• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.501-508
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• 2001

Free vibration analysis of multi-delaminated composite beam-columns subjected to axial compression load is performed in the present study. In order to investigate the effects of multi-delaminations on the natural frequency and elastic buckling load of multi-delaminated beam-columns, the general kinematic continuity conditions are derived from the assumption of constant slope and curvature at the multi-delamination tip. Characteristic equation of multi-delaminated beam-column is obtained by dividing the global multi-delaminated beam-columns into segments and by imposing recurrence relation from the continuity conditions on each sub-beam-column. The natural frequency and elastic buckling load of multi-delaminated beam-columns according to the incremental load of axial compression, which is limited to the maximum elastic buckling load of sound laminated beam-column, are obtained. It is found that the sizes, locations and numbers of multi-delaminations have significant effect on natural frequency and elastic buckling load, especially the latter ones.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.3
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• pp.523-534
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• 2002

Free vibration and buckling analysis of multi-delaminated composite beam-columns subjected to axial compressive load is performed in the present study In order to investigate the effects of multi-delaminations on the natural frequency and the elastic buckling load of multi-delaminated beam-columns, the general kinematic continuity conditions are derived from the assumption of constant slope and curvature at the multi-dclamination tip. The characteristic equation of multi-delaminated beam-column is obtained by dividing the global multi-delauunated beam-columns into segments and by imposing recurrence relation from the continuity conditions on each sub-beam-column. The natural frequency and the elastic buck)ing load of multi-delaminated beam-columns according to the incremental load of axial compression, which is limited to the maximum elastic buckling load of sound laminated beam-column, are obtained. It is found that the sizes, locations and numbers of multi-delaminations have significant effect on natural frequency and elastic buckling load, especially the latter ones.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.4
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• pp.469-479
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• 2001

In the present study, free vibration analysis of multi-delaminated beams is performed. In order to investigate the effects of mu1ti-delaminations on the dynamic characteristics of multi-delaminated beams, the general kinematic continuity conditions are derived from the assumption of constant curvature at the multi-delamination tip. Frequency equations of multi-delaminated beams are obtained by dividing the global multi-delaminated beam into beam segments and by imposing recurrence relation from the continuity conditions un each sub-beam. The comparisons between the results of numerical analysis obtained by finite element analysis and those of present analysis give good agreement with each other. It is shown that the effects of multi-delaminations on free vibration characteristics of laminated beams could be used to detect their sizes, types and locations from the results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.25-32
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• 2002

Free vibration analysis of radialiy multi-delaminated beams with through-the-width multi-delamination is performed in the present study. The multiple delaminations are considered to be in a radial manner through the thickness from the top surface of the beam. The natural frequencies of the radially multi-delaminated beams are calculated from a new algorithm that is based on the single compound delaminated beam model. That is, beams with radial multi-delaminations are regarded as the sum of a single compound delamlnated beam that is the single sub-delaminated beam from the top surface of global beam. Each result of frequency equation for the single delaminated beam with unknown boundary conditions obtained through continuity conditions Is updated to the next one, With these sequential operations, the final frequency equation of radially multi-delaminated beams is obtained for both ends boundary conditions of global beam. The numerical results carried out for the beams are compared with those of some references to give the reliance on the proposed algorithm and to investigate the effects of the shape, number, size of multi-delaminations on the natural frequency. Compared with the other previously presented model, the proposed algorithm is more flexible in modeling and formulating as the total array size of frequency equation is always four by four. Therefore, the proposed algorithm will reduce the effort of user in formulating the physical model to the numerical model.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.83-89
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• 2000

Dynamic characteristics of multi-delaminated composite beams are presented in this work. In order to investigate the effects of sizes, locations and types of delaminations on composite beams, the general kinematic governing equations are derived and solved by dividing the delaminated beam and imposing the continuity conditions into each sub-beam The results show dynamic behaviors are varied according to the sizes, types and locations of delaminations through the laminated composite beams. It is shown that the effects of delaminations on the dynamic characteristics of composite beams could be used to detect their sizes, types and locations from the results.

• Journal of Korean Society of Steel Construction
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• v.13 no.3
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• pp.233-244
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• 2001

In this study, flexural rigidity reduction of multi-delaminated composite beams are investigated. In order to evaluate the flexural rigidity reduction. Performed theoretical analysis. In order to investigate flexural rigidity reduction about effects of delamination on composite beams, the general kinematic governing equations are derived and solved by dividing the delaminated beam and imposing the continuity conditions into each sub-beam. For condition to appear multiple delamination through the laminated composite beams, the flexural rigidity reduction are compared according to many stacking sequences and several forms for delaminations. The present study could be used to evaluate the flexural rigidity reduction of composite laminated beams on multi-delaminations.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.25-32
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• 2004

In this proposed work new finite element model for multi-delaminated plates is proposed. In the current analysis procedures of multi-delaminated plates, plate element based on Mindlin plate theory is used in order to obtain accurate results of out-of-plane displacement of thick plate. And for delaminated region, plate element based on Kirchhoff plate theory is considered. To satisfy the displacement continuity conditions, displacement vector based on Kirchhoff theory is transformed to displacement of transition element. The numerical results show that the effect of delaminations on the modal parameters of delaminated composites plates is dependent not only on the size, the location and the number of the delaminations but also on the mode number and boundary conditions. Kirchhoff based model have higher natural frequency than Mindlin based model and natural frequency of the presented model is closed to Mindlin based model.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.229-236
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• 2004

A new three-node triangular shell element based on higher order zig-zag theory is developed for laminated composite shells with multiple delaminations. The present higher order zig-zag shell theory is described in a general curvilinear coordinate system and in general tensor notation. All the complicated curvatures of surface including twisting curvatures can be described in an exact manner in the present shell element because this element is based on geometrically exact surface representation. The displacement field of the proposed finite element includes slope of deflection. which requires continuity between element interfaces. Thus the nonconforming shape function of Specht's three-node triangular plate bending element is employed to interpolate out-of-plane displacement. The present element passes the bending and twisting patch tests in flat surface configurations. The developed element is evaluated through the buckling problems of composite cylindrical shells with multiple delaminations. Through the numerical examples it is demonstrated that the proposed shell element is efficient because it has minimal degrees of freedom per node. The accuracy of the present element is demonstrated in the prediction of buckling loads and buckling modes of shells with multiple delaminations. The present shell element should serve as a powerful tool in the prediction of buckling loads and modes of multi-layered thick laminated shell structures with arbitrary-shaped multiple delaminations.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.10a
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• pp.69-72
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• 2004

A new three-node triangular shell element based on higher order zig-zag theory is developed for laminated composite shells with multiple delaminations. The present higher order zig-zag shell theory is described in a general curvilinear coordinate system and in general tensor notation. All the complicated curvatures of surface including twisting curvatures can be described in an exact manner in the present shell element because this element is based on geometrically exact surface representation. The displacement field of the proposed finite element includes slope of deflection, which requires continuity between element interfaces. Thus the nonconforming shape function of Specht's three-node triangular plate bending element is employed to interpolate out-of-plane displacement. The present element passes the bending and twisting patch tests in flat surface configurations. The developed element is evaluated through the eigenvalue problems of composite cylindrical shells with multiple delaminations. Through the numerical examples it is demonstrated that the proposed shell element is efficient because it has minimal degrees of freedom per node. The present shell element should serve as a powerful tool in the prediction of natural frequency and modes of multi-layered thick laminated shell structures with arbitrary-shaped multiple delaminations.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.10
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• pp.183-190
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• 2003

Major device failures such as die cracking, interfacial delamination and warpage in flip chip packages are due to excessive heat and thermal gradients- There have been significant researches toward understanding the thermal performance of electronic packages, but the majority of these studies do not take into account the combined effects of thermo-mechanical interactions of the different package constituents. This paper investigates the thermo-mechanical performance of flip chip package constituents based on the finite element method with thermo-mechanically coupled elements. Delaminations with different lengths between the silicon die and underfill resin interfaces were introduced to simulate the defects induced during the assembly processes. The temperature gradient fields and the corresponding stress distributions were analyzed and the results were compared with isothermal case. Parametric studies have been conducted with varying thermal conductivities of the package components, substrate board configurations. Compared with the uniform temperature distribution model, the model considering the temperature gradients provided more accurate stress profiles in the solder interconnections and underfill fillet. The packages with prescribed delaminations resulted in significant changes in stress in the solder. From the parametric study, the coefficients of thermal expansion and the package configurations played significant roles in determining the stress level over the entire package, although they showed little influence on stresses profile within the individual components. These observations have been implemented to the multi-board layer chip scale packages (CSP), and its results are discussed.