• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.4
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• pp.380-387
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• 2009

The reliability concerns of solder interconnections in flip chip PBGA packages are produced mainly by the mismatch of coefficient of thermal expansion(CTE) between the module and PCB. Finite element analysis has been employed extensively to simulate thermal loading for solder joint reliability and deformation of packages in electronic packages. The objective of this paper is to study the thermo-mechanical behavior of FC-PBGA package assemblies subjected to temperature change, with an emphasis on the effect of the finite element model, material models and temperature conditions. Numerical results are compared with the experimental results by using $moir{\acute{e}}$ interferometry. Result shows that the bending displacements of the chip calculated by the finite element analysis with viscoplastic material model is in good agreement with those by $moir{\acute{e}}$ inteferometry.

• Structural Engineering and Mechanics
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• v.50 no.2
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• pp.181-199
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• 2014

Locking phenomenon is a mesh problem and can be staved off with mesh refinement. If the studier is not preferred going to the solution with increasing mesh size or the computer memory can stack over flow than using higher order plate finite element or using integration techniques is a solution for this problem. The purpose of this paper is to show the shear locking phenomenon can be avoided by increase low order finite element mesh size of the plates and to study shear locking-free analysis of thick plates using Mindlin's theory by using higher order displacement shape function and to determine the effects of various parameters such as the thickness/span ratio, mesh size on the linear responses of thick plates subjected to uniformly distributed loads. 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, 4-, 8- and 17-noded quadrilateral finite elements are used. 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.

• Structural Engineering and Mechanics
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• v.9 no.1
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• pp.99-110
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• 2000

The objective of this paper is to extend the use of the improved degenerated shell element to the linear and the large displacement analysis of plates and shells with laminated composites. In the formulation of the element stiffness, the combined use of three different techniques was made. This element is free of serious shear/membrane locking problems and undesirable compatible/commutable spurious kinematic deformation modes. The total Lagrangian approach has been utilized for the definition of the deformation and the solution to the nonlinear equilibrium equations is obtained by the Newton-Raphson method. The applicability and accuracy of this improved degenerated shell element in the analysis of laminated composite plates and shells are demonstrated by solving several numerical examples.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.1
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• pp.100-114
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• 1996

In this paper, a new thin-walled beam finite elcment is developed to overmome the difficulties in the analysis of real structures by existing beam elements. The element is formulated by extending Benscoter's assumption and also by adopting the concept of the curvature-based element. It is applicable to the analysis of the beams with arbitrary cross-sectional shapes. The results obtained show that the element is locking-free and the accuracy of the finite element solutions is remarkably improved.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.35 no.11
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• pp.479-486
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• 1986

It is necessary to consider a rotor movement in dynamic analysis on the flux distribution of electric machinery by FEM. Therefore, if air-gap domain was subdivided into triangular elements, computation results contain errors due to variation of element shape in air-gap because the nodal points corresponding to the rotor are displaced in analyzing domain for the time difference. In order to reduce this errors, the paper presents a application of a Macro Air-gap Element that interpolation function is obtained analytically and a means to join it with linear triangular elements in the rotating machine or in the linear machine. At the end of paper, setting up analytic domain model, it compares analytic solution with the computation results of Macro Air-gap Element appliction and that of linear triangular element subdivision only to each cases of nodal displacement. And it carries out that errors due to variation of element shape are reduced effectively by application of a Macro air-gap element.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.65-72
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• 1997

This study is the bending analysis of rectangular plates with 4-sides simply supported by Finite Element Method using substructuring technique. In finite element method, as the more number of finite element, the more dimension of matrix, it is difficult to obtain accuracy solution. In this paper substructuring technique is applied to finite element method in order to reduce the dimension of matrix according to the number of finite element mesh. To validate finite element method using substructuring technique, deflections and moments of rectangular plates by that method is compared with those of references. Considering the symmetry of the plate and load, one fourth of plate is analyzed. Operating time and the error of solutions according to the number of finite element mesh and substructure are compared with each other.

• Journal of Mechanical Science and Technology
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• v.15 no.11
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• pp.1499-1506
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• 2001

Various transition elements are used in general for the effective finite element analysis of complicated mechanical structures. In this paper, a solid-to-beam transition finite element, which can b e used for connecting a C1-continuity beam element to a continuum solid element, is proposed. The shape functions of the transition finite element are derived to meet the compatibility condition, and a transition element equation is formulated by the conventional finite element procedure. In order to show the effectiveness and convergence characteristics of the proposed transition element, numerical tests are performed for various examples. As a result of this study, following conclusions are obtained. (1) The proposed transition element, which meets the compatibility of the primary variables, exhibits excellent accuracy. (2) In case of using the proposed transition element, the number of nodes in the finite element model may be considerably reduced and the model construction becomes more convenient. (3) This formulation method can be applied to the usage of higher order elements.

• Coupled systems mechanics
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• v.2 no.4
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• pp.389-410
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• 2013

Three-dimensional Lagrangian fluid finite element is applied to seismic response analysis of an oil storage tank with a floating roof. The fluid element utilized in the present analysis is formulated based on the displacement finite element method considering only volumetric elasticity and its element stiffness matrix is derived by using one-point integration method in order to avoid volumetric locking. The method usually adds a rotational penalty stiffness to satisfy the irrotational condition for fluid motion and modifies element mass matrices through the projected mass method to suppress spurious hourglass-mode appeared in compensation for one-point integration. In the fluid element utilized in the present paper, a small hourglass stiffness is employed. The fluid and structure domains for the objective oil storage tank are modeled by eight-node solid elements and four-node shell elements, respectively, and the transient response of the floating roof structure or the free surface are evaluated by implicit direct time integration method. The results of seismic response analyses are compared with those by other method and the validation of the present analysis using three-dimensional Lagrangian fluid finite elements is shown.

• Structural Engineering and Mechanics
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• v.5 no.1
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• pp.33-49
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• 1997

A method of analysis is proposed for curved multicell box girder grillages. The method can be used to analyze box girder grillages comprising straight and/or curved segments. Each segment can be modelled by a number of beam elements. Each element has three nodes and the nodal degrees of freedom (DOF) consist of the six DOF for a conventional beam plus DOF to account for torsional warping, distortion, distortional warping, and shear lag. This element is an extension of a straight element that was developed earlier. For a more realistic analysis of the intersection regions of non-colinear box girder segments, the concept of a rigid connector is introduced, and the compatibility requirements between adjoining elements in those regions are discussed. The results of the analysis showed good agreement with the shell finite element results, but the proposed method of analysis needs a fraction of the time and effort compared to the shell finite element analysis.

• Structural Engineering and Mechanics
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• v.65 no.3
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• pp.263-274
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• 2018

In this study, we propose a frequency domain spectral element method (SEM) for the vibration analysis of a multi-span beam subjected to a moving point force. This study is an extension of the authors' previous study for a single-span beam subjected to a moving point force, where the two-element model-based SEM was applied. In this study, each span of a multi-span beam is represented by the Timoshenko beam model and the moving point force is transformed into the frequency domain as a series of each stationary point force distributed on the multi-span beam. The span at which a stationary point force is located is represented by two-element model, but all other spans are represented by one-element models. The vibration responses to a moving point force are obtained by superposing all individual vibration responses generated by each stationary point force. The high accuracy and computational efficiency of the proposed SEM are verified by comparing the solutions by SEM with exact analytical solutions by the integral transform method (ITM) as well as the solutions by the finite element method (FEM).