• Steel and Composite Structures
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• v.18 no.6
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• pp.1353-1368
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• 2015

A finite element model is presented for the analysis of composite steel-concrete beams based on a refined high-order theory. The employed theory satisfies all the kinematic and stress continuity conditions at the layer interfaces and considers effects of the transverse normal stress and transverse flexibility. The global displacement components, described by polynomial or combinations of polynomial and exponential expressions, are superposed on local ones chosen based on the layerwise or discrete-layer concepts. The present finite model does not need the incorporating any shear correction factor. Moreover, in the present $C^1$-continuous finite element model, the number of unknowns is independent of the number of layers. The proposed finite element model is validated by comparing the present results with those obtained from the three-dimensional (3D) finite element analysis. In addition to correctly predicting the distribution of all stress components of the composite steel-concrete beams, the proposed finite element model is computationally economic.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.2
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• pp.69-79
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• 2008

Multigrid methods finite element/finite volume methods and their convergence properties are reviewed in a general setting. Some early theoretical results in simple finite element methods in variational setting method are given and extension to nonnested-noninherited forms are presented. Finally, the parallel theory for nonconforming element[13] and for cell centered finite difference methods [15, 23] are discussed.

• Journal of the korean Society of Automotive Engineers
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• v.13 no.3
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• pp.58-67
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• 1991

A theory of continuum damage mechanics based on the theory of materials of type N was developed and its nonlinear finite element approximation and numerical simulation was carried out. To solve the finite elastoplasticity problems, reasonable kinematics of large deformed solids was introduced and constitutive relations based on the theory of materials of type-N were derived. These highly nonlinear equations were reduced to the incremental weak formulation and approximated by the theory of nonlinear finite element method. Two types of problems, compression moulding problem and pure bending problem, were solved for aluminum 2024.

• Structural Engineering and Mechanics
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• v.27 no.3
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• pp.311-331
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• 2007

The purpose of this paper is to study shear locking-free analysis of thick plates using Mindlin's theory and to determine the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick plates subjected to uniformly distributed loads. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 8- and 17-noded quadrilateral finite elements are used. Graphs and tables are presented that should help engineers in the design of thick plates. It is concluded that 17-noded finite element converges to exact results much faster than 8-noded finite element, and that it is better to use 17-noded finite element for shear-locking free analysis of plates. It is also concluded, in general, that the maximum displacement and bending moment increase with increasing aspect ratio, and that the results obtained in this study are better than the results given in the literature.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.33-41
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• 2018

In this paper, using modified couple stress theory in place of classical continuum theory, and using shell model in place of beam model, vibrational behavior of nanotubes is investigated via the finite element method. Accordingly classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have taken on great appeal. In the present work the mass-stiffness matrix for cylindrical shell element is developed, and by means of size-dependent finite element formulation is extended to more precisely account for nanotube vibration. In addition to modified couple stress cylindrical shell element, the classical cylindrical shell element can also be defined by setting length scale parameter to zero in the equations. The boundary condition were assumed simply supported at both ends and it is shown that the natural frequency of nano-scale shell using the modified coupled stress theory is larger than that using the classical shell theory and the results of Ansys. The results have indicated using the modified couple stress cylindrical shell element, the rigidity of the nano-shell is greater than that in the classical continuum theory, which results in increase in natural frequencies. Besides, in addition to reducing the number of elements required, the use of this type of element also increases convergence speed and accuracy.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.35 no.1
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• pp.54-59
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• 1999

High-speed electronic digital computers have enabled engineers to employ various numerical discretization techniques for solutions of complex problems. The Finite Element Method is one of the such technique. The Finite Element Method is one of the numerical analysis based on the concepts of fundamental mathematical approximation. Three dimensional plate structures used often in partition of ship, box girder and frame are analyzed by Finite Element Method. In design of structures, the static deflections, stress concentrations and dynamic deflections must be considered. However, these problem belong to geometrically nonlinear mechanical structure analysis. The analysis of each element is independent, but coupling occurs in assembly process of elements. So, to overcome such a difficulty the shell theory which includes transformation matrix and a fictitious rotational stiffness is taken into account. Also, the Mindlin's theory which is considered the effect of shear deformation is used. The Mindlin's theory is based on assumption that the normal to the midsurface before deformation is "not necessarily normal to the midsurface after deformation", and is more powerful than Kirchoff's theory in thick plate analysis. To ensure that a small number of element can represent a relatively complex form of the type which is liable to occur in real, rather than in academic problem, eight-node quadratic isoparametric elements are used. are used.

• Structural Engineering and Mechanics
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• v.6 no.7
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• pp.727-746
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• 1998

Finite element models and numerical results are presented for bending and natural vibration using the unified third-order plate theory developed in Part 1 of this paper. The unified third-order theory contains the classical, first-order, and other third-order plate theories as special cases. Analytical solutions are developed using the Navier and L$\acute{e}$vy solution procedures (see Part 1 of the paper). Displacement finite element models of the unified third-order theory are developed herein. The finite element models are based on $C^0$ interpolation of the inplane displacements and rotation functions and $C^1$ interpolation of the transverse deflection. Numerical results of bending and natural vibration are presented to evaluate the accuracy of various plate theories.

• Structural Engineering and Mechanics
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• v.65 no.3
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• pp.213-222
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• 2018

The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin's theory with shear locking free fourth order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency paramerets of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

• Structural Engineering and Mechanics
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• v.19 no.5
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• pp.477-501
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• 2005

In this study, a new smart beam finite element is proposed for the finite element modeling of beam-type smart structures that are equipped with bonded plate-type piezoelectric sensors and actuators. Constitutive equations for the direct piezoelectric effect and converse piezoelectric effect of piezoelectric materials are considered in the formulation. By using a 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. The proposed smart beam finite element is applied to the free vibration control adopting a constant gain feedback scheme. The electrical force vector, which is obtained in deriving an equation of motion, is the control force equivalent to that in existing literature. Validity of the proposed element is shown through comparing the analytical results of the verification examples with those of other previous researchers. With the use of smart beam finite elements, simulation of free vibration control is demonstrated by sensing the voltage of the piezoelectric sensors and by applying the voltages to the piezoelectric actuators.

• Structural Engineering and Mechanics
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• v.33 no.3
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• pp.373-385
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• 2009

The purpose of this paper is to study shear locking-free parametric earthquake analysis of thick and thin plates using Mindlin's theory, to determine the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick and thin plates subjected to earthquake excitations. In the analysis, finite element method is used for spatial integration and the Newmark-${\beta}$ method is used for the time integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can be effectively used in the earthquake analysis of thick and thin plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.