• Steel and Composite Structures
• /
• v.28 no.5
• /
• pp.541-557
• /
• 2018

This paper presents the influence of carbon nanotubes (CNTs) waviness and aspect ratio on the vibrational behavior of functionally graded nanocomposite sandwich annular sector plates resting on two-parameter elastic foundations. The carbon nanotube-reinforced (CNTR) sandwich plate has smooth variation of CNT fraction along the thickness direction. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an 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. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak's elastic foundation coefficients, sandwich plate thickness, face sheets thickness and plate aspect ratio are investigated on the free vibration of the sandwich plates with wavy CNT-reinforced face sheets. 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 sandwich 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.

• Journal of Welding and Joining
• /
• v.13 no.4
• /
• pp.122-131
• /
• 1995

An automatic welding equipment for thick plates requires the capability of the seam tracking of the weld line which often includes misalignment of the workpiece and variation of groove width. In this study, an automatic welding equipment and control algorithms based on the arc sensor were proposed for the GMA welding of thick plates which had misalignment and gap variation. The developed system being constituted with 5 axis can be automatically controlled by computer and also automnatically set the welding conditions such as welding current, and voltage. The proposed algorithms for the seam tracking in multi-pass welding of the thick plates were constituted as follows : the detection of weaving-end point for findng the variation of groove width, the control of welding velocity for acquiring a constant thickness deposition of weld metal, and the calculation of groove width and height of an arbitrary pass in the multi-pass weld. As results of the application of the system, it was revealed that the system had a good capability in seam tracking and made an excellent weld quality in V groove butt joint.

• Steel and Composite Structures
• /
• v.16 no.4
• /
• pp.375-387
• /
• 2014

The purpose of this paper is to propose a method for evaluation of varying stiffness coefficients of tailored conical shells (TCS). Furthermore, a comparison between buckling loads of these shells under axial load with the different fiber path is performed. A circular truncated conical shell subjected to axial compression is taken into account. Three different theoretical path containing geodesic path, constant curvature path and constant angle path has been considered to describe the angle variation along the cone length, along cone generator of a conical shell are offered. In the TCS with the arbitrary fiber path, the thickness and the ply orientation are assumed to be functions of the shell coordinates and influencing stiffness coefficients of the structure. The stiffness coefficients and the buckling loads of shells are calculated basing on classical shells theory (CST) and using finite-element analysis (FEA) software. The obtained results for TCS with arbitrary fiber path, thickness and ply orientation are derived as functions of shell longitudinal coordinate and influencing stiffness coefficients of structures. Furthermore, the buckling loads based on fiber path and ply orientation at the start of tailored fiber get to be different. The extent of difference for tailored fiber with start angle lower than 20 degrees is not significant. The results in this paper show that using tailored fiber placement could be applied for producing conical shells in order to have greater buckling strengths and lower weight. This work demonstrates the use of fiber path definitions for calculated stiffness coefficients and buckling loads of conical shells.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.16 no.2
• /
• pp.197-206
• /
• 2003

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid and hollow hemispherical shells of revolution of arbitrary wall thickness having arbitrary constraints on their boundaries. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components μ/sub Φ/, μ/sub z/, and μ/sub θ/ in the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the Φ and z directions. Potential (strain) and kinetic energies of the hemispherical shells are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies obtained by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Novel numerical results are presented for solid and hollow hemispheres with linear thickness variation. The effect on frequencies of a small axial conical hole is also discussed. Comparisons are made for the frequencies of completely free, thick hemispherical shells with uniform thickness from the present 3-D Ritz solutions and other 3-D finite element ones.

• Structural Engineering and Mechanics
• /
• v.75 no.2
• /
• pp.247-269
• /
• 2020

A finite strip formulation was developed for buckling and free vibration analysis of laminated composite plates based on different shear deformation plate theories. The different shear deformation theories such as Zigzag higher order, Refined Plate Theory (RPT) and other higher order plate theories by variation of transverse shear strains through plate thickness in the parabolic form, sine and exponential were adopted here. The two loaded opposite edges of the plate were assumed to be simply supported and remaining edges were assumed to have arbitrary boundary conditions. The polynomial shape functions are applied to assess the in-plane and out-of-plane deflection and rotation of the normal cross-section of plates in the transverse direction. The finite strip procedure based on the virtual work principle was applied to derive the stiffness, geometric and mass matrices. Numerical results were obtained based on various shear deformation plate theories to verify the proposed formulation. The effects of length to thickness ratios, modulus ratios, boundary conditions, the number of layers and fiber orientation of cross-ply and angle-ply laminates were determined. The additional results on the same effects in the interaction of biaxial in-plane loadings on the critical buckling load were determined as well.

