quantities related to the stress-strain state which appear as a result of the action of the uniformly normal additional opening forces acting on the penny-shaped crack's edges are made within the scope of the aforementioned three-dimensional linearized field equations solution which is obtained with the use of the FEM modelling. Numerical results of the energies and ERR and the influence of the problem parameters on these quantities are presented and discussed for the PZT- 5H/Al/PZT-5H, PZT-4/Al/PZT-4, $BaTiO_3/Al/BaTiO_3$ and PZT-5H/StPZT-5H sandwich plates. In particular, it is established that the magnitude of the influence of the piezoelectricity and initial loading on the ERR increases with crack radius length.

• Steel and Composite Structures
• /
• v.18 no.1
• /
• pp.1-28
• /
• 2015

In this paper, the dynamic response of functionally gradient steel (FGS) composite cylindrical panels in steady-state thermal environments subjected to impulsive loads is investigated for the first time. FGSs composed of graded ferritic and austenitic regions together with bainite and martensite intermediate layers are analyzed. Thermo-mechanical material properties of FGS composites are predicted according to the microhardness profile of FGS composites and approximated with appropriate functions. Based on the three-dimensional theory of thermo-elasticity, the governing equations of motionare derived in spatial and time domains. These equations are solved using the hybrid Fourier series expansion-Galerkin finite element method-Newmark approach for simply supported boundary conditions. The present solution is then applied to the thermo-elastic dynamic analysis of cylindrical panels with three different arrangements of material compositions of FGSs including ${\alpha}{\beta}{\gamma}M{\gamma}$, ${\alpha}{\beta}{\gamma}{\beta}{\alpha}$ and ${\gamma}{\beta}{\alpha}{\beta}{\gamma}$ composites. Benchmark results on the displacement and stress time-histories of FGS cylindrical panels in thermal environments under various pulse loads are presented and discussed in detail. Due to the absence of similar results in the specialized literature, this paper is likely to fill a gap in the state of the art of this problem, and provide pertinent results that are instrumental in the design of FGS structures under time-dependent mechanical loadings.

• Journal of the Korean Society for Advanced Composite Structures
• /
• v.1 no.3
• /
• pp.1-9
• /
• 2010

In this paper, we used various shear deformation functions for modelling isotropic, symmetric composite and sandwich plates discretized by a mixed finite element method based on the Lagrangian/Hermite interpolation functions. These shear deformation theories uses polynomial, trigonometric, hyperbolic and exponential functions through the thickness direction, allowing for zero transverse shear stresses at the top and bottom surfaces of the plate. All shear deformation functions are compared with other available analytical/3D elasticity solutions, are predicted the reasonable accuracy for investigated problems. Particularly, The present results show that the use of exponential shear deformation theory (Karama et al. 2003; Aydogu 2009) provides very good solutions for composite and sandwich plates.

• Geomechanics and Engineering
• /
• v.24 no.3
• /
• pp.267-280
• /
• 2021

The research presented in this paper deals with dynamic stability analysis of the graphene nanoplatelets (GPLs) reinforced composite spinning disk. The presented small-scaled structure is simulated as a disk covered by viscoelastic substrate which is two-parametric. The centrifugal and Coriolis impacts due to the spinning are taken into account. The stresses and strains would be obtained using the first-order-shear-deformable-theory (FSDT). For Poisson ratio, as well as various amounts of mass densities, the mixture rule is employed, while a modified Halpin-Tsai model is inserted for achieving the elasticity module. The structure's boundary conditions (BCs) are obtained employing GPLs reinforced composite (GPLRC) spinning disk's governing equations applying principle of Hamilton which is based on minimum energy and ultimately have been solved employing numerical approach called generalized-differential quadrature-method (GDQM). Spinning disk's dynamic properties with different boundary conditions (BCs) are explained due to the curves drawn by Matlab software. Also, the simply-supported boundary conditions is applied to edges 𝜃=𝜋/2, and 𝜃=3𝜋/2, while, cantilever, respectively, is analyzed in R=R_i, and R₀. The final results reveal that the GPLs' weight fraction, viscoelastic substrate, various GPLs' pattern, and rotational velocity have a dramatic influence on the amplitude, and vibration behavior of a GPLRC rotating cantilevered disk. As an applicable result in related industries, the spinning velocity impact on the frequency is more effective in the higher radius ratio's amounts.