• Composites Research
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• v.18 no.2
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• pp.30-37
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• 2005

In this paper, geometrically non-linear finite element analyses were performed to study the mechanical behavior of the material system of the envelope of stratospheric airships. The microstructure of the load-bearing plain weave layer was identified and modeled. The Updated Lagrangian formulation was employed to consider the geometric non-linearity as well as the induced structural non-linearity for the fiber tows. The stress-strain behavior was predicted and the effective elastic modulus was calculated by numerical experiments. It was found the non-linear stress-strain curves were largely different from those by linear analysis. And non-linear elastic moduli were much higher than linear elastic moduli. The difference was more distinguishable when the tow waviness ratio was smaller.

• Computers and Concrete
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• v.5 no.3
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• pp.217-241
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• 2008

In this paper, a total strain-based hysteretic material model based on MCFT is proposed for non-linear finite element analysis of reinforced concrete structures. Although many concrete models have been proposed for simulating behavior of structures under cyclic loading conditions, accurate simulations remain challenging due to uncertainties in materials, pitfalls of crude assumptions of existing models, and limited understanding of failure mechanisms. The proposed model is equipped with a fully generalized hysteresis rule and is formulated for 2D plane stress non-linear finite element analysis. The proposed model has been formulated in a tangent stiffness-based finite element scheme so that it can be used for most general finite element analysis packages. Moreover, it eliminates the need to check that tensile stresses can be transmitted across a crack. The tension stiffening model is a function of the bar orientation and any orientation can be accommodated. The proposed model has been verified with a series of experimental results of 2D RC planar panels. This study also demonstrates how parameters of the proposed model associated with cyclic damage modeling influences the pinched cyclic shear behavior.

• Journal of KSNVE
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• v.10 no.3
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• pp.531-535
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• 2000

A three-parameter model of viscoelastic damper which has a non-linear spring as an element is incorporated into an oscillator. The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by get analytic solutions of the system. The frequency-response curves show that multiple solutions co-exist and that the jump phenomena can occur. In addition it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurences of such non-linear phenomena. A direct time intergration of the original equation of motion validifies the use of the harmonic balance method to this sort of problem.

• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.677-697
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• 2010

This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

• Biomaterials and Biomechanics in Bioengineering
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• v.2 no.4
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• pp.207-223
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• 2015

In this paper a method for simultaneous swift non-linear analysis and optimal design/posture of mechanical/biomechanical systems is presented. The method is developed to get advantages of iterations in non-linear analysis and/or generations in genetic algorithm (GA) for the purpose of efficient analysis within the optimal design/posture. The method is applicable for both size and geometry optimizations wherein material and geometry non-linearity are present. In addition to established mechanical systems, the method can solve biomechanical models of human musculoskeletal system. Optimization-based procedures are popular methods for resolving the redundancy at joints wherein the number of unknown muscle forces is far more than the number of equilibrium equations. These procedures involve optimization of a cost function(s) which is assumed to be consistent with the central nervous system's strategy when activating muscles to assure equilibrium. However, because of the complexity of biomechanical problems (i.e., due to non-linear biomaterial, large deformation, redundancy of the problem and so on) efficient analysis are required within optimization procedures as suggested in this paper.

• Advances in nano research
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• v.9 no.3
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• pp.211-220
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• 2020

This paper investigates the effect of linear and non-linear distribution of carbon nanotube volume fraction in the FG-CNTRC beams on the critical buckling by using higher-order shear deformation theories. Here, the material properties of the CNTRC beams are assumed to be graded in the thickness direction according to a new exponential power law distribution in terms of the carbon nanotube volume fractions. The single-walled carbon nanotube is aligned and distributed in the polymeric matrix with different patterns of reinforcement; the material properties of the CNTRC beams are described by using the rule of mixture. The governing equations are derived through using Hamilton's principle. The Navier solution method is used under the specified boundary conditions for simply supported CNTRC beams. The mathematical models provided in this work are numerically validated by comparison with some available results. New results of critical buckling with the non-linear distribution of CNT volume fraction in different patterns are presented and discussed in detail, and compared with the linear distribution. Several aspects of beam types, CNT volume fraction, exponent degree (n), aspect ratio, etc., are taken into this investigation. It is revealed that the influences of non-linearity distribution in the beam play an important role to improve the mechanical properties, especially in buckling behavior. The results show that the X-Beam configuration is the strongest among all different types of CNTRC beams in supporting the buckling loads.

• Structural Engineering and Mechanics
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• v.68 no.3
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• pp.299-312
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• 2018

In this paper, an extended finite element method is proposed to analyze both geometric and material non-linear behavior of general Functionally Graded Material (FGM) plate-shell type structures. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the elastoplastic behavior of the ceramic particle-reinforced metal-matrix FGM plates-shells. The standard quadrilateral 4-nodes shell element with three rotational and three translational degrees of freedom per node, S4, is extended in the present study, to deal with elasto-plastic analysis of geometrically non-linear FGM plate-shell structures. The elastoplastic material properties are assumed to vary smoothly through the thickness of the plate-shell type structures. The nonlinear approach is based on Mori-Tanaka model to underline micromechanics and locally determine the effective FGM properties and self-consistent method of Suquet for the homogenization of the stress-field. The elasto-plastic behavior of the ceramic/metal FGM is assumed to follow Ludwik hardening law. An incremental formulation of the elasto-plastic constitutive relation is developed to predict the tangent operator. In order to to highlight the effectiveness and the accuracy of the present finite element procedure, numerical examples of geometrically non-linear elastoplastic functionally graded plates and shells are presented. The effects of the geometrical parameters and the volume fraction index on nonlinear responses are performed.

• Computers and Concrete
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• v.15 no.4
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• pp.547-562
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• 2015

A two-dimensional multi-layered finite elements modeling of reinforced concrete structures at non-linear behaviour under monotonic and cyclical loading is presented. The non-linearity material is characterized by several phenomena such as: the physical non-linearity of the concrete and steels materials, the behaviour of cracked concrete and the interaction effect between materials represented by the post-cracking filled. These parameters are taken into consideration in this paper to examine the response of the reinforced concrete structures at the non-linear behaviour. Four examples of application are presented. The numerical results obtained, are in a very good agreement with available experimental data and other numerical models of the literature.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2005.11a
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• pp.103-106
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• 2005

The material properties of membrane for stratospheric airship is experimentally investigated. Mechanical tensile properties of the membrane material at room, high and low temperature are measured using instron with thermal chamber. Experimentaly, material non-linearity is observed at room and high temperature. In order to simulate material non-linearity caused by the uniaxial extension curve of a woven fabric, the nonlinear hyperelastic problem is considered with finite clement program of ABAQS. Numerical results are compared with experimental results.

• Steel and Composite Structures
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• v.42 no.6
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• pp.779-789
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• 2022

This work presents a non-linear cylindrical bending analysis of functionally graded plate reinforced by single-walled carbon nanotubes (SWCNTs) in thermal environment using a simple integral higher-order shear deformation theory (HSDT). This theory does not require shear correction factors and the transverse shear stresses vary parabolically through the thickness. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTCRs) are considered to be graded in the thickness direction, and are estimated through a micromechanical model. The non-linear strain-displacement relations in the Von Karman sense are used to study the effect of geometric non-linearity and the solution is obtained by minimization of the total potential energy. The numerical illustrations concern the nonlinear bending response of FG-CNTRC plates under different sets of thermal environmental conditions, from which results for uniformly distributed CNTRC plates are obtained as benchmarks.