• Computational Structural Engineering
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• v.6 no.4
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• pp.83-88
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• 1993

A time-discontinuous Galerkin method based upon using a finite element formulation in time has evolved. This method, working from the differential equation viewpoint, is different from those which have been generally used. They admit discontinuities with respect to the time variable at each time step. In particular, the elements can be chosen arbitrarily at each time step with no connection with the elements corresponding to the previous step. Interpolation functions and weighting functions are taken to be discontinuous across inter-element boundaries. These methods lead to a unconditional stable higher-order accurate ordinary differential equation solver.

• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
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• v.2 no.3
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• pp.26-31
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• 1991

The scattering property of TMz illuminated a elliptic dielectric cylinders with arbitrary cross section are analyzed by the boundary element techniques. The boundary element equations are for- mulated via Maxwell's equations, weighted residual of Green's theorem, and the boundary conditions. The unknown surface fields on the boundaries are then calculated by the boundary element integral equations. Once the surface fields are found, the scattered fields in far-zone and scattering widths (SW) are readily determined. To show the validity and usefulness of this formulation, computations are compared with those obtained using analytical method and one layer circular cylinder. As exten- sion to arbitrary cross-sectioned cylinders, plane wave scattering from a elliptic dielectric cylinders are numerically analyzed. A general computer program has been developed using the quadratic ele- ments(Higher order borndary elements) and the Gaussian quadrature.

• Earthquakes and Structures
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• v.16 no.1
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• pp.55-67
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• 2019

The finite solutions of deflection and the corresponding in-plane stress values of the graded sandwich shallow shell structure are computed in this research article via a higher-order polynomial shear deformation kinematics. The shell structural equilibrium equation is derived using the variational principle in association with a nine noded isoprametric element (nine degrees of freedom per node). The deflection values are computed via an own customized MATLAB code including the current formulation. The stability of the current finite element solutions including their accuracies have been demonstrated by solving different kind of numerical examples. Additionally, a few numerical experimentations have been conducted to show the influence of different design input parameters (geometrical and material) on the flexural strength of the graded sandwich shell panel including the geometrical configurations.

• Structural Engineering and Mechanics
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• v.86 no.3
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• pp.291-309
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• 2023

This paper addresses the finite element modeling of functionally graded porous (FGP) beams for free vibration and buckling behaviour cases. The formulated finite element is based on simple and efficient higher order shear deformation theory. The key feature of this formulation is that it deals with Euler-Bernoulli beam theory with only three unknowns without requiring any shear correction factor. In fact, the presented two-noded beam element has three degrees of freedom per node, and the discrete model guarantees the interelement continuity by using both C⁰ and C¹ continuities for the displacement field and its first derivative shape functions, respectively. The weak form of the governing equations is obtained from the Hamilton principle of FGP beams to generate the elementary stiffness, geometric, and mass matrices. By deploying the isoparametric coordinate system, the derived elementary matrices are computed using the Gauss quadrature rule. To overcome the shear-locking phenomenon, the reduced integration technique is used for the shear strain energy. Furthermore, the effect of porosity distribution patterns on the free vibration and buckling behaviours of porous functionally graded beams in various parameters is investigated. The obtained results extend and improve those predicted previously by alternative existing theories, in which significant parameters such as material distribution, geometrical configuration, boundary conditions, and porosity distributions are considered and discussed in detailed numerical comparisons. Determining the impacts of these parameters on natural frequencies and critical buckling loads play an essential role in the manufacturing process of such materials and their related mechanical modeling in aerospace, nuclear, civil, and other structures.

