• Steel and Composite Structures
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• 제42권1호
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• pp.23-32
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• 2022

In this paper, a nonlinear numerical method to solve the large deflection problem is introduced. And the non-dimensional load-deflection behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates is parametrically investigated. The large deflection problem is formulated according to the von Kármán nonlinear theory and the (1,1,0)^* hierarchical model, and it is approximated by 2-D natural element method (NEM). The shear locking phenomenon is suppressed by the selectively reduced integration method. The nonlinear matrix equations are solved by combining the incremental loading scheme and the Newton-Raphson iteration method. The proposed method is validated from the benchmark experiments, where the propose method shows an excellent agreement with the reference methods. The nonlinear behavior of FG-CNTRC plates is evaluated in terms of the non-dimensional load-deflection curve, and it is parametrically investigated with respect to the existence/non-existence and gradient pattern of CNTs, the width-to-thickness and aspect ratios of plates and the type of boundary conditions. The non-dimensional central deflection is significantly reduced when CNTs and added, and it decreases with the volume fraction of CNTs. But, it shows a uniform increase in proportion to the width-to-thickness and aspect ratios. Both the gradient pattern of CNTs and the type of boundary conditions do also show the remarkable effects.

• Structural Engineering and Mechanics
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• 제67권6호
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• pp.565-578
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• 2018

This research article reported the nonlinear finite solutions of the nonlinear flexural strength and stress behaviour of nano sandwich graded structural shell panel under the combined thermomechanical loading. The nanotube sandwich structural model is derived mathematically using the higher-order displacement polynomial including the full geometrical nonlinear strain-displacement equations via Green-Lagrange relations. The face sheets of the sandwich panel are assumed to be carbon nanotube-reinforced polymer composite with temperature dependent material properties. Additionally, the numerical model included different types of nanotube distribution patterns for the sandwich face sheets for the sake of variable strength. The required equilibrium equation of the graded carbon nanotube sandwich structural panel is derived by minimizing the total potential energy expression. The energy expression is further solved to obtain the deflection values (linear and nonlinear) via the direct iterative method in conjunction with finite element steps. A computer code is prepared (MATLAB environment) based on the current higher-order nonlinear model for the numerical analysis purpose. The stability of the numerical solution and the validity are verified by comparing the published deflection and stress values. Finally, the nonlinear model is utilized to explore the deflection and the stresses of the nanotube-reinforced (volume fraction and distribution patterns of carbon nanotube) sandwich structure (different core to face thickness ratios) for the variable type of structural parameter (thickness ratio, aspect ratio, geometrical configurations, constraints at the edges and curvature ratio) and unlike temperature loading.

• Structural Engineering and Mechanics
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• 제72권1호
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• pp.71-81
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• 2019

The objective of this paper is to develop a size-dependent nonlinear model of beams for fluid-conveying nanotubes with an initial deflection. The nonlinear frequency response of the nanotube is analysed via an Euler-Bernoulli model. Size influences on the behaviour of the nanosystem are described utilising the nonlocal strain gradient theory (NSGT). Relative motions at the inner wall of the nanotube is taken into consideration via Beskok-Karniadakis model. Formulating kinetic and elastic energies and then employing Hamilton's approach, the nonlinear motion equations are derived. Furthermore, Galerkin's approach is employed for discretisation, and then a continuation scheme is developed for obtaining numerical results. It is observed that an initial deflection significantly alters the frequency response of NSGT nanotubes conveying fluid. For small initial deflections, a hardening nonlinearity is found whereas a softening-hardening nonlinearity is observed for large initial deflections.

• Steel and Composite Structures
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• 제33권2호
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• pp.307-318
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• 2019

This is the first attempt to consider the nonlinear bending analysis of porous functionally graded (FG) thick annular and circular nanoplates resting on Kerr foundation. The size effects are captured based on modified couple stress theory (MCST). The material properties of the porous FG nanostructure are assumed to vary smoothly through the thickness according to a power law distribution of the volume fraction of the constituent materials. The elastic medium is modeled by Kerr elastic foundation which consists of two spring layers and one shear layer. The governing equations are extracted based on Hamilton's principle and two variables refined plate theory. Utilizing generalized differential quadrature method (GDQM), the nonlinear static behavior of the nanostructure is obtained under different boundary conditions. The effects of various parameters such as material length scale parameter, boundary conditions, and geometrical parameters of the nanoplate, elastic medium constants, porosity and FG index are shown on the nonlinear deflection of the annular and circular nanoplates. The results indicate that with increasing the material length scale parameter, the nonlinear deflection is decreased. In addition, the dimensionless nonlinear deflection of the porous annular nanoplate is diminished with the increase of porosity parameter. It is hoped that the present work may provide a benchmark in the study of nonlinear static behavior of porous nanoplates.

