• 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.

• Computers and Concrete
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• v.19 no.1
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• pp.1-6
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• 2017

Prestressed concrete I-girders are subject to different load types at their construction stages. At the time of strand release, i.e., detensioning, prestressed concrete girders are under the effect of dead and prestressing loads. At this stage, the camber, total net upward deflection, of prestressed girder is summation of the upward deflection due to the prestressing force and the downward deflection due to dead loads. For the calculation of the upward deflection, it is generally considered that prestressed concrete I-girder behaves linear-elastic. However, the field measurements on total net upward deflection of prestressed I-girder after detensioning show contradictory results. In this paper, camber calculations with the linear-elastic beam and elastic-stability theories are presented. One of a typical precast I-girder with 120 cm height and 31.5 m effective span length is selected as a case study. 3D finite element model (FEM) of the girder is developed by SAP2000 software, and the deflections of girder are obtained from linear and nonlinear-static analyses. Only geometric nonlinearity is taken into account. The material test and field measurement of this study are performed at prestressing girder plant. The results of the linear-elastic beam and elastic-stability theories are compared with FEM results and field measurements. It is seen that the camber predicted by elastic-stability theory gives acceptable results than the linear-elastic beam theory while strand releasing.

• Computers and Concrete
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• v.23 no.1
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• pp.11-23
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• 2019

Nowadays, the characterization of Ultra-High Performance Fiber-Reinforced Concrete (UHPFRC) tensile behavior still remains a challenge for researchers. For this purpose, a simplified closed-form non-linear hinge model based on the Third Point Bending Test (ThirdPBT) was developed by the authors. This model has been used as the basis of a simplified inverse analysis methodology to derive the tensile material properties from load-deflection response obtained from ThirdPBT experimental tests. In this paper, a non-linear finite element model (FEM) is presented with the objective of validate the closed-form non-linear hinge model. The state determination of the closed-form model is straightforward, which facilitates further inverse analysis methodologies to derive the tensile properties of UHPFRC. The accuracy of the closed-form non-linear hinge model is validated by a robust non-linear FEM analysis and a set of 15 Third-Point Bending tests with variable depths and a constant slenderness ratio of 4.5. The numerical validation shows excellent results in terms of load-deflection response, bending curvatures and average longitudinal strains when resorting to the discrete crack approach.

• Structural Engineering and Mechanics
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• v.1 no.1
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• pp.87-102
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• 1993

A $C^{\circ}$ continuous finite element formulation of a higher order displacement theory is presented for predicting linear and geometrically non-linear in the sense of von Karman transient responses of composite and sandwich plates. The displacement model accounts for non-linear cubic variation of tangential displacement components through the thickness of the laminate and the theory requires no shear correction coefficients. In the time domain, the explicit central difference integrator is used in conjunction with the special mass matrix diagonalization scheme which conserves the total mass of the element and included effects due to rotary inertia terms. The parametric effects of the time step, finite element mesh, lamination scheme and orthotropy on the linear and geometrically non-linear responses are investigated. Numerical results for central transverse deflection, stresses and stress resultants are presented for square/rectangular composite and sandwich plates under various boundary conditions and loadings and these are compared with the results from other sources. Some new results are also tabulated for future reference.

• Structural Engineering and Mechanics
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• v.35 no.2
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• pp.191-203
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• 2010

To investigate the critical buckling load and post-buckling behavior of an axially loaded pile entirely embedded in soil, the non-linear large deflection differential equation for a pinned pile, based on the Winkler-model and the discretionary distribution function of the foundation coefficient along pile shaft, was established by energy method. Assuming that the deflection function was a power series of some perturbation parameter according to the boundary condition and load in the pile, the non-linear large deflection differential equation was transformed to a series of linear differential equations by using perturbation approach. By taking the perturbation parameter at middle deflection, the higher-order asymptotic solution of load-deflection was then found. Effect of ratios of soil depth to pile length, and ratios of pile stiffness to soil stiffness on the critical buckling load and performance of piles (entirely embedded and partially embedded) after flexural buckling were analyzed. Results show that the buckling load capacity increases as the ratios of pile stiffness to soil stiffness increasing. The pile performance will be more stable when ratios of soil depth to pile length, and soil stiffness to pile stiffness decrease.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.11a
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• pp.546-552
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• 2000

Dynamic behavior of laminated composite plates undergoing moderately large deflection is investigated taking into account the viscoelastic behavior of material properties. Based on von Karman's non-linear deformation theory and Boltzmann's superposition principle, non-linear and hereditary type governing equations are derived. Finite element analysis and the method of multiple scales is applied to examine the effect of large amplitude on the dissipative nature of viscoelastic laminated plates.