• 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.90 no.3
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• pp.233-252
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• 2024

This research explores a new finite element model for the free vibration analysis of bi-directional functionally graded (BDFG) beams. The model is based on an efficient higher-order shear deformation beam theory that incorporates a trigonometric warping function for both transverse shear deformation and stress to guarantee traction-free boundary conditions without the necessity of shear correction factors. The proposed two-node beam element has three degrees of freedom per node, and the inter-element continuity is retained using both C1 and C0 continuities for kinematics variables. In addition, the mechanical properties of the (BDFG) beam vary gradually and smoothly in both the in-plane and out-of-plane beam's directions according to an exponential power-law distribution. The highly elevated performance of the developed model is shown by comparing it to conceptual frameworks and solution procedures. Detailed numerical investigations are also conducted to examine the impact of boundary conditions, the bi-directional gradient indices, and the slenderness ratio on the free vibration response of BDFG beams. The suggested finite element beam model is an excellent potential tool for the design and the mechanical behavior estimation of BDFG structures.

• Proceedings of the KIEE Conference
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• 2006.07c
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• pp.1494-1495
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• 2006

A complete finite element analysis method for discharge onset process, which is governed and coupled by charge transport equation and electric field equation, was presented. The charge transport equation of first order was transformed into a second-order one by utilizing the artificial diffusion scheme. The two second-order equations were analyzed by the finite element formulation which is well-developed for second-order ones. The Fowler-Nordheim injection boundary condition was adopted for charge transport equation. After verifying the numerical results by comparing to the analytic solutions using parallel plane electrodes with one carrier system, we extended the result to blade-plane electrodes in 2D xy geometry with three carriers system. Radius of the sharp tip was taken to be 50 ${\mu}m$. When this sharp geometry was solved by utilizing the space discretizing methods, the very sharp tip was found to cause a singularity in electric field and space charge distribution around the tip. To avoid these numerical difficulties in the FEM, finer meshes, a higher order shape function, and artificial diffusion scheme were employed.

• Steel and Composite Structures
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• v.34 no.2
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• pp.279-288
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• 2020

The computational post-buckling strength of the tilted sandwich composite shell structure is evaluated in this article. The computational responses are obtained using a mathematical model derived using the higher-order type of polynomial kinematic in association with the through-thickness stretching effect. Also, the sandwich deformation behaviour of the flexible soft-core sandwich structural model is expressed mathematically with the help of a generic nonlinear strain theory i.e. Green-Lagrange type strain-displacement relations. Subsequently, the model includes all of the nonlinear strain terms to account the actual deformation and discretized via displacement type of finite element. Further, the computer code is prepared (MATLAB environment) using the derived higher-order formulation in association with the direct iterative technique for the computation of temperature carrying capacity of the soft-core sandwich within the post-buckled regime. Further, the nonlinear finite element model has been tested to show its accuracy by solving a few numerical experimentations as same as the published example including the consistency behaviour. Lastly, the derived model is utilized to find the temperature load-carrying capacity under the influences of variable factors affecting the soft-core type sandwich structural design in the small (finite) strain and large deformation regime including the effect of tilt angle.

• Structural Engineering and Mechanics
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• v.77 no.1
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• pp.57-74
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• 2021

The thermal eigenvalue responses of the graded sandwich shell structure are evaluated numerically under the variable thermal loadings considering the temperature-dependent properties. The polynomial type rule-based sandwich panel model is derived using higher-order type kinematics considering the shear deformation in the framework of the equivalent single-layer theory. The frequency values are computed through an own home-made computer code (MATLAB environment) prepared using the finite element type higher-order formulation. The sandwich face-sheets and the metal core are discretized via isoparametric quadrilateral Lagrangian element. The model convergence is checked by solving the similar type published numerical examples in the open domain and extended for the comparison of natural frequencies to have the final confirmation of the model accuracy. Also, the influence of each variable structural parameter, i.e. the curvature ratios, core-face thickness ratios, end-support conditions, the power-law indices and sandwich types (symmetrical and unsymmetrical) on the thermal frequencies of FG sandwich curved shell panel model. The solutions are helping to bring out the necessary influence of one or more parameters on the frequencies. The effects of individual and the combined parameters as well as the temperature profiles (uniform, linear and nonlinear) are examined through several numerical examples, which affect the structural strength/stiffness values. The present study may help in designing the future graded structures which are under the influence of the variable temperature loading.

• 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.