• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.6 s.177
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• pp.1593-1600
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• 2000

A method based on frequency domain approaches is presented for the nonlinear parameters identification of structure having nonlinear joints. The finite element model of linear substructure is us ed to calculating its frequency response functions needed in parameter identification process. This method is easily applicable to a complex real structure having nonlinear elements since it uses the frequency response function of finite element model. Since this method is performed in frequency domain, the number of equations required to identify the unknown parameters can be easily increased as many as it needed, just by not only varying excitation amplitude but also selecting excitation frequencies. The validity of this method is tested numerically and experimentally with a cantilever beam having the nonlinear element. It was verified through examples that the method is useful to identify the nonlinear parameters of a structure having arbitary nonlinear boundaries.

• East Asian mathematical journal
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• v.33 no.3
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• pp.295-308
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• 2017

We introduce a Crank-Nicolson characteristic finite element method to construct approximate solutions of a nonlinear Sobolev equation with a convection term. And for the Crank-Nicolson characteristic finite element method, we obtain the higher order of convergence in the temporal direction and in the spatial direction in $L^2$ normed space.

• Advances in nano research
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• v.15 no.2
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• pp.141-153
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• 2023

The main objective of this paper is to develop the finite element study on the nonlinear free vibration of functionally graded nanocomposite spherical shells reinforced with graphene platelets under the first-order shear deformation shell theory and von Kármán nonlinear kinematic relations. The governing equations are presented by introducing the full asymmetric nonlinear strain-displacement relations followed by the constitutive relations and energy functional. The extended Halpin-Tsai model is utilized to specify the overall Young's modulus of the nanocomposite. Then, the finite element formulation is derived and the quadrilateral 8-node shell element is implemented for finite element discretization. The nonlinear sets of dynamic equations are solved by the use of the harmonic balance technique and iterative method to find the nonlinear frequency response. Several numerical examples are represented to highlight the impact of involved factors on the large-amplitude vibration responses of nanocomposite spherical shells. One of the main findings is that for some geometrical and material parameters, the fundamental vibrational mode shape is asymmetric and the axisymmetric formulation cannot be appropriately employed to model the nonlinear dynamic behavior of nanocomposite spherical shells.

• Journal of Ship and Ocean Technology
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• v.12 no.2
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• pp.1-15
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• 2008

The main idea of this paper introduce stochastic structural parameters and random dynamic excitation directly into the dynamic functional variational formulations, and developed the nonlinear dynamic analysis of a stochastic variational principle and the corresponding stochastic finite element method via the weighted residual method and the small parameter perturbation technique. An interpolation method was adopted, which is based on representing the random field in terms of an interpolation rule involving a set of deterministic shape functions. Direct integration Wilson-${\theta}$ Method was adopted to solve finite element equations. Numerical examples are compared with Monte-Carlo simulation method to show that the approaches proposed herein are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.

• Structural Engineering and Mechanics
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• v.9 no.1
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• pp.89-97
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• 2000

A modified constitutive model has been developed for nonlinear finite element analysis of axisymmetric reinforced concrete structures, and then implemented into an existing finite element program. By comparing with the experimental results available, the present model has been validated.

• Structural Engineering and Mechanics
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• v.51 no.4
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• pp.601-625
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• 2014

Based on continuum mechanics and the principle of virtual displacements, incremental total Lagrangian formulation (T.L.) and incremental updated Lagrangian formulation (U.L.) were presented. Both T.L. and U.L. considered the large displacement stiffness matrix, which was modified to be symmetrical matrix. According to the incremental updated Lagrangian formulation, small strain, large displacement, finite rotation of three dimensional Timoshenko fiber beam element tangent stiffness matrix was developed. Considering large displacement and finite rotation, a new type of tangent stiffness matrix of the beam element was developed. According to the basic assumption of plane section, the displacement field of an arbitrary fiber was presented in terms of nodal displacement of centroid of cross-area. In addition, shear deformation effect was taken account. Furthermore, a nonlinear finite element method program has been developed and several examples were tested to demonstrate the accuracy and generality of the three dimensional beam element.

• East Asian mathematical journal
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• v.34 no.5
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• pp.601-614
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• 2018

In this paper, we introduce an extrapolated higher order characteristic finite element method to approximate solutions of nonlinear Sobolev equations with a convection term and we establish the higher order of convergence in the temporal and the spatial directions with respect to $L^2$ norm.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.257-270
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• 2018

An extrapolated Crank-Nicolson characteristic finite element method is introduced for approximate solutions of nonlinear Sobolev equations with a convection term. And we obtain the higher order of convergence for approximate solutions in the temporal and the spatial directions with respect to $L^2$ norm.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.23-40
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• 1998

Mixed finite element method is developed to approxi-mate the solution of the initial-boundary value problem for a strongly nonlinear second-order hyperbolic equation in divergence form. Exis-tence and uniqueness of the approximation are proved and optimal-order $L\infty$-in-time $L^2$-in-space a priori error estimates are derived for both the scalar and vector functions approximated by the method.

• Coupled systems mechanics
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• v.7 no.6
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• pp.691-705
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• 2018

In this paper, nonlinear displacements of laminated composite beams are investigated under non-uniform temperature rising with temperature dependent physical properties. Total Lagrangian approach is used in conjunction with the Timoshenko beam theory for nonlinear kinematic model. Material properties of the laminated composite beam are temperature dependent. In the solution of the nonlinear problem, incremental displacement-based finite element method is used with Newton-Raphson iteration method. The distinctive feature of this study is nonlinear thermal analysis of Timoshenko Laminated beams full geometric non-linearity and by using finite element method. In this study, the differences between temperature dependent and independent physical properties are investigated for laminated composite beams for nonlinear case. Effects of fiber orientation angles, the stacking sequence of laminates and temperature on the nonlinear displacements are examined and discussed in detail.