• Structural Engineering and Mechanics
• /
• v.37 no.5
• /
• pp.529-542
• /
• 2011

Three dimensional solutions for free vibrations analysis of functionally graded fiber reinforced cylindrical panel are presented, using differential quadrature method (DQM). The orthotropic panel is simply supported at the edges and is assumed to have an arbitrary variation of reinforcement volume fraction in the radial direction. Suitable displacement functions that identically satisfy the simply supported boundary condition are used to reduce the equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which can be solved by differential quadrature method to obtain natural frequencies. The main contribution of this work is presenting useful results for continuous grading of fiber reinforcement in the thickness direction of a cylindrical panel and comparison with similar discrete laminate composite ones. Results indicate that significant improvement is found in natural frequency of a functionally graded fiber reinforced composite panel due to the reduction in spatial mismatch of material properties.

• Structural Engineering and Mechanics
• /
• v.38 no.6
• /
• pp.753-765
• /
• 2011

The radial vibration behaviors of a circular cylindrical composite piezoelectric transducer (CPT) are investigated. The CPT is composed of a piezoelectric ring polarized in the radial direction and an elastic ring graded in power-law variation form along the radial direction. The governing equations for plane stress state problem under the harmonic excitation are derived and the exact solutions for both piezoelectric and functionally graded elastic rings are obtained. The characteristic equations for resonant and anti-resonant frequencies are established. The presented methodology is fit to carry out the parametric investigation for composite piezoelectric transducers (CPTs) with arbitrary thickness in radial direction. With the aid of numerical analysis, the relationship between the radial vibration behaviors of the cylindrical CPT and the material inhomogeneity index of the functionally graded elastic ring as well as the geometric parameters of the CPTs are illustrated and some important features are reported.

• Journal of Welding and Joining
• /
• v.3 no.2
• /
• pp.52-63
• /
• 1985

Fillet welded joints, specially in ship structure, are well known the critical part where stress concentrate or crack initiates and grows. This paper is concerned with the study of the behavior of fatigue crack growth t the root and toe of load carrying cruciform fillet welded joints under three points bending by the determination of stress intensity factor from the J-Integral, using the Finite Element Method. The stress intensity factor was investigated in accordance to the variation of the weld size (H/Tp). weld penetration (a/W) and plate thickness (2a'/Tp). As mixed mode is occurred on account of shearing force under the three points bending, Stern's reciprocal theory is applied to confirm which mode is the major one. The main results may be summarized as follows 1) The calculation formula of the stress intensity factor at the both of root and toe of the joint was obtained to estimate the stress intensity factor in the arbitrary case. 2) The change of stress field around crack tip gives much influence on each other at the roof and toe as H/Tp decreases. 3) Mode I is a major mode under the three points bending.

• 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.

• Smart Structures and Systems
• /
• v.30 no.3
• /
• pp.245-253
• /
• 2022

A two-layer beam consisting of an elastoplastic layer and a functional layer made of shape memory alloy (SMA) TiNi is considered. Constitutive relations for SMA are set by a microstructural model capable to calculate strain increment produced by arbitrary increments of stress and temperature. This model exploits the approximation of small strains. The equations to calculate the variations of the strain and the internal variables are based on the experimentally registered temperature kinetics of the martensitic transformations with an account of the crystallographic features of the transformation and the laws of equilibrium thermodynamics. Stress and phase distributions over the beam height are calculated by steps, by solving on each step the boundary-value problem for given increments of the bending moment (or curvature) and the tensile force (or relative elongation). Simplifying Bernoulli's hypotheses are applied. The temperature is considered homogeneous. The first stage of the numerical experiment is modeling of preliminary deformation of the beam by bending or stretching at a temperature corresponding to the martensitic state of the SMA layer. The second stage simulates heating and subsequent cooling across the temperature interval of the martensitic transformation. The curvature variation depends both on the total thickness of the beam and on the ratio of the layer's thicknesses.