• Steel and Composite Structures
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• v.14 no.6
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• pp.605-620
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• 2013

This paper provides an innovative iteration technique for the large deflection problem of annular plate. After some manipulation, the problem is reduced to a couple of ODEs (ordinary differential equation). Among them, one is derived from the plane stress problem for plate, and other is derived from the bending of plate. Since the large deflection for plate is assumed in the problem, the relevant non-linear terms appear in the resulting ODEs. The pseudo-linearization procedure is suggested to solve the problem and the nonlinear ODEs can be solved in the way for the solution of linear ODE. To obtain the final solution, it is necessary to use the iteration. Several numerical examples are provided. In the study, the assumed value for non-dimensional loading is larger than those in the available references.

• Steel and Composite Structures
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• v.13 no.1
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• pp.71-89
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• 2012

The paper investigates beam lateral buckling stability according to linear and non-linear models. Closed form solutions for single-symmetric cross sections are first derived according to a non-linear model considering flexural-torsional coupling and pre-buckling deformation effects. The closed form solutions are compared to a beam finite element developed in large torsion. Effects of pre-buckling deflection and gradient moment on beam stability are not well known in the literature. The strength of singly symmetric I-beams under gradient moments is particularly investigated. Beams with T and I cross-sections are considered in the study. It is concluded that pre-buckling deflections effects are important for I-section with large flanges and analytical solutions are possible. For beams with T-sections, lateral buckling resistance depends not only on pre-buckling deflection but also on cross section shape, load distribution and buckling modes. Effects of pre-buckling deflections are important only when the largest flange is under compressive stresses and positive gradient moments. For negative gradient moments, all available solutions fail and overestimate the beam strength. Numerical solutions are more powerful. Other load cases are investigated as the stability of continuous beams. Under arbitrary loads, all available solutions fail, and recourse to finite element simulation is more efficient.

• Steel and Composite Structures
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• v.6 no.5
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• pp.401-415
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• 2006

Based on a non-linear model taking into account flexural-torsional couplings, analytical solutions are derived for lateral buckling of simply supported I beams under some representative load cases. A closed form is established for lateral buckling moments. It accounts for bending distribution, load height application and pre-buckling deflections. Coefficients $C_1$ and $C_2$ affected to these parameters are then derived. Regard to well known linear stability solutions, these coefficients are not constant but depend on another coefficient $k_1$ that represents the pre-buckling deflection effects. In numerical simulations, shell elements are used in mesh process. The buckling loads are achieved from solutions of eigenvalue problem and by bifurcations observed on non linear equilibrium paths. It is proved that both the buckling loads derived from linear stability and eigenvalue problem lead to poor results, especially for I sections with large flanges for which the behaviour is predominated by pre-buckling deflection and the coefficient $k_1$ is large. The proposed solutions are in good agreement with numerical bifurcations observed on non linear equilibrium paths.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.387-395
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• 1991

Large deflection behavior of cylindrically orthotropic thin circular plates is investigated by the numerical technique of differential quadrature. Governing equations are derived in terms of transverse deflection and stress function and a Newton-Raphson technique is used to solve the nonlinear systems of equations. For small values of degree of differential quadrature (N.leq.13), as the degree of differential quadrature increases, the center deflection converges. However, as N increases further, the center deflection diverges by ill-conditioning in the weighting coefficients. As the orthotropic parameter increases, the center deflection decreases and behaves linear for the loads. At center, the stress is affected mainly by orthotropic parameter, while the stress is affected mainly by boundary condition at edge.