• Structural Engineering and Mechanics
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• 제51권2호
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• pp.333-347
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• 2014

Nonlinear bending of super-elliptical plates of uniform thickness under uniform transverse pressure was investigated by the Ritz method. The material was assumed to be homogeneous and isotropic. The contribution of the boundary conditions at the point supports was introduced by the Lagrange multipliers. The solution was obtained by the Newton-Raphson method. The influence of the location of the point supports on the central deflection was highlighted by sensitivity analysis. An approximate relationship between the central deflection and the super-elliptical power was obtained using the method of least squares. The critical points where the maximum deflection may develop, and the influence of nonlinearity were highlighted. The nonlinearity was found to be sensitive to the aspect ratio. The accuracy of the algorithm was validated by comparing the central deflection with the solutions of elliptical and rectangular plates.

• Computers and Concrete
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• 제25권6호
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• pp.537-549
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• 2020

Geometrically nonlinear axisymmetric bending analysis of shear deformable circular plates on a nonlinear three-parameter elastic foundation was made. Plates ranging from "thin" to "moderately thick" were investigated for three types of material: isotropic, transversely isotropic, and orthotropic. The differential equations were discretized by means of the finite difference method (FDM) and the differential quadrature method (DQM). The Newton-Raphson method was applied to find the solution. A parametric investigation using seven unknowns per node was presented. The novelty of the paper is that detailed numerical simulations were made to highlight the combined effects of the material properties and the boundary conditions on (i) the deflection, (ii) the stress resultants, and (iii) the external load. The formulation was verified through comparison studies. It was observed that the results are highly influenced from the boundary conditions, and from the material properties.

• International Journal of Aeronautical and Space Sciences
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• 제7권1호
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• pp.99-105
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• 2006

In this study, nonlinear static and dynamic aeroelastic analyses for a high-aspect-ratio wing have been performed. To achieve these aims, the transonic small disturbance (TSD) theory for the aerodynamic analysis and the large deflection beam theory considering a geometrical nonlinearity for the structural analysis are applied, respectively. For the coupling between fluid and structure, the transformation of a displacement from the structural mesh to the aerodynamic grid is performed by a shape function which is used for the finite element and the inverse transformation of force by work equivalent load method. To validate the current method, the present analysis results of a high-aspect-ratio wing are compared with the experimental results. Static deformations in the vertical and torsional directions caused by an angle of attack and gravity loading are compared with experimental results. Also, static and dynamic aeroelastic characteristics are investigated. The comparisons of the flutter speed and frequency between a linear and nonlinear analysis are presented.

• International Journal of Aeronautical and Space Sciences
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• 제9권2호
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• pp.41-47
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• 2008

The nonlinear structural analyses of high-aspect-ratio structures were performed. For the high-aspect-ratio structures, it is important to understand geometric nonlinearity due to large deflections. To consider geometric nonlinearity, finite element analyses based on the large deflection beam theory were introduced. Comparing experimental data and the present nonlinear analysis results, the current results were proved to be very accurate for the static and dynamic behaviors for both isotropic and anisotropic beams.

• 한국도로학회논문집
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• 제18권6호
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• pp.35-40
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• 2016

OBJECTIVES : The objective of this study is to analyze the nonlinear behavior of block pavements using multi-load level falling weight deflectometer (FWD) deflections. METHODS : Recently, block pavements are employed not only in sidewalks, but also in roadways. For the application of block pavements in roadways, the structural capacities of subbase and subgrade are important factors that support the carry traffic load. Multi-load level FWD testing was conducted on block pavements to analyze their nonlinear behavior. The deflection ratio due to the increase in load was analyzed to estimate the nonlinearity of block pavements. Finite element method with nonlinear soil model was applied to simulate the actual nonlinear behavior of the block pavement under different levels of load. RESULTS : The results of the FWD testing show that the center deflections in block pavements are approximately ten times greater than that in asphalt pavements. The deflection ratios of the block pavement due to the increase in the load range from 1.2 to 1.5, indicating that the deflection increased by 20~50%. The material coefficients of the nonlinear soil model were determined by comparing the measured deflections with the predicted deflections using the finite element method. CONCLUSIONS : In this study, the nonlinear behavior of block pavements was reviewed using multi-load level FWD testing. The deflection ratio proposed in this study can estimate the nonlinearity of block pavements. The use of nonlinear soil model in subbase and subgrade increases the accuracy of predicting deflections in finite element method.

• Structural Engineering and Mechanics
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• 제54권3호
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• pp.433-451
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• 2015

This paper focuses on large deflection static behavior of edge cracked simple supported beams subjected to a non-follower transversal point load at the midpoint of the beam by using the total Lagrangian Timoshenko beam element approximation. The cross section of the beam is circular. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. It is known that large deflection problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of Aluminum. In the study, the effects of the location of crack and the depth of the crack on the non-linear static response of the beam are investigated in detail. The relationships between deflections, end rotational angles, end constraint forces, deflection configuration, Cauchy stresses of the edge-cracked beams and load rising are illustrated in detail in nonlinear case. Also, the difference between the geometrically linear and nonlinear analysis of edge-cracked beam is investigated in detail.