• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.05a
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• pp.155-158
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• 2001

The layup optimization by genetic algorithm (GA) for the strength of laminated composites with free-edge is presented. For the calculation of interlaminar stresses of composite laminates with free edges, extended Kantorovich method is applied. In the formulation of GA, repair strategy is adopted for the satisfaction of given constraints. In order to consider the bounded uncertainty of material properties, convex modeling is used. Results of GA optimization with scattered properties are compared with those of optimization with nominal properties. The GA combined with convex modeling can work as a practical tool for light weight design of laminated composite structures since uncertainties are always encountered in composite materials.

• Steel and Composite Structures
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• v.29 no.4
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• pp.483-491
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• 2018

Timoshenko beam model is widely exploited in the literature to examine the mechanical behavior of stubby beam-like components. Timoshenko beam theory is well-known to require the shear correction factor in order to recognize the nonuniform shear distribution at a section. While a variety of shear correction factors are appeared in the literature so far, there is still no consensus on the most appropriate form of the shear correction factor. The Saint-Venant's flexure problem is first revisited in the frame work of the classical theory of elasticity and a highly accurate approximate closed-form solution is presented employing the extended Kantorovich method. The resulted approximate solution for the elasticity field is then employed to introduce two shear correction factors consistent with the Cowper's and energy approaches. The mathematical form of the proposed shear correction factors are then simplified and compared with the results available in the literature over an extended range of Poisson's and aspect ratios. The proposed shear correction factors do not exhibit implausible issue of negative values and do not result in numerical instabilities too. Based on the comprehensive discussion on the shear correction factors, a piecewise definition of shear correction factor is introduced for rectangular cross-sections having excellent agreement with the numerical results in the literature for both shallow and deep cross-sections.

• Steel and Composite Structures
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• v.22 no.6
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• pp.1301-1336
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• 2016

In this paper, the free vibrations of a short cylindrical nanotube made of piezoelectric material are studied based on the consistent couple stress theory and using the shear deformable cylindrical theory. This new model has only one length scale parameter and can consider the size effects of nanostructures in nanoscale. To model size effects in nanoscale, and considering the nanotube material which is piezoelectric, the consistent couple stress theory is used. First, using Hamilton's principle, the equations of motion and boundary condition of the piezoelectric cylindrical nanoshell are developed. Afterwards, using Navier approach and extended Kantorovich method (EKM), the governing equations of the system with simple-simple (S-S) and clamped-clamped (C-C) supports are solved. Afterwards, the effects of size parameter, geometric parameters (nanoshell length and thickness), and mechanical and electric properties (piezoelectric effect) on nanoshell vibrations are investigated. Results demonstrate that the natural frequency on nanoshell in nanoscale is extremely dependent on nanoshell size. Increase in size parameter, thickness and flexoelectric effect of the material leads to increase in frequency of vibrations. Moreover, increased nanoshell length and diameter leads to decreased vibration frequency.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.345-351
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• 2007

Using more precise majorizing sequences we provide a finer convergence analysis than before [1], [7] of Newton's method in Riemannian manifolds with the following advantages: weaker hypotheses, finer error bounds on the distances involved and a more precise information on the location of the singularity of the vector field.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.35-45
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• 2008

In cases sufficient conditions for the semilocal convergence of Newtonlike methods are violated, we start with a modified Newton-like method (whose weaker convergence conditions hold) until we stop at a certain finite step. Then using as a starting guess the point found above we show convergence of the Newtonlike method to a locally unique solution of a nonlinear operator equation in a Banach space setting. A numerical example is also provided.

• Advances in Computational Design
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• v.5 no.1
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• pp.55-89
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• 2020

For the first time, an accurate analytical solution, based on coupled three-dimensional (3D) piezoelasticity equations, is presented for free vibration analysis of the angle-ply elastic and piezoelectric flat laminated panels under arbitrary boundary conditions. The present analytical solution is applicable to composite, sandwich and hybrid panels having arbitrary angle-ply lay-up, material properties, and boundary conditions. The modified Hamiltons principle approach has been applied to derive the weak form of governing equations where stresses, displacements, electric potential, and electric displacement field variables are considered as primary variables. Thereafter, multi-term multi-field extended Kantorovich approach (MMEKM) is employed to transform the governing equation into two sets of algebraic-ordinary differential equations (ODEs), one along in-plane (x) and other along the thickness (z) direction, respectively. These ODEs are solved in closed-form manner, which ensures the same order of accuracy for all the variables (stresses, displacements, and electric variables) by satisfying the boundary and continuity equations in exact manners. A robust algorithm is developed for extracting the natural frequencies and mode shapes. The numerical results are reported for various configurations such as elastic panels, sandwich panels and piezoelectric panels under different sets of boundary conditions. The effect of ply-angle and thickness to span ratio (s) on the dynamic behavior of the panels are also investigated. The presented 3D analytical solution will be helpful in the assessment of various 1D theories and numerical methods.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.29-40
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• 2000

We provide semilocal convergence theorems for Newton-like methods in Banach space using outer and generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Frechet-derivative. This way our Newton-Kantorovich hypotheses differ from earlier ones. Our results can be used to solve undetermined systems, nonlinear least square problems and ill-posed nonlinear operator equations.

• Structural Engineering and Mechanics
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• v.35 no.2
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• pp.217-240
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• 2010

A semi-analytical method is presented for accurately prediction of the free vibration behavior of generally laminated composite plates with arbitrary boundary conditions. The method employs the technique of separation of spatial variables within Hamilton's principle to obtain the equations of motion, including two systems of coupled ordinary homogeneous differential equations. Subsequently, by applying the laminate constitutive relations into the resulting equations two sets of coupled ordinary differential equations with constant coefficients, in terms of displacements, are achieved. The obtained differential equations are solved for the natural frequencies and corresponding mode shapes, with the use of the exact state-space approach. The formulation is exploited in the framework of the first-order shear deformation theory to incorporate the effects of transverse shear deformation and rotary inertia. The efficiency and accuracy of the present method are demonstrated by obtaining solutions to a wide range of problems and comparing them with finite element analysis and previously published results.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.251-266
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• 2014

In this paper, we use Newton's method to approximate a locally unique solution of an equation in Banach spaces and introduce recurrent functions to provide a weaker semilocal convergence analysis for Newton's method than before [1]-[13], in some interesting cases, provided that the Fr$\acute{e}$chet-derivative of the operator involved is p-H$\ddot{o}$lder continuous (p${\in}$(0, 1]). Numerical examples involving two boundary value problems are also provided.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.267-275
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• 2012

We present new results for the local convergence of Newton's method to a unique solution of an equation in a Banach space setting. Under a flexible gamma-type condition [12], [13], we extend the applicability of Newton's method by enlarging the radius and decreasing the ratio of convergence. The results can compare favorably to other ones using Newton-Kantorovich and Lipschitz conditions [3]-[7], [9]-[13]. Numerical examples are also provided.