• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.327-334
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• 2001

This paper presents a non-linear analysis procedure for plane frame structures by finite element formulation with assumptions of Timoshenko beam theory. Finite element displacement method based on Lagrangian formulation is used and two-noded and isoparametric line element is adopted to represent finite element model. The layered approach is used for the elasto-plastic analysis of the plane frame structures with rectangular and I cross sections. A load incremental method combined with the tangent stiffness and the initial stiffness methods for each load increment is used for the solution of non-linear equations. Numerical examples are presented to investigate the behavior and the accuracy of the elasto-plastic non-linear application and the results of this study are compared with other solutions using the concept of plastic hinge.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.2
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• pp.183-195
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• 2003

In this study, the method of the finite element modeling for free vibration control of beam-type smart structures with bonded plate-type piezoelectric sensors and actuators is proposed. Constitutive equations for the direct piezoelectric effect and converse piezoelectric effect of piezoelectric materials are considered. By using the variational principle, the equations of motion for the smart beam finite element are derived. The proposed 2-node beam finite element is an isoparametric element based on Timoshenko beam theory. Therefore, by analyzing beam-type smart structures with smart beam finite elements, it is possible to simulate the control of the structural behavior by applying voltages to piezoelectric actuators and monitoring of the structural behavior by sensing voltages of piezoelectric sensors. By using the smart beam finite element and constant-gain feed back control scheme, the formulation of the free nitration control for the beam structures with bonded plate-tyPe Piezoelectric sensors and actuators is proposed.

• Structural Engineering and Mechanics
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• v.21 no.1
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• pp.19-33
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• 2005

An improved shear deformable thin-walled curved beam theory to overcome the drawback of currently available beam theories is newly proposed for the spatially coupled free vibration and elastic analysis. For this, the displacement field considering the shear deformation effects is presented by introducing displacement parameters defined at the centroid and shear center axes. Next the elastic strain and kinetic energies considering the shear effects due to the shear forces and the restrained warping torsion are rigorously derived. Then the equilibrium equations are consistently derived for curved beams with non-symmetric thin-walled sections. It should be noticed that this formulation can be easily reduced to the warping-free beam theory by simply putting the sectional properties associated with warping to zero for curved beams with L- or T-shaped sections. Finally in order to illustrate the validity and the accuracy of this study, finite element solutions using the isoparametric curved beam elements are presented and compared with those in available references and ABAQUS's shell elements.

• Computers and Concrete
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• v.34 no.5
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• pp.625-648
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• 2024

A new finite element model is formulated and implemented in this analysis to assess the free vibration and elastic stability behaviors of functionally graded carbon nanotube-reinforced (FG-CNTRC) nanocomposite beams. The developed model is founded on an efficient Quasi-3D shear deformation beam theory. The traction-free boundary conditions are guaranteed with no shear correction factors by integrating the hyperbolic warping function for transverse shear deformation and stress through the thickness coordinate. The suggested two-node beam element has four degrees of freedom per node, and the discrete model maintains inter-element continuity by using both C1 and C0 continuities for the kinematics variables. As a result, the isoparametric coordinate system is used to produce the elementary stiffness, geometric, and mass matrices to improve the current formulation. The weak form of the variational principle is used to generate the governing equations. Following the distribution patterns and CNT volume fraction, the mechanical characteristics of used FG-CNTRC beams change gradually over the beam thickness. The high performance of the present beam element is demonstrated by comparing current results to those predicted by previous theories and solution procedures. In addition, detailed numerical research is conducted to investigate the effects of boundary conditions, distribution patterns, and slenderness ratio on the free vibration and buckling responses of FG-CNTRC beams. An appropriate reinforcement technique based on optimum distribution patterns can significantly improve computational efficiencies. The developed finite element beam model is computationally efficient and can be explored as a helpful design and optimization tool for CNT-reinforced nanocomposite structures.

• Magazine of the Korea Concrete Institute
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• v.8 no.3
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• pp.187-195
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• 1996

A finite element formulation based on the CFT(Compression Field Theory), considering the effect of compression softening in cracked concrete, and macro-scopic and rotating crack models etc., was presented for the nonlinear behaviour of structural concrete. Considering the computational efficency and the ability of modelling the post-ultimate behaviour as major concerns, the Incremental displacement solution algorithm involving initial material stiffnesses and the relaxation procedure for fast convergence was adopted and formulated in a type of 8-noded quadrilateral isoparametric elements. The analysis program NASCOM(Non1inear Analysis of Structural Concrete by FEM : Monotonic Loading) developed in this way enables the predictions of strength and deformation capacities in a full range, crack patterns and their corresponding widths, and yield extents of reinforcement. As the verification purpose of NASCOM, the predictions were made for Bhide's Panel(PB21) and Leonhardt's deep beam tests. The predicted results shows somewhat stiff behaviour for the panel test, and vice versa for deep beam tests. More refining process would be necessary hereafter in terms of more accurately simulating the effects of tension-stiffening and compression softening in concrete.

• Selected Papers of The Society of Naval Architects of Korea
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• v.1 no.1
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• pp.91-100
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• 1993

A displacement-based finite element method Is presented for the geometrically nonlinear analysis of eccentrically stiffened plates. A nonlinear degenerated shell element and a nonlinear degenerated eccentric isoparametric beam (isobeam) element are formulated on the basis of Total Agrangian and Updated Lagrangian descriptions. In the formulation of the isobeam element, some additional local decrees of freedom are implementd to describe the stiffener's local plate buckling modes. Therefore this element can be effectively employed to model the eccentric stiffener with fewer D.O.F's than the case of a degenerated shell element. Some detailed buckling and nonlinear analyses of an eccentrically stiffened plate are performed to estimate the critical buckling loads and the post buckling behaviors including the local plate buckling of the stiffeners discretized with the degenerated shell elements and the isobeam elements. The critical buckling loads are found to be higher than the analytical plate buckling load but lower than Euler buckling load of the corresponding column, i.e, buckling strength requirements of the Classification Societies for the stiffened plates.

• Structural Engineering and Mechanics
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• v.88 no.1
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• pp.83-94
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• 2023

An accurate and highly efficient inverse element labelled iPCB is developed based on the inverse finite element method (iFEM) for real-time shape estimation of plane-curved structures (such as arch bridges) utilizing onboard strain data. This inverse problem, named shape sensing, is vital for the design of smart structures and structural health monitoring (SHM) procedures. The iPCB formulation is defined based on a least-squares variational principle that employs curved Timoshenko beam theory as its baseline. The accurate strain-displacement relationship considering tension-bending coupling is used to establish theoretical and measured section strains. The displacement fields of the isoparametric element iPCB are interpolated utilizing nonuniform rational B-spline (NURBS) basis functions, enabling exact geometric modelling even with a very coarse mesh density. The present formulation is completely free from membrane and shear locking. Numerical validation examples for different curved structures subjected to different loading conditions have been performed and have demonstrated the excellent prediction capability of iPCBs. The present formulation has also been shown to be practical and robust since relatively accurate predictions can be obtained even omitting the shear deformation contributions and considering polluted strain measures. The current element offers a promising tool for real-time shape estimation of plane-curved structures.

• Computers and Concrete
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• v.34 no.4
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• pp.447-476
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• 2024

The current research proposes an innovative finite element model established within the context of higher-order beam theory to examine the bending and buckling behaviors of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams resting on Winkler-Pasternak elastic foundations. This two-node beam element includes four degrees of freedom per node and achieves inter-element continuity with both C¹ and C⁰ continuities for kinematic variables. The isoparametric coordinate system is implemented to generate the elementary stiffness and geometric matrices as a way to enhance the existing model formulation. The weak variational equilibrium equations are derived from the principle of virtual work. The mechanical properties of FG-CNTRC beams are considered to vary gradually and smoothly over the beam thickness. The current investigation highlights the influence of porosity dispersions through the beam cross-section, which is frequently omitted in previous studies. For this reason, this analysis offers an enhanced comprehension of the mechanical behavior of FG-CNTRC beams under various boundary conditions. Through the comparison of the current results with those published previously, the proposed finite element model demonstrates a high rate of efficiency and accuracy. The estimated results not only refine the precision in the mechanical analysis of FG-CNTRC beams but also offer a comprehensive conceptual model for analyzing the performance of porous composite structures. Moreover, the current results are crucial in various sectors that depend on structural integrity in specific environments.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.5
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• pp.413-420
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• 2012

In this study, the Kernel integration scheme for 2D linear elastic direct boundary element method has been discussed on the basis of subparametric element. Usually, the isoparametric based boundary element uses same polynomial order in the both basis function and mapping function. On the other hand, the order of mapping function is lower than the order of basis function to define displacement field when the subparametric concept is used. While the logarithmic numerical integration is generally used to calculate Kernel integration as well as Cauchy principal value approach, new formulation has been derived to improve the accuracy of numerical solution by algebraic modification. The subparametric based direct boundary element has been applied to 2D elliptical partial differential equation, especially for plane stress/strain problems, to demonstrate whether the proposed algebraic expression for integration of singular Kernel function is robust and accurate. The problems including cantilever beam and square plate with a cutout have been tested since those are typical examples of simple connected and multi connected region cases. It is noted that the number of DOFs has been drastically reduced to keep same degree of accuracy in comparison with the conventional isoparametric based BEM. It is expected that the subparametric based BEM associated with singular Kernel function integration scheme may be extended to not only subparametric high order boundary element but also subparametric high order dual boundary element.

• Interaction and multiscale mechanics
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• v.4 no.1
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• pp.17-34
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• 2011

This paper deals with the modeling of the plane frame structure-foundation-soil system. The superstructure along with the foundation beam is idealized as beam bending elements. The soil medium near the foundation beam with stress concentrated is idealized by isoparametric finite elements, and infinite elements are used to represent the far field of the soil media. This paper presents the modeling of shear wall structure-foundation and soil system using the optimal membrane triangular, super and conventional finite elements. Particularly, an alternative formulation is presented for the optimal triangular elements aimed at reducing the programming effort and computational cost. The proposed model is applied to a plane frame-combined footing-soil system. It is shown that the total settlement obtained from the non-linear interactive analysis is about 1.3 to 1.4 times that of the non-interactive analysis. Furthermore, the proposed model was found to be efficient in simulating the shear wall-foundation-soil system, being able to yield results that are similar to those obtained by the conventional finite element method.