• Advances in nano research
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• v.12 no.1
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• pp.37-47
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• 2022

In this paper, the non-linear static analysis of Timoshenko nanobeams consisting of bi-directional functionally graded material (BFGM) with immovable ends is investigated. The scratching in the FG nanobeam mid-plane, is the source of nonlinearity of the bending problems. The nonlocal theory is used to investigate the non-linear static deflection of nanobeam. In order to simplify the formulation, the problem formulas is derived according to the physical middle surface. The Hamilton principle is employed to determine governing partial differential equations as well as boundary conditions. Moreover, the differential quadrature method (DQM) and direct iterative method are applied to solve governing equations. Present results for non-linear static deflection were compared with previously published results in order to validate the present formulation. The impacts of the nonlocal factors, beam length and material property gradient on the non-linear static deflection of BFG nanobeams are investigated. It is observed that these parameters are vital in the value of the non-linear static deflection of the BFG nanobeam.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.8 s.239
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• pp.1051-1060
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• 2005

Nonlinear Response Optimization using Equivalent Static Loads (NROESL) method/algorithm is proposed to perform optimization of non-linear response structures. The conventional method spends most of the total design time on nonlinear analysis. The NROESL algorithm makes the equivalent static load cases for each response and repeatedly performs linear response optimization and uses them as multiple loading conditions. The equivalent static loads are defined as the loads in the linear analysis, which generates the same response field as those in non-linear analysis. The algorithm is validated for the convergence and the optimality. The proposed algorithm is applied to a simple mathematical problem to verify the convergence and the optimality.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.134-141
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• 1997

A geometrically non-linear finite element formulation of spatial cable networks is presented using three cable elements. Firstly, derivation procedures of tangent stiffness and mass matrices for the space truss element and the elastic catenary cable element, and the isoparametric cable element are summarized. The load incremental method based on Newton-Raphson iteration method and the dynamic relaxation method are presented in order to determine the initial static state of cable nets subjected to self-weights and support motions. Furthermore, static non-linear analysis of cable structures under additional live loads are performed based on the initial configuration. Challenging example problems are presented and discussed in order to demonstrate the feasibility of the present finite element method and investigate static non-linear behaviors of cable nets.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.1256-1261
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• 2004

Nonlinear Response Optimization using Equivalent Static Loads (NROESL) method/algorithm is proposed to perform optimization of non-linear response structures. It is more expensive to carry out nonlinear response optimization than linear response optimization. The conventional method spends most of the total design time on nonlinear analysis. Thus, the NROESL algorithm makes the equivalent static load cases for each response and repeatedly performs linear response optimization and uses them as multiple loading conditions. The equivalent static loads are defined as the loads in the linear analysis, which generates the same response field as those in non-linear analysis. The algorithm is validated for the convergence and the optimality. The function satisfies the descent condition at each cycle and the NROESL algorithm converges. It is mathematically validated that the solution of the algorithm satisfies the Karush-Kuhn-Tucker necessary condition of the original nonlinear response optimization problem. The NROESL algorithm is applied to two structural problems. Conventional optimization with sensitivity analysis using the finite difference method is also applied to the same examples. The results of the optimizations are compared. The proposed method is very efficient and derives good solutions.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.999-1004
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• 2004

A numerical method and algorithms is proposed to perform optimization of non-linear response structures. An analytical and numerical method based finite element method is also proposed for the transformation of non-linear response into linear response. Loads transformed from this method are defined as the equivalent linear loads. With the loads and the transformed response, linear static optimization is performed for nonlinear response structure with geometric and/or material non-linearity. The results of the optimization are compared with them of typical non-linear response optimization using finite difference method. The proposed method is very efficient and derives good solution.

• Proceeding of EDISON Challenge
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• 2016.03a
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• pp.262-267
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• 2016

In this paper, to design Human Powered Aircraft(HPAC) with high aspect ratio wing which behave with large displacement under lift distribution causing a failure itself, then steel wire has been designed to prevent its failure. unit load method is used to calculate reaction force on wire and Optimal Triangle(OPT) membrane is employed to analyze its main wing spar with large displacement. EDISON CSD solver, linear static analysis and co-rotational nonlinear static anaysis both using OPT membrane produce behaviors of beam for each case of wire location about main wing spar, and aerodynamic coefficient also, by using aerodynamic analysis tool.

• Proceeding of EDISON Challenge
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• 2015.03a
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• pp.239-245
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• 2015

In this paper, to examine the difference between the linear and non-linear static, dynamic analysis for a structure, a cantilevered beam was used. Then, an external transverse static and dynamic loads were applied at the free end of the beam. Classical theories were used for the linear analysis and the EDISON CSD solver, co-rotational dynamic FEM program, was used for nonlinear analysis. In the static analysis, effects of the load for the beam deflection were observed in the linear and nonlinear analysis. Then, normalized displacement of tip of the beam was predicted for different frequency ration and a significant difference was obtained in the vicinity of the resonant frequency. In addition, effects of frequency and time for the beam deflection were investigated to find the frequency delay.

• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.15-30
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• 2007

In the paper, one focuses on the problem of duality in non-linear programming, applied to the solution of no-tension problems by means of Limit Analysis (LA) theorems for Not Resisting Tension (NRT) models. In details, one demonstrates that, starting from the application of the duality theory to the non-linear program defined by the static theorem approach for a discrete NRT model, this procedure results in the definition of a dual problem that has a significant physical meaning: the formulation of the kinematic theorem.

• Earthquakes and Structures
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• v.4 no.3
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• pp.241-264
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• 2013

Since the beginning of the twentieth century, the progressive and rapid spread of reinforced concrete (RC) has led to the adoption of mixed masonry-RC solutions, such as the confined masonry. However, together with structures conceived with a definite role for earthquake behaviour, the spreading of RC technology has caused the birth of mixed solutions inspired more by functional aspects than by structural ones, such as: internal masonry walls replaced by RC frames, RC walls inserted to build staircases or raising made from RC frames. Usually, since these interventions rise from a spontaneous build-up, any capacity design or ductility concepts are neglected being designed only to bear vertical loads: thus, the vulnerability assessment of this class becomes crucial. To investigate the non-linear seismic response of these structures, suitable models and effective numerical tools are needed. Among the various modelling approaches proposed in the literature and codes, the authors focus their attention on the equivalent frame model. After a brief description of the adopted model and its numerical validation, the authors aim to point out some specific peculiarities of the seismic response of mixed masonry-RC structures and their repercussions on safety verification procedures (referring in particular way to the non-linear static ones). In particular, the results of non-linear static analyses performed parametrically to various configurations representative of different interventions are discussed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.5
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• pp.467-475
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• 2015

In this paper, the behaviour of a cantilevered beam was predicted to examine the difference between linear and non-linear static, dynamic analysis for a structure by using CR nonlinear formulation. Then, external transverse static and dynamic loads were applied at the free tip of the beam. Classical theories were used for the present linear analysis and co-rotational dynamic FEM program was used for the present nonlinear analysis. In the static analysis, effects of the load for the beam deflection were observed in both linear and nonlinear analysis. Then, normalized displacement at the tip of the beam was predicted for different frequency ratio and a significant difference was obtained in the vicinity of the resonant frequency. In addition, effects of frequency and time for the beam deflection were investigated to find the frequency